From ae727526285fadd3f9305b296be4979d9ab42548 Mon Sep 17 00:00:00 2001 From: Observatorio-de-Matematica <141172160+Observatorio-de-Matematica@users.noreply.github.com> Date: Sat, 19 Oct 2024 20:44:13 -0500 Subject: [PATCH] Change in the file extension The files with the .wxmx file extension were converted to the .wxm extension, the content was not modified. The .wxmx files are not readable in GitHub, but the .wxm files are readable. --- Commands/Maxima Files/Calculus.wxm | 55 +++++ Commands/Maxima Files/Complex_Numbers.wxm | 140 ++++++++++++ Commands/Maxima Files/Factorials.wxm | 90 ++++++++ Commands/Maxima Files/Log.wxm | 65 ++++++ Commands/Maxima Files/Matrix.wxm | 217 ++++++++++++++++++ Commands/Maxima Files/Plot2d-1.wxm | 40 ++++ Commands/Maxima Files/Plot2d.wxm | 88 +++++++ Commands/Maxima Files/Plot3d.wxm | 44 ++++ Commands/Maxima Files/Trignometry.wxm | 190 ++++++++++++++++ Commands/Maxima Files/basics.wxm | 139 +++++++++++ Commands/Maxima Files/functions.wxm | 198 ++++++++++++++++ Commands/Maxima Files/limit.wxm | 70 ++++++ Questions/Maxima file/03-Sep-2020.wxm | 201 ++++++++++++++++ Questions/Maxima file/07-Oct-2020.wxm | 262 +++++++++++++++++++++ Questions/Maxima file/14-Sep-2020.wxm | 266 ++++++++++++++++++++++ Questions/Maxima file/24-Sep-2020.wxm | 188 +++++++++++++++ Questions/Maxima file/Eq.wxm | 156 +++++++++++++ 17 files changed, 2409 insertions(+) create mode 100644 Commands/Maxima Files/Calculus.wxm create mode 100644 Commands/Maxima Files/Complex_Numbers.wxm create mode 100644 Commands/Maxima Files/Factorials.wxm create mode 100644 Commands/Maxima Files/Log.wxm create mode 100644 Commands/Maxima Files/Matrix.wxm create mode 100644 Commands/Maxima Files/Plot2d-1.wxm create mode 100644 Commands/Maxima Files/Plot2d.wxm create mode 100644 Commands/Maxima Files/Plot3d.wxm create mode 100644 Commands/Maxima Files/Trignometry.wxm create mode 100644 Commands/Maxima Files/basics.wxm create mode 100644 Commands/Maxima Files/functions.wxm create mode 100644 Commands/Maxima Files/limit.wxm create mode 100644 Questions/Maxima file/03-Sep-2020.wxm create mode 100644 Questions/Maxima file/07-Oct-2020.wxm create mode 100644 Questions/Maxima file/14-Sep-2020.wxm create mode 100644 Questions/Maxima file/24-Sep-2020.wxm create mode 100644 Questions/Maxima file/Eq.wxm diff --git a/Commands/Maxima Files/Calculus.wxm b/Commands/Maxima Files/Calculus.wxm new file mode 100644 index 0000000..8a160eb --- /dev/null +++ b/Commands/Maxima Files/Calculus.wxm @@ -0,0 +1,55 @@ +/* [wxMaxima batch file version 1] [ DO NOT EDIT BY HAND! ]*/ +/* [ Created with wxMaxima version 22.04.0 ] */ +/* [wxMaxima: title start ] +Calculus + [wxMaxima: title end ] */ + + +/* [wxMaxima: input start ] */ +f(x):= x^2 - 1; +/* [wxMaxima: input end ] */ + + +/* [wxMaxima: input start ] */ +diff(f(x), x); +/* [wxMaxima: input end ] */ + + +/* [wxMaxima: input start ] */ +diff(f(x), x, 2); +/* [wxMaxima: input end ] */ + + +/* [wxMaxima: input start ] */ +integrate(f(x), x); +/* [wxMaxima: input end ] */ + + +/* [wxMaxima: input start ] */ +integrate(f(x), x , 1, 10); +/* [wxMaxima: input end ] */ + + +/* [wxMaxima: input start ] */ +f(x):= x^2 - 3*x + sin(x) - 1; +/* [wxMaxima: input end ] */ + + +/* [wxMaxima: input start ] */ +df(x):= ''(diff(f(x), x)); +/* [wxMaxima: input end ] */ + + +/* [wxMaxima: input start ] */ +d2f(x):= ''(diff(f(x), x, 2)); +/* [wxMaxima: input end ] */ + + +/* [wxMaxima: input start ] */ +intf(x):= ''(integrate(f(x), x)); +/* [wxMaxima: input end ] */ + + + +/* Old versions of Maxima abort on loading files that end in a comment. */ +"Created with wxMaxima 22.04.0"$ diff --git a/Commands/Maxima Files/Complex_Numbers.wxm b/Commands/Maxima Files/Complex_Numbers.wxm new file mode 100644 index 0000000..b136fe3 --- /dev/null +++ b/Commands/Maxima Files/Complex_Numbers.wxm @@ -0,0 +1,140 @@ +/* [wxMaxima batch file version 1] [ DO NOT EDIT BY HAND! ]*/ +/* [ Created with wxMaxima version 22.04.0 ] */ +/* [wxMaxima: title start ] +Complex Numbers + [wxMaxima: title end ] */ + + +/* [wxMaxima: input start ] */ +z=x+y%i; +/* [wxMaxima: input end ] */ + + +/* [wxMaxima: input start ] */ +z2=r*cos(Θ)+r*sin(Θ)*%i; +/* [wxMaxima: input end ] */ + + +/* [wxMaxima: input start ] */ +z3=r*%e^(%i*Θ); +/* [wxMaxima: input end ] */ + + +/* [wxMaxima: input start ] */ +z1: x1+y1*%i; +/* [wxMaxima: input end ] */ + + +/* [wxMaxima: input start ] */ +z2: x2 + y2*%i; +/* [wxMaxima: input end ] */ + + +/* [wxMaxima: input start ] */ +z1 + z2; +/* [wxMaxima: input end ] */ + + +/* [wxMaxima: input start ] */ +rectform(%); +/* [wxMaxima: input end ] */ + + +/* [wxMaxima: input start ] */ +rectform(z1*z2); +/* [wxMaxima: input end ] */ + + +/* [wxMaxima: input start ] */ +rectform(z1/z2); +/* [wxMaxima: input end ] */ + + +/* [wxMaxima: input start ] */ +rectform(z1^2); +/* [wxMaxima: input end ] */ + + +/* [wxMaxima: input start ] */ +rectform((2*%i)*(2 + 3*%i)); +/* [wxMaxima: input end ] */ + + +/* [wxMaxima: input start ] */ +rectform((4 + 5*%i)/(-2 + 7*%i)); +/* [wxMaxima: input end ] */ + + +/* [wxMaxima: input start ] */ +rectform((3+5*%i)^2); +/* [wxMaxima: input end ] */ + + +/* [wxMaxima: input start ] */ +z1: r1%e^(%i*Θ1); z2:r2*%e^(%i*Θ2); +/* [wxMaxima: input end ] */ + + +/* [wxMaxima: input start ] */ +polarform(z1+z2); +/* [wxMaxima: input end ] */ + + +/* [wxMaxima: input start ] */ +polarform(z1*z2); +/* [wxMaxima: input end ] */ + + +/* [wxMaxima: input start ] */ +polarform((2-2*%i)*(5-7*%i)); +/* [wxMaxima: input end ] */ + + +/* [wxMaxima: input start ] */ +polarform(5+3*%i); +/* [wxMaxima: input end ] */ + + +/* [wxMaxima: input start ] */ +polarform(3+3*%i); +/* [wxMaxima: input end ] */ + + +/* [wxMaxima: input start ] */ +realpart(x + %i*y); +/* [wxMaxima: input end ] */ + + +/* [wxMaxima: input start ] */ +realpart(5 + 7*%i); +/* [wxMaxima: input end ] */ + + +/* [wxMaxima: input start ] */ +imagpart(5 + 7*%i); +/* [wxMaxima: input end ] */ + + +/* [wxMaxima: input start ] */ +imagpart((2+3*%i)/(1 + 4*%i)); +/* [wxMaxima: input end ] */ + + +/* [wxMaxima: input start ] */ +realpart((2+3*%i)/(1 + 4*%i)); +/* [wxMaxima: input end ] */ + + +/* [wxMaxima: input start ] */ +realpart((2 + 3*%i)/ (1 + 4*%i)); +/* [wxMaxima: input end ] */ + + +/* [wxMaxima: input start ] */ +demoivre(%e^(%i*Θ)); +/* [wxMaxima: input end ] */ + + + +/* Old versions of Maxima abort on loading files that end in a comment. */ +"Created with wxMaxima 22.04.0"$ diff --git a/Commands/Maxima Files/Factorials.wxm b/Commands/Maxima Files/Factorials.wxm new file mode 100644 index 0000000..6524d1a --- /dev/null +++ b/Commands/Maxima Files/Factorials.wxm @@ -0,0 +1,90 @@ +/* [wxMaxima batch file version 1] [ DO NOT EDIT BY HAND! ]*/ +/* [ Created with wxMaxima version 22.04.0 ] */ +/* [wxMaxima: title start ] +Factorials + [wxMaxima: title end ] */ + + +/* [wxMaxima: input start ] */ +5!; +/* [wxMaxima: input end ] */ + + +/* [wxMaxima: input start ] */ +n!; +/* [wxMaxima: input end ] */ + + +/* [wxMaxima: input start ] */ +gamma(x); +/* [wxMaxima: input end ] */ + + +/* [wxMaxima: input start ] */ +gamma(3); +/* [wxMaxima: input end ] */ + + +/* [wxMaxima: input start ] */ +gamma(5); +/* [wxMaxima: input end ] */ + + +/* [wxMaxima: input start ] */ +beta(5, 3); +/* [wxMaxima: input end ] */ + + +/* [wxMaxima: input start ] */ +beta(x, y); +/* [wxMaxima: input end ] */ + + +/* [wxMaxima: input start ] */ +makefact(gamma(x)); +/* [wxMaxima: input end ] */ + + +/* [wxMaxima: input start ] */ +makefact(beta(x, y)); +/* [wxMaxima: input end ] */ + + +/* [wxMaxima: input start ] */ +makefact(gamma(x+y)/x!); +/* [wxMaxima: input end ] */ + + +/* [wxMaxima: input start ] */ +makegamma((x+1)!/(x+y)!); +/* [wxMaxima: input end ] */ + + +/* [wxMaxima: input start ] */ +makegamma(z!*y!*x!); +/* [wxMaxima: input end ] */ + + +/* [wxMaxima: input start ] */ +makegamma(beta(x, y)); +/* [wxMaxima: input end ] */ + + +/* [wxMaxima: input start ] */ +minfactorial((x+5)!/x!); +/* [wxMaxima: input end ] */ + + +/* [wxMaxima: input start ] */ +minfactorial((x+5)!*(x+2)!/(x!^2)); +/* [wxMaxima: input end ] */ + + +/* [wxMaxima: input start ] */ +minfactorial((n+1)!/(n+3)!); +/* [wxMaxima: input end ] */ + + + +/* Old versions of Maxima abort on loading files that end in a comment. */ +"Created with wxMaxima 22.04.0"$ diff --git a/Commands/Maxima Files/Log.wxm b/Commands/Maxima Files/Log.wxm new file mode 100644 index 0000000..f69605e --- /dev/null +++ b/Commands/Maxima Files/Log.wxm @@ -0,0 +1,65 @@ +/* [wxMaxima batch file version 1] [ DO NOT EDIT BY HAND! ]*/ +/* [ Created with wxMaxima version 22.04.0 ] */ +/* [wxMaxima: title start ] +LOG + [wxMaxima: title end ] */ + + +/* [wxMaxima: input start ] */ +log(x); +/* [wxMaxima: input end ] */ + + +/* [wxMaxima: input start ] */ +log(10); +/* [wxMaxima: input end ] */ + + +/* [wxMaxima: input start ] */ +log_base(a, b):= log(a)/log(b); +/* [wxMaxima: input end ] */ + + +/* [wxMaxima: input start ] */ +log_base(4, 2), numer; +/* [wxMaxima: input end ] */ + + +/* [wxMaxima: input start ] */ +log_base(1000, 10), numer; +/* [wxMaxima: input end ] */ + + +/* [wxMaxima: input start ] */ +log(x*y),logexpand:super; +/* [wxMaxima: input end ] */ + + +/* [wxMaxima: input start ] */ +log(y^k), logexpand:super; +/* [wxMaxima: input end ] */ + + +/* [wxMaxima: input start ] */ +log(y/x^k), logexpand:super; +/* [wxMaxima: input end ] */ + + +/* [wxMaxima: input start ] */ +log(x)+log(y), logcontract; +/* [wxMaxima: input end ] */ + + +/* [wxMaxima: input start ] */ +2*log(y), logcontract; +/* [wxMaxima: input end ] */ + + +/* [wxMaxima: input start ] */ +log(y) - 3*log(x), logcontract; +/* [wxMaxima: input end ] */ + + + +/* Old versions of Maxima abort on loading files that end in a comment. */ +"Created with wxMaxima 22.04.0"$ diff --git a/Commands/Maxima Files/Matrix.wxm b/Commands/Maxima Files/Matrix.wxm new file mode 100644 index 0000000..6d8d338 --- /dev/null +++ b/Commands/Maxima Files/Matrix.wxm @@ -0,0 +1,217 @@ +/* [wxMaxima batch file version 1] [ DO NOT EDIT BY HAND! ]*/ +/* [ Created with wxMaxima version 22.04.0 ] */ +/* [wxMaxima: title start ] +Matrix + [wxMaxima: title end ] */ + + +/* [wxMaxima: input start ] */ +A: matrix([1, 2, 3], [4, 5, 6], [7, 8, 9]); +/* [wxMaxima: input end ] */ + + +/* [wxMaxima: input start ] */ +B: matrix([1], [2], [3]); +/* [wxMaxima: input end ] */ + + +/* [wxMaxima: input start ] */ +C: matrix([1, 2, 3]); +/* [wxMaxima: input end ] */ + + +/* [wxMaxima: input start ] */ +D: matrix([9, 8, 7], [6, 5, 4], [3, 2, 1]); +/* [wxMaxima: input end ] */ + + +/* [wxMaxima: input start ] */ +2*A; +/* [wxMaxima: input end ] */ + + +/* [wxMaxima: input start ] */ +A + A; +/* [wxMaxima: input end ] */ + + +/* [wxMaxima: input start ] */ +A + D; +/* [wxMaxima: input end ] */ + + +/* [wxMaxima: input start ] */ +A - D; +/* [wxMaxima: input end ] */ + + +/* [wxMaxima: input start ] */ +A*A; /*element wise product*/ +/* [wxMaxima: input end ] */ + + +/* [wxMaxima: input start ] */ +A.A; /*matrix multipication*/ +/* [wxMaxima: input end ] */ + + +/* [wxMaxima: input start ] */ +A.D; +/* [wxMaxima: input end ] */ + + +/* [wxMaxima: input start ] */ +A.B; +/* [wxMaxima: input end ] */ + + +/* [wxMaxima: input start ] */ +C.A; +/* [wxMaxima: input end ] */ + + +/* [wxMaxima: input start ] */ +A^3; /*element wise*/ +/* [wxMaxima: input end ] */ + + +/* [wxMaxima: input start ] */ +A^^3; +/* [wxMaxima: input end ] */ + + +/* [wxMaxima: input start ] */ +addrow(A, C); +/* [wxMaxima: input end ] */ + + +/* [wxMaxima: input start ] */ +addcol(A, B); +/* [wxMaxima: input end ] */ + + +/* [wxMaxima: input start ] */ +row(A, 1); +/* [wxMaxima: input end ] */ + + +/* [wxMaxima: input start ] */ +col(A, 1); +/* [wxMaxima: input end ] */ + + +/* [wxMaxima: input start ] */ +A[1, 1]; +/* [wxMaxima: input end ] */ + + +/* [wxMaxima: input start ] */ +A[3, 3]; +/* [wxMaxima: input end ] */ + + +/* [wxMaxima: input start ] */ +transpose(A); +/* [wxMaxima: input end ] */ + + +/* [wxMaxima: input start ] */ +determinant(A); +/* [wxMaxima: input end ] */ + + +/* [wxMaxima: input start ] */ +E: matrix([1, 2, 3], [3, 2, 1], [1, 4, 1]); +/* [wxMaxima: input end ] */ + + +/* [wxMaxima: input start ] */ +determinant(E); +/* [wxMaxima: input end ] */ + + +/* [wxMaxima: input start ] */ +invert(E); +/* [wxMaxima: input end ] */ + + +/* [wxMaxima: input start ] */ +E^^-1; +/* [wxMaxima: input end ] */ + + +/* [wxMaxima: input start ] */ +echelon(E); +/* [wxMaxima: input end ] */ + + +/* [wxMaxima: input start ] */ +eigenvalues(E); +/* [wxMaxima: input end ] */ + + +/* [wxMaxima: input start ] */ +eigenvectors(E); +/* [wxMaxima: input end ] */ + + +/* [wxMaxima: input start ] */ +rank(E); +/* [wxMaxima: input end ] */ + + +/* [wxMaxima: input start ] */ +nullity(E); +/* [wxMaxima: input end ] */ + + +/* [wxMaxima: input start ] */ +adjoint(E); +/* [wxMaxima: input end ] */ + + +/* [wxMaxima: input start ] */ +minor(E, 1, 2); +/* [wxMaxima: input end ] */ + + +/* [wxMaxima: input start ] */ +ident(3); +/* [wxMaxima: input end ] */ + + +/* [wxMaxima: input start ] */ +diagmatrix(3, 2); +/* [wxMaxima: input end ] */ + + +/* [wxMaxima: input start ] */ +diag_matrix(3, 2, 5); +/* [wxMaxima: input end ] */ + + +/* [wxMaxima: input start ] */ +zeromatrix(3, 3); +/* [wxMaxima: input end ] */ + + +/* [wxMaxima: input start ] */ +eq1: x + 2*y + z = 1; +eq2: x + 3*y = 1/2; +eq3: 2*x + y + 4*z = 3; +/* [wxMaxima: input end ] */ + + +/* [wxMaxima: input start ] */ +F: coefmatrix([eq1, eq2, eq3], [x, y, z]); +/* [wxMaxima: input end ] */ + + +/* [wxMaxima: input start ] */ +charpoly(F, x); +/* [wxMaxima: input end ] */ + + + +/* Old versions of Maxima abort on loading files that end in a comment. */ +"Created with wxMaxima 22.04.0"$ diff --git a/Commands/Maxima Files/Plot2d-1.wxm b/Commands/Maxima Files/Plot2d-1.wxm new file mode 100644 index 0000000..60d0a52 --- /dev/null +++ b/Commands/Maxima Files/Plot2d-1.wxm @@ -0,0 +1,40 @@ +/* [wxMaxima batch file version 1] [ DO NOT EDIT BY HAND! ]*/ +/* [ Created with wxMaxima version 22.04.0 ] */ +/* [wxMaxima: input start ] */ +wxplot2d([x^2], [x, -5, 5],[style, [points, 3, 0, 0]]); +/* [wxMaxima: input end ] */ + + +/* [wxMaxima: input start ] */ +wxplot2d([x^2], [x, -5, 5],[style, [points, 3, 1, 1]]); +/* [wxMaxima: input end ] */ + + +/* [wxMaxima: input start ] */ +wxplot2d([x^2], [x, -5, 5],[style, [points, 3, 2, 2]]); +/* [wxMaxima: input end ] */ + + +/* [wxMaxima: input start ] */ +wxplot2d([x^2], [x, -5, 5],[style, [points, 3, 3, 3]]); +/* [wxMaxima: input end ] */ + + +/* [wxMaxima: input start ] */ +wxplot2d([x^2], [x, -5, 5],[style, [points, 3, 4, 4]]); +/* [wxMaxima: input end ] */ + + +/* [wxMaxima: input start ] */ +wxplot2d([x^2], [x, -5, 5],[style, [points, 3, 5, 5]]); +/* [wxMaxima: input end ] */ + + +/* [wxMaxima: input start ] */ +wxplot2d([x^3], [x, -3, 3], [color, red]); /*valid colors are red, green, blue, magenta, cyan, yellow, orange, violet, brown, gray, black, white*/ +/* [wxMaxima: input end ] */ + + + +/* Old versions of Maxima abort on loading files that end in a comment. */ +"Created with wxMaxima 22.04.0"$ diff --git a/Commands/Maxima Files/Plot2d.wxm b/Commands/Maxima Files/Plot2d.wxm new file mode 100644 index 0000000..8cdb11a --- /dev/null +++ b/Commands/Maxima Files/Plot2d.wxm @@ -0,0 +1,88 @@ +/* [wxMaxima batch file version 1] [ DO NOT EDIT BY HAND! ]*/ +/* [ Created with wxMaxima version 22.04.0 ] */ +/* [wxMaxima: title start ] +Plot 2D + [wxMaxima: title end ] */ + + +/* [wxMaxima: input start ] */ +wxplot2d(sin(x), [x, -2*%pi, 2*%pi]); +/* [wxMaxima: input end ] */ + + +/* [wxMaxima: input start ] */ +wxplot2d([sin(x), cos(x)], [x, -2*%pi, 2*%pi]); +/* [wxMaxima: input end ] */ + + +/* [wxMaxima: input start ] */ +wxplot2d(sin(x), [x, -2*%pi, 2*%pi], [color, red]); +/* [wxMaxima: input end ] */ + + +/* [wxMaxima: input start ] */ +wxplot2d(sin(x), [x, -2*%pi, 2*%pi], [color, blue]); +/* [wxMaxima: input end ] */ + + +/* [wxMaxima: input start ] */ +wxplot2d(sin(x), [x, -2*%pi, 2*%pi], [color, "#00FFFF"], grid2d, [axes, solid]); +/* [wxMaxima: input end ] */ + + +/* [wxMaxima: input start ] */ +f(x):= sin(x)$ +g(x):= cos(x)$ +wxplot2d([f(x), g(x)], [x, -2*%pi, 2*%pi], [style, [points, 0.5, "#DDDDDD"], + [lines, 5, "#000000"]], [box, true], [grid2d, true], [axes, solid], + [title, "Trignometry"], [legend, "f(x)", "g(x)"], + [label, ["x", 2*%pi + 0.1, 0], ["x'", -2*%pi - 0.3, 0], + ["y", -0.1, 1.1], ["y'", -0.1, -1.05]], + [xtics, -2*%pi, %pi, 2*%pi], [ytics, false], + [xlabel, "time (sec)"], [ylabel, "Velocity (cm/sec)"])$ +/* [wxMaxima: input end ] */ + + +/* [wxMaxima: input start ] */ +wxplot2d([floor(x), signum(x)], [x, -5.5, 5.5], [y, -5.2, 5.2], + [style, [points, 2, "#FF00FF", 4], [points, 2, "#00FF00", 3]]); +/* [wxMaxima: input end ] */ + + +/* [wxMaxima: input start ] */ +wxplot2d([parametric, 2*cos(t), 2*sin(t), [t, -%pi, %pi]], + [style, [points, 2, "#00FF00", 4]], [yx_ratio, 1]); +/* [wxMaxima: input end ] */ + + +/* [wxMaxima: input start ] */ +wxplot2d([discrete, [[1, 2], [2, 3], [3, 4], [4, 5], [5, 6]]], [style, [points, 5, 2, 3]]); +/* [wxMaxima: input end ] */ + + +/* [wxMaxima: input start ] */ +wxplot2d(makelist(sin(n*x), n, 1, 10), [x, -%pi, %pi]); +/* [wxMaxima: input end ] */ + + +/* [wxMaxima: input start ] */ +with_slider(n, makelist(n/10, n, 1, 20), sin(n*x), [x, -%pi, %pi]); /*for animations*/ +/* [wxMaxima: input end ] */ + + +/* [wxMaxima: input start ] */ +wxplot2d([parametric, 3*cos(t), 2*sin(t), [t, -%pi, %pi]]); +/* [wxMaxima: input end ] */ + + +/* [wxMaxima: input start ] */ +wxplot2d([%e^x, x^2], [x, -2, 2], [style ,[lines, 1, 1], [points, 1, 2, 3]], + [legend, "e^x", "x^2"], [title, "graph"], + [xtics, -2, 0.5, 2], [ytics, 0, %e^-1, %e^2], + [xlabel, "domain"], [ylabel, "range"]); +/* [wxMaxima: input end ] */ + + + +/* Old versions of Maxima abort on loading files that end in a comment. */ +"Created with wxMaxima 22.04.0"$ diff --git a/Commands/Maxima Files/Plot3d.wxm b/Commands/Maxima Files/Plot3d.wxm new file mode 100644 index 0000000..85f4cd3 --- /dev/null +++ b/Commands/Maxima Files/Plot3d.wxm @@ -0,0 +1,44 @@ +/* [wxMaxima batch file version 1] [ DO NOT EDIT BY HAND! ]*/ +/* [ Created with wxMaxima version 22.04.0 ] */ +/* [wxMaxima: title start ] +3D PLOTS + [wxMaxima: title end ] */ + + +/* [wxMaxima: input start ] */ +wxplot3d(%e^(-x^2-y^2), [x, -2, 2], [y, -2, 2]); +/* [wxMaxima: input end ] */ + + +/* [wxMaxima: input start ] */ +wxplot3d(%e^(-x^2-y^2), [x, -2, 2], [y, -2, 2], [grid, 50, 50]); +/* [wxMaxima: input end ] */ + + +/* [wxMaxima: input start ] */ +wxplot3d(atan(-x^2+y^3/4),[x,-4,4],[y,-4,4],[grid,50,50], [mesh_lines_color, red]); + +/* [wxMaxima: input end ] */ + + +/* [wxMaxima: input start ] */ +wxplot3d([cos(a)*sin(b), sin(a)*sin(b), cos(b)], + [a,0,2*%pi], [b,0,%pi], [mesh_lines_color, false], + [grid,40,40], [same_xyz, true], [title, "Sphere"], [axes, solid]); +/* [wxMaxima: input end ] */ + + +/* [wxMaxima: input start ] */ +wxplot3d([x^2 + y^2, -x^2-y^2, x^2-y^2, [x, -2, 2], [y, -2, 2]]); +/* [wxMaxima: input end ] */ + + +/* [wxMaxima: input start ] */ +wxplot3d(x^2 + y^2, [x, -2, 2], [y, -2, 2], + [xlabel, "time (sec)"], [ylabel, "Velocity (cm/sec)"], [zlabel, "area"]); +/* [wxMaxima: input end ] */ + + + +/* Old versions of Maxima abort on loading files that end in a comment. */ +"Created with wxMaxima 22.04.0"$ diff --git a/Commands/Maxima Files/Trignometry.wxm b/Commands/Maxima Files/Trignometry.wxm new file mode 100644 index 0000000..12498fd --- /dev/null +++ b/Commands/Maxima Files/Trignometry.wxm @@ -0,0 +1,190 @@ +/* [wxMaxima batch file version 1] [ DO NOT EDIT BY HAND! ]*/ +/* [ Created with wxMaxima version 22.04.0 ] */ +/* [wxMaxima: title start ] +Trignometry + [wxMaxima: title end ] */ + + +/* [wxMaxima: input start ] */ +sin(%pi); +/* [wxMaxima: input end ] */ + + +/* [wxMaxima: input start ] */ +asin(0); +/* [wxMaxima: input end ] */ + + +/* [wxMaxima: input start ] */ +cos(%pi); +/* [wxMaxima: input end ] */ + + +/* [wxMaxima: input start ] */ +acos(-1); +/* [wxMaxima: input end ] */ + + +/* [wxMaxima: input start ] */ +tan(%pi/4); +/* [wxMaxima: input end ] */ + + +/* [wxMaxima: input start ] */ +atan(1); +/* [wxMaxima: input end ] */ + + +/* [wxMaxima: input start ] */ +wxplot2d([sin(x), cos(x), tan(x)], [x, -%pi/2 + 0.1, %pi/2 - 0.1]); +/* [wxMaxima: input end ] */ + + +/* [wxMaxima: input start ] */ +sinh(0); +/* [wxMaxima: input end ] */ + + +/* [wxMaxima: input start ] */ +cosh(0); +/* [wxMaxima: input end ] */ + + +/* [wxMaxima: input start ] */ +tanh(0); +/* [wxMaxima: input end ] */ + + +/* [wxMaxima: input start ] */ +asinh(0); +/* [wxMaxima: input end ] */ + + +/* [wxMaxima: input start ] */ +acosh(1); +/* [wxMaxima: input end ] */ + + +/* [wxMaxima: input start ] */ +atanh(0); +/* [wxMaxima: input end ] */ + + +/* [wxMaxima: input start ] */ +wxplot2d([sinh(x), cosh(x), tanh(x)], [x, -2, 2]); +/* [wxMaxima: input end ] */ + + +/* [wxMaxima: input start ] */ +diff(sin(x), x); +/* [wxMaxima: input end ] */ + + +/* [wxMaxima: input start ] */ +diff(cos(x), x); +/* [wxMaxima: input end ] */ + + +/* [wxMaxima: input start ] */ +diff(tan(x), x); +/* [wxMaxima: input end ] */ + + +/* [wxMaxima: input start ] */ +diff(sinh(x), x); +/* [wxMaxima: input end ] */ + + +/* [wxMaxima: input start ] */ +diff(cosh(x), x); +/* [wxMaxima: input end ] */ + + +/* [wxMaxima: input start ] */ +diff(tanh(x), x); +/* [wxMaxima: input end ] */ + + +/* [wxMaxima: input start ] */ +integrate(sin(x), x); +/* [wxMaxima: input end ] */ + + +/* [wxMaxima: input start ] */ +integrate(cos(x), x); +/* [wxMaxima: input end ] */ + + +/* [wxMaxima: input start ] */ +integrate(tan(x), x); +/* [wxMaxima: input end ] */ + + +/* [wxMaxima: input start ] */ +integrate(sinh(x), x); +/* [wxMaxima: input end ] */ + + +/* [wxMaxima: input start ] */ +integrate(cosh(x), x); +/* [wxMaxima: input end ] */ + + +/* [wxMaxima: input start ] */ +integrate(tanh(x), x); +/* [wxMaxima: input end ] */ + + +/* [wxMaxima: input start ] */ +trigexpand(sin(10*x + y)); +/* [wxMaxima: input end ] */ + + +/* [wxMaxima: input start ] */ +trigexpand(sinh(x + y)); +/* [wxMaxima: input end ] */ + + +/* [wxMaxima: input start ] */ +trigreduce(cos(10*x)*sin(y)+sin(10*x)*cos(y)); +/* [wxMaxima: input end ] */ + + +/* [wxMaxima: input start ] */ +sin(x)^2 + cos(x)^2; +/* [wxMaxima: input end ] */ + + +/* [wxMaxima: input start ] */ +trigsimp(sin(x)^2 + cos(x)^2); +/* [wxMaxima: input end ] */ + + +/* [wxMaxima: input start ] */ +sin(3*a)/sin(a+%pi/3); +/* [wxMaxima: input end ] */ + + +/* [wxMaxima: input start ] */ +trigrat(sin(3*a)/sin(a+%pi/3)); +/* [wxMaxima: input end ] */ + + +/* [wxMaxima: input start ] */ +exponentialize(sinh(x)); +/* [wxMaxima: input end ] */ + + +/* [wxMaxima: input start ] */ +exponentialize(cosh(x)); +/* [wxMaxima: input end ] */ + + +/* [wxMaxima: input start ] */ +exponentialize(tanh(x)); +/* [wxMaxima: input end ] */ + + + +/* Old versions of Maxima abort on loading files that end in a comment. */ +"Created with wxMaxima 22.04.0"$ diff --git a/Commands/Maxima Files/basics.wxm b/Commands/Maxima Files/basics.wxm new file mode 100644 index 0000000..278bdef --- /dev/null +++ b/Commands/Maxima Files/basics.wxm @@ -0,0 +1,139 @@ +/* [wxMaxima batch file version 1] [ DO NOT EDIT BY HAND! ]*/ +/* [ Created with wxMaxima version 22.04.0 ] */ +/* [wxMaxima: title start ] +Basics + [wxMaxima: title end ] */ + + +/* [wxMaxima: input start ] */ +%pi; +%e; +%i; +/* [wxMaxima: input end ] */ + + +/* [wxMaxima: input start ] */ +bfloat(%pi); +%e, numer; +/* [wxMaxima: input end ] */ + + +/* [wxMaxima: input start ] */ +bfloat(%pi), fpprec:100; +%e, bfloat, fpprec=100; +/* [wxMaxima: input end ] */ + + +/* [wxMaxima: input start ] */ +a: 10; +/* [wxMaxima: input end ] */ + + +/* [wxMaxima: input start ] */ +b: 20; +/* [wxMaxima: input end ] */ + + +/* [wxMaxima: input start ] */ +a + b; +/* [wxMaxima: input end ] */ + + +/* [wxMaxima: input start ] */ +V: m*s*k; +/* [wxMaxima: input end ] */ + + +/* [wxMaxima: input start ] */ +V, m: 10, s: 20, k: 30; +/* [wxMaxima: input end ] */ + + +/* [wxMaxima: input start ] */ +V, m=10, s=20, k=30; +/* [wxMaxima: input end ] */ + + +/* [wxMaxima: input start ] */ +z: 'a^2; +/* [wxMaxima: input end ] */ + + +/* [wxMaxima: input start ] */ +ev(z); +/* [wxMaxima: input end ] */ + + +/* [wxMaxima: input start ] */ +f(a):= a^2; +/* [wxMaxima: input end ] */ + + +/* [wxMaxima: input start ] */ +f(2); +/* [wxMaxima: input end ] */ + + +/* [wxMaxima: input start ] */ +f(a, b, c) := a + b + c; +/* [wxMaxima: input end ] */ + + +/* [wxMaxima: input start ] */ +f(a, b, a + b); +/* [wxMaxima: input end ] */ + + +/* [wxMaxima: input start ] */ +f(x):= if x%2 = 0 then 3*x/2 else x + 1; +/* [wxMaxima: input end ] */ + + +/* [wxMaxima: input start ] */ +f(10); +/* [wxMaxima: input end ] */ + + +/* [wxMaxima: input start ] */ +f(11); +/* [wxMaxima: input end ] */ + + +/* [wxMaxima: input start ] */ +f(12); +/* [wxMaxima: input end ] */ + + +/* [wxMaxima: input start ] */ +for i:0 while i <= 10 do(print(f(i))); +/* [wxMaxima: input end ] */ + + +/* [wxMaxima: input start ] */ +makelist(f(x), x, 1, 100); +/* [wxMaxima: input end ] */ + + +/* [wxMaxima: input start ] */ +sin(x) + cos(x); +/* [wxMaxima: input end ] */ + + +/* [wxMaxima: input start ] */ +%, x = 0; /*to get the last output we use %*/ +/* [wxMaxima: input end ] */ + + +/* [wxMaxima: input start ] */ +%o1, numer; /*to get a output from any line we use %oN*/ +/* [wxMaxima: input end ] */ + + +/* [wxMaxima: input start ] */ +%i26, x = %pi; /*to get a input from any line we use %iN*/ +/* [wxMaxima: input end ] */ + + + +/* Old versions of Maxima abort on loading files that end in a comment. */ +"Created with wxMaxima 22.04.0"$ diff --git a/Commands/Maxima Files/functions.wxm b/Commands/Maxima Files/functions.wxm new file mode 100644 index 0000000..73129a3 --- /dev/null +++ b/Commands/Maxima Files/functions.wxm @@ -0,0 +1,198 @@ +/* [wxMaxima batch file version 1] [ DO NOT EDIT BY HAND! ]*/ +/* [ Created with wxMaxima version 22.04.0 ] */ +/* [wxMaxima: title start ] +Functions + [wxMaxima: title end ] */ + + +/* [wxMaxima: input start ] */ +next_prime(10); +/* [wxMaxima: input end ] */ + + +/* [wxMaxima: input start ] */ +prev_prime(10); +/* [wxMaxima: input end ] */ + + +/* [wxMaxima: input start ] */ +binomial(10, 2); +/* [wxMaxima: input end ] */ + + +/* [wxMaxima: input start ] */ +max(10, 5); +/* [wxMaxima: input end ] */ + + +/* [wxMaxima: input start ] */ +min(10, 5); +/* [wxMaxima: input end ] */ + + +/* [wxMaxima: input start ] */ +mean([10, 11, 12]); +/* [wxMaxima: input end ] */ + + +/* [wxMaxima: input start ] */ +median([10, 11, 12]); +/* [wxMaxima: input end ] */ + + +/* [wxMaxima: input start ] */ +mod(10, 3); +/* [wxMaxima: input end ] */ + + +/* [wxMaxima: input start ] */ +abs(-10); +/* [wxMaxima: input end ] */ + + +/* [wxMaxima: input start ] */ +abs(10); +/* [wxMaxima: input end ] */ + + +/* [wxMaxima: input start ] */ +floor(0.5); +/* [wxMaxima: input end ] */ + + +/* [wxMaxima: input start ] */ +round(0.6); +/* [wxMaxima: input end ] */ + + +/* [wxMaxima: input start ] */ +load(functs); +/* [wxMaxima: input end ] */ + + +/* [wxMaxima: input start ] */ +permutation(10, 3); +/* [wxMaxima: input end ] */ + + +/* [wxMaxima: input start ] */ +combination(10, 3); +/* [wxMaxima: input end ] */ + + +/* [wxMaxima: input start ] */ +eq1: x^2 + 2*x + 1 = 0 ; +/* [wxMaxima: input end ] */ + + +/* [wxMaxima: input start ] */ +solve(eq1); +/* [wxMaxima: input end ] */ + + +/* [wxMaxima: input start ] */ + multiplicities; +/* [wxMaxima: input end ] */ + + +/* [wxMaxima: input start ] */ +f(x):= x^2 - 5*x; +/* [wxMaxima: input end ] */ + + +/* [wxMaxima: input start ] */ +solve(f(x)=2, x); +/* [wxMaxima: input end ] */ + + +/* [wxMaxima: input start ] */ +kill(eq1); +/* [wxMaxima: input end ] */ + + +/* [wxMaxima: input start ] */ +eq1: x + y + z = 1; +/* [wxMaxima: input end ] */ + + +/* [wxMaxima: input start ] */ +eq2: x - 2*y + 2*z = 2 ; +/* [wxMaxima: input end ] */ + + +/* [wxMaxima: input start ] */ +eq3: x - y - z = 0; +/* [wxMaxima: input end ] */ + + +/* [wxMaxima: input start ] */ +solve([eq1, eq2, eq3], [x, y, z]); +/* [wxMaxima: input end ] */ + + +/* [wxMaxima: input start ] */ +factor(x^2 + 2*x + 1); /*only works if eqn only has real roots*/ +/* [wxMaxima: input end ] */ + + +/* [wxMaxima: input start ] */ +expand((x+1)*(x+2)*(x+3)*(x+4)*(x+5)); +/* [wxMaxima: input end ] */ + + +/* [wxMaxima: input start ] */ +factor(x^5+15*x^4+85*x^3+225*x^2+274*x+120); +/* [wxMaxima: input end ] */ + + +/* [wxMaxima: input start ] */ +partfrac ( 1/(x^2*(x^2 + 1)), x); +/* [wxMaxima: input end ] */ + + +/* [wxMaxima: input start ] */ +sum(i^2, i, 0, 10); +/* [wxMaxima: input end ] */ + + +/* [wxMaxima: input start ] */ +simpsum: true$ +sum(i^2, i, 0, n); +/* [wxMaxima: input end ] */ + + +/* [wxMaxima: input start ] */ +prod(i, i, 1, 5); +/* [wxMaxima: input end ] */ + + +/* [wxMaxima: input start ] */ +simpproduct: true$ +prod(i, i, 1, n); +/* [wxMaxima: input end ] */ + + +/* [wxMaxima: input start ] */ +simpproduct: true$ +prod(i, i, 1, n); +/* [wxMaxima: input end ] */ + + +/* [wxMaxima: input start ] */ +sum(sin(i), i, 0, n); +/* [wxMaxima: input end ] */ + + +/* [wxMaxima: input start ] */ +sqrt(x); +/* [wxMaxima: input end ] */ + + +/* [wxMaxima: input start ] */ +makelist(x^2, x, 1, 10); +/* [wxMaxima: input end ] */ + + + +/* Old versions of Maxima abort on loading files that end in a comment. */ +"Created with wxMaxima 22.04.0"$ diff --git a/Commands/Maxima Files/limit.wxm b/Commands/Maxima Files/limit.wxm new file mode 100644 index 0000000..9069ea3 --- /dev/null +++ b/Commands/Maxima Files/limit.wxm @@ -0,0 +1,70 @@ +/* [wxMaxima batch file version 1] [ DO NOT EDIT BY HAND! ]*/ +/* [ Created with wxMaxima version 22.04.0 ] */ +/* [wxMaxima: title start ] +Limits + [wxMaxima: title end ] */ + + +/* [wxMaxima: input start ] */ +f(x):= 1/x^2; +/* [wxMaxima: input end ] */ + + +/* [wxMaxima: input start ] */ +limit(f(x), x, 0); +/* [wxMaxima: input end ] */ + + +/* [wxMaxima: input start ] */ +f(x):= 1/x^4; +/* [wxMaxima: input end ] */ + + +/* [wxMaxima: input start ] */ +limit(f(x), x, ∞); +/* [wxMaxima: input end ] */ + + +/* [wxMaxima: input start ] */ +f(x):= 1/x; +/* [wxMaxima: input end ] */ + + +/* [wxMaxima: input start ] */ +limit(f(x), x, 0, minus); +/* [wxMaxima: input end ] */ + + +/* [wxMaxima: input start ] */ +limit(f(x), x, 0, plus); +/* [wxMaxima: input end ] */ + + +/* [wxMaxima: input start ] */ +limit(f(x), x, 0); +/* [wxMaxima: input end ] */ + + +/* [wxMaxima: input start ] */ +f(x):= abs(x/(abs(x))); +/* [wxMaxima: input end ] */ + + +/* [wxMaxima: input start ] */ +limit(f(x), x, 0, minus); +/* [wxMaxima: input end ] */ + + +/* [wxMaxima: input start ] */ +limit(f(x), x, 0, plus); +/* [wxMaxima: input end ] */ + + +/* [wxMaxima: input start ] */ +limit(f(x), x, 0); +/* [wxMaxima: input end ] */ + + + +/* Old versions of Maxima abort on loading files that end in a comment. */ +"Created with wxMaxima 22.04.0"$ diff --git a/Questions/Maxima file/03-Sep-2020.wxm b/Questions/Maxima file/03-Sep-2020.wxm new file mode 100644 index 0000000..c02497b --- /dev/null +++ b/Questions/Maxima file/03-Sep-2020.wxm @@ -0,0 +1,201 @@ +/* [wxMaxima batch file version 1] [ DO NOT EDIT BY HAND! ]*/ +/* [ Created with wxMaxima version 22.04.0 ] */ +/* [wxMaxima: title start ] +03 Sep 2020 + [wxMaxima: title end ] */ + + +/* [wxMaxima: comment start ] +Q Evaluate 2^10, 3^10, 4^10 + [wxMaxima: comment end ] */ + + +/* [wxMaxima: input start ] */ +2^10; +3^10; +4^10; +/* [wxMaxima: input end ] */ + + +/* [wxMaxima: comment start ] +Q find the value of 10π upto 100 decimal places + [wxMaxima: comment end ] */ + + +/* [wxMaxima: input start ] */ +bfloat(10*π), fpprec:100; +/* [wxMaxima: input end ] */ + + +/* [wxMaxima: comment start ] +Q Let M = [[1, 2, 3], + [3, 2, 1], + [1, 1, 1]] +find M+M, M.M, M^3, [1, 0, 1].M + [wxMaxima: comment end ] */ + + +/* [wxMaxima: input start ] */ +M: matrix([1, 2, 3], [3, 2, 1], [1, 1, 1]); +/* [wxMaxima: input end ] */ + + +/* [wxMaxima: input start ] */ +M+M; +/* [wxMaxima: input end ] */ + + +/* [wxMaxima: input start ] */ +M.M; +/* [wxMaxima: input end ] */ + + +/* [wxMaxima: input start ] */ +M^^3; +/* [wxMaxima: input end ] */ + + +/* [wxMaxima: input start ] */ +[1, 0, 1].M; +/* [wxMaxima: input end ] */ + + +/* [wxMaxima: comment start ] +Q Find Sin²(π/4) + [wxMaxima: comment end ] */ + + +/* [wxMaxima: input start ] */ +sin(%pi/4)^2; +/* [wxMaxima: input end ] */ + + +/* [wxMaxima: comment start ] +Q Find 8C4 + [wxMaxima: comment end ] */ + + +/* [wxMaxima: input start ] */ +binomial(8, 4); +/* [wxMaxima: input end ] */ + + +/* [wxMaxima: comment start ] +Q Find factors of 80 + [wxMaxima: comment end ] */ + + +/* [wxMaxima: input start ] */ +factor(80); +/* [wxMaxima: input end ] */ + + +/* [wxMaxima: comment start ] +Q Find next and previous prime of 2020 + [wxMaxima: comment end ] */ + + +/* [wxMaxima: input start ] */ +next_prime(2020); +/* [wxMaxima: input end ] */ + + +/* [wxMaxima: input start ] */ +prev_prime(2020); +/* [wxMaxima: input end ] */ + + +/* [wxMaxima: comment start ] +Q Find 10P3 + [wxMaxima: comment end ] */ + + +/* [wxMaxima: input start ] */ +load(functs)$ +/* [wxMaxima: input end ] */ + + +/* [wxMaxima: input start ] */ +permutation(10, 3); +/* [wxMaxima: input end ] */ + + +/* [wxMaxima: comment start ] +Q Find 10Πi=1 i^3 and nΣi=1 i^3 + [wxMaxima: comment end ] */ + + +/* [wxMaxima: input start ] */ +prod(i^3, i, 1, 10); +/* [wxMaxima: input end ] */ + + +/* [wxMaxima: input start ] */ +simpsum: true$ +sum(i^3, i, 1, n); +/* [wxMaxima: input end ] */ + + +/* [wxMaxima: comment start ] +Q Find numeric value of e² + [wxMaxima: comment end ] */ + + +/* [wxMaxima: input start ] */ +%e^2, numer; +/* [wxMaxima: input end ] */ + + +/* [wxMaxima: comment start ] +Q Find the remainder when 193 divided by 7 + [wxMaxima: comment end ] */ + + +/* [wxMaxima: input start ] */ +mod(193, 7); +/* [wxMaxima: input end ] */ + + +/* [wxMaxima: comment start ] +Q Let f(x)= x³ + log(x), find f(1) + [wxMaxima: comment end ] */ + + +/* [wxMaxima: input start ] */ +f(x):= x^3 + log(x); +/* [wxMaxima: input end ] */ + + +/* [wxMaxima: input start ] */ +f(1); +/* [wxMaxima: input end ] */ + + +/* [wxMaxima: comment start ] +Q Find the derivative of x³ + log(x) + e^x + [wxMaxima: comment end ] */ + + +/* [wxMaxima: input start ] */ +diff(x^3 + log(x) + %e^x, x); +/* [wxMaxima: input end ] */ + + +/* [wxMaxima: comment start ] +Q Find the double derivative of the above function and also find the integral between 0 to 1 of the above function + [wxMaxima: comment end ] */ + + +/* [wxMaxima: input start ] */ +diff(x^3 + log(x) + %e^x, x, 2); +/* [wxMaxima: input end ] */ + + +/* [wxMaxima: input start ] */ +integrate(x^3 + log(x) + %e^x, x, 0, 1); +/* [wxMaxima: input end ] */ + + + +/* Old versions of Maxima abort on loading files that end in a comment. */ +"Created with wxMaxima 22.04.0"$ diff --git a/Questions/Maxima file/07-Oct-2020.wxm b/Questions/Maxima file/07-Oct-2020.wxm new file mode 100644 index 0000000..0b1466d --- /dev/null +++ b/Questions/Maxima file/07-Oct-2020.wxm @@ -0,0 +1,262 @@ +/* [wxMaxima batch file version 1] [ DO NOT EDIT BY HAND! ]*/ +/* [ Created with wxMaxima version 22.04.0 ] */ +/* [wxMaxima: comment start ] +Q Write the Command for plotting the graph of y = xsin(1/x) and Z = xy/(x² + y²) + [wxMaxima: comment end ] */ + + +/* [wxMaxima: input start ] */ +wxplot2d(x*sin(1/x), [x, -2, 2]); +/* [wxMaxima: input end ] */ + + +/* [wxMaxima: input start ] */ +wxplot3d(x*y/(x^2 + y^2), [x, -2, 2], [y, -2, 2]); +/* [wxMaxima: input end ] */ + + +/* [wxMaxima: comment start ] +Q Write Command for +1. Scaler matrix of order 4 with fixed entry -2 +2. identity matrix of order 4 +3. digonal matrix [[1, 0, 0], + [0, 2, 0], + [0, 0, 1]] +4. for adding column [[5], + [6]] + in the matrix A = [[0, 2], + [3, 5]] + also give sytax for adding row [[5, 6]]. + Also write for charactarstic polynomial for A and inverse of A. +5. eigen values and eigen vectors of matrix A +6. limit of g(x) at x = c +7. integrating f(x) = 1 + x^2 within the limits 0 to 10 + [wxMaxima: comment end ] */ + + +/* [wxMaxima: input start ] */ +diagmatrix(4, -2); +/* [wxMaxima: input end ] */ + + +/* [wxMaxima: input start ] */ +ident(4); +/* [wxMaxima: input end ] */ + + +/* [wxMaxima: input start ] */ +diag_matrix(1, 2, 1); +/* [wxMaxima: input end ] */ + + +/* [wxMaxima: input start ] */ +A: matrix([0, 2], [3, 5]); +/* [wxMaxima: input end ] */ + + +/* [wxMaxima: input start ] */ +addcol(A, [5, 6]); +/* [wxMaxima: input end ] */ + + +/* [wxMaxima: input start ] */ +addrow(A, [5, 6]); +/* [wxMaxima: input end ] */ + + +/* [wxMaxima: input start ] */ +charpoly(A, x); +/* [wxMaxima: input end ] */ + + +/* [wxMaxima: input start ] */ +invert(A); +/* [wxMaxima: input end ] */ + + +/* [wxMaxima: input start ] */ +eigenvalues(A); +/* [wxMaxima: input end ] */ + + +/* [wxMaxima: input start ] */ +eigenvectors(A); +/* [wxMaxima: input end ] */ + + +/* [wxMaxima: input start ] */ +limit(g(x), x, c); +/* [wxMaxima: input end ] */ + + +/* [wxMaxima: input start ] */ +integrate(1+x^2, x, 0, 10); +/* [wxMaxima: input end ] */ + + +/* [wxMaxima: comment start ] +Q Let A & B be two matrix find +1. A*B(usual) +2. A^2(Usual) +3. rank of A +4. nullity of A +5. determinant of A +6. tranpose of A +7. inverse of A + [wxMaxima: comment end ] */ + + +/* [wxMaxima: input start ] */ +A: matrix([0, 2], [3, 5]); +/* [wxMaxima: input end ] */ + + +/* [wxMaxima: input start ] */ +B: matrix([1, 2], [3, 4]); +/* [wxMaxima: input end ] */ + + +/* [wxMaxima: input start ] */ +A.B; +/* [wxMaxima: input end ] */ + + +/* [wxMaxima: input start ] */ +A^^2; +/* [wxMaxima: input end ] */ + + +/* [wxMaxima: input start ] */ +rank(A); +/* [wxMaxima: input end ] */ + + +/* [wxMaxima: input start ] */ +nullity(A); +/* [wxMaxima: input end ] */ + + +/* [wxMaxima: input start ] */ +determinant(A); +/* [wxMaxima: input end ] */ + + +/* [wxMaxima: input start ] */ +transpose(A); +/* [wxMaxima: input end ] */ + + +/* [wxMaxima: input start ] */ +invert(A); +/* [wxMaxima: input end ] */ + + +/* [wxMaxima: comment start ] +Q f(x) = (x²)²-2x² +1. find zeros of f(x) +2. Plot graph of f(x) +3. find f'(x) and zeros of f'(x) +4. find f''(x) and zeros of f''(x) +5. plot graph of f(x), f'(x) and f''(x) +6. find factors of f(x) + [wxMaxima: comment end ] */ + + +/* [wxMaxima: input start ] */ +f(x):= (x^2)^2 - 2*x^2; +/* [wxMaxima: input end ] */ + + +/* [wxMaxima: input start ] */ +solve(f(x)=0, x); +/* [wxMaxima: input end ] */ + + +/* [wxMaxima: input start ] */ +multiplicities; +/* [wxMaxima: input end ] */ + + +/* [wxMaxima: input start ] */ +df(x):= ''(diff(f(x), x)); +/* [wxMaxima: input end ] */ + + +/* [wxMaxima: input start ] */ +solve(df(x)=0, x); +/* [wxMaxima: input end ] */ + + +/* [wxMaxima: input start ] */ +multiplicities; +/* [wxMaxima: input end ] */ + + +/* [wxMaxima: input start ] */ +d2f(x):=''(diff(f(x), x, 2)); +/* [wxMaxima: input end ] */ + + +/* [wxMaxima: input start ] */ +solve(d2f(x)=0, x); +/* [wxMaxima: input end ] */ + + +/* [wxMaxima: input start ] */ +multiplicities; +/* [wxMaxima: input end ] */ + + +/* [wxMaxima: input start ] */ +wxplot2d([f(x), df(x), d2f(x)], [x, -2, 2]); +/* [wxMaxima: input end ] */ + + +/* [wxMaxima: input start ] */ +factor(f(x)); +/* [wxMaxima: input end ] */ + + +/* [wxMaxima: comment start ] +Q Solve the system of eqn using inverse method +2x + 3y - 4z = 4 +x + 2y + 3z = 6 +x - y + z = 2 + [wxMaxima: comment end ] */ + + +/* [wxMaxima: input start ] */ +eq1: 2*x + 3*y - 4*z = 4; +eq2: x + 2*y + 3*z = 6; +eq3: x - y + z = 2; +/* [wxMaxima: input end ] */ + + +/* [wxMaxima: input start ] */ +A: coefmatrix([eq1, eq2, eq3], [x, y, z]); +/* [wxMaxima: input end ] */ + + +/* [wxMaxima: input start ] */ +determinant(A); +/* [wxMaxima: input end ] */ + + +/* [wxMaxima: input start ] */ +Ainv: invert(A); +/* [wxMaxima: input end ] */ + + +/* [wxMaxima: input start ] */ +B: matrix([4], [6], [2]); +/* [wxMaxima: input end ] */ + + +/* [wxMaxima: input start ] */ +Ainv.B; +/* [wxMaxima: input end ] */ + + + +/* Old versions of Maxima abort on loading files that end in a comment. */ +"Created with wxMaxima 22.04.0"$ diff --git a/Questions/Maxima file/14-Sep-2020.wxm b/Questions/Maxima file/14-Sep-2020.wxm new file mode 100644 index 0000000..1633e10 --- /dev/null +++ b/Questions/Maxima file/14-Sep-2020.wxm @@ -0,0 +1,266 @@ +/* [wxMaxima batch file version 1] [ DO NOT EDIT BY HAND! ]*/ +/* [ Created with wxMaxima version 22.04.0 ] */ +/* [wxMaxima: title start ] +14-Sep-2020 + [wxMaxima: title end ] */ + + +/* [wxMaxima: comment start ] +Q Plot the graph of y = c*x^2, and analyse the effects of c by taking different choices for c + [wxMaxima: comment end ] */ + + +/* [wxMaxima: input start ] */ +f(x, c):=c*x^2; +/* [wxMaxima: input end ] */ + + +/* [wxMaxima: input start ] */ +wxplot2d(makelist(f(x, c), c, -3, 3), [x, -2, 2]); +/* [wxMaxima: input end ] */ + + +/* [wxMaxima: comment start ] +c is affecting the slope of c*x^2 + + [wxMaxima: comment end ] */ + + +/* [wxMaxima: comment start ] +Q plot the graph of +(i) Sin(x) in [-Π, Π] +(ii) Sin(2x + 3) in [-Π, Π] +(iii) Sin(x) and Sin(2x + 3) in [-Π, Π] simultanously + + [wxMaxima: comment end ] */ + + +/* [wxMaxima: input start ] */ +wxplot2d(sin(x), [x, -%pi, %pi]); +/* [wxMaxima: input end ] */ + + +/* [wxMaxima: input start ] */ +wxplot2d(sin(2*x + 3), [x, -%pi, %pi]); +/* [wxMaxima: input end ] */ + + +/* [wxMaxima: input start ] */ +wxplot2d([sin(x), sin(2*x + 3)], [x, -%pi, %pi]); +/* [wxMaxima: input end ] */ + + +/* [wxMaxima: comment start ] +Q plot the graph of +f(x) = 5*x + 3 +g(x) = x +h(x) = x - 2 +z(x) = -2 * x +in [-3, 3] simultanuosly. +Find the points of intersections of these lines + [wxMaxima: comment end ] */ + + +/* [wxMaxima: input start ] */ +f(x) := 5*x + 3; +g(x) := x; +h(x) := x - 2; +z(x) := -2 * x; +/* [wxMaxima: input end ] */ + + +/* [wxMaxima: input start ] */ +wxplot2d([f(x), g(x), h(x), z(x)], [x, -%pi, %pi]); +/* [wxMaxima: input end ] */ + + +/* [wxMaxima: input start ] */ +solve(f(x) = g(x)); +/* [wxMaxima: input end ] */ + + +/* [wxMaxima: input start ] */ +solve(f(x) = h(x)); +/* [wxMaxima: input end ] */ + + +/* [wxMaxima: input start ] */ +solve(f(x) = z(x)); +/* [wxMaxima: input end ] */ + + +/* [wxMaxima: input start ] */ +solve(g(x) = h(x)); +/* [wxMaxima: input end ] */ + + +/* [wxMaxima: input start ] */ +solve(g(x) = z(x)); +/* [wxMaxima: input end ] */ + + +/* [wxMaxima: input start ] */ +solve(h(x) = z(x)); +/* [wxMaxima: input end ] */ + + +/* [wxMaxima: comment start ] +Q Plot the piecewise function defined as +f(x)= 0 if x < 0, 0 for 0 ≤ x ≤ 1, -1 for x > 1 + [wxMaxima: comment end ] */ + + +/* [wxMaxima: input start ] */ +f(x) := if x < 0 then 1 else if x ≥ 0 and x ≤ 1 then 0 else -1; +/* [wxMaxima: input end ] */ + + +/* [wxMaxima: input start ] */ +wxplot2d(f(x), [x, -2, 2]); +/* [wxMaxima: input end ] */ + + +/* [wxMaxima: comment start ] +Q Expand (x-1)^4 + [wxMaxima: comment end ] */ + + +/* [wxMaxima: input start ] */ +expand((x - 1)^4); +/* [wxMaxima: input end ] */ + + +/* [wxMaxima: comment start ] +Q Find the roots of x^4 + x^2 + 1 = 0 + [wxMaxima: comment end ] */ + + +/* [wxMaxima: input start ] */ +solve(x^4 + x^2 + 1 = 0); +/* [wxMaxima: input end ] */ + + +/* [wxMaxima: input start ] */ +multiplicities; +/* [wxMaxima: input end ] */ + + +/* [wxMaxima: comment start ] +Q Find the first, second and third derivatives of following functions +f(x)= sec(x) +g(x)= |x| +h(x)= x^(1/2) + log(x) + [wxMaxima: comment end ] */ + + +/* [wxMaxima: input start ] */ +f(x):=sec(x); +g(x):=abs(x); +h(x):=x^(1/2) + log(x); +/* [wxMaxima: input end ] */ + + +/* [wxMaxima: input start ] */ +for i: 1 while i≤3 do print(diff(f(x), x, i)); +/* [wxMaxima: input end ] */ + + +/* [wxMaxima: input start ] */ +for i: 1 while i≤3 do print(diff(g(x), x, i)); +/* [wxMaxima: input end ] */ + + +/* [wxMaxima: input start ] */ +for i: 1 while i≤3 do print(diff(h(x), x, i)); +/* [wxMaxima: input end ] */ + + +/* [wxMaxima: comment start ] +Q Find the indefinate integral of xlog(x) and sin³(x)*cos²(x) +also find ∫xlog(x) from 0 to e and ∫sin³(x)*cos²(x) from -π to π + [wxMaxima: comment end ] */ + + +/* [wxMaxima: input start ] */ +f(x):=x*log(x); +/* [wxMaxima: input end ] */ + + +/* [wxMaxima: input start ] */ +g(x):=(sin(x)^3) * (cos(x)^2); +/* [wxMaxima: input end ] */ + + +/* [wxMaxima: input start ] */ +integrate(f(x), x); +/* [wxMaxima: input end ] */ + + +/* [wxMaxima: input start ] */ +integrate(g(x), x); +/* [wxMaxima: input end ] */ + + +/* [wxMaxima: input start ] */ +integrate(f(x), x, 0, %e); +/* [wxMaxima: input end ] */ + + +/* [wxMaxima: input start ] */ +integrate(g(x), x, -%pi, %pi); +/* [wxMaxima: input end ] */ + + +/* [wxMaxima: comment start ] +Q Find 12Σi=1 √i + [wxMaxima: comment end ] */ + + +/* [wxMaxima: input start ] */ +∑(sqrt(i), i, 1, 12); +/* [wxMaxima: input end ] */ + + +/* [wxMaxima: comment start ] +Q Find the values of x and y satisfying the equations x² - y² = 0 and 2y² + x² - x - y - 1 = 0 + [wxMaxima: comment end ] */ + + +/* [wxMaxima: input start ] */ +solve([x^2 - y^2 = 0, 2*y^2 + x^2 - x - y -1 = 0]); +/* [wxMaxima: input end ] */ + + +/* [wxMaxima: comment start ] +Q Find the solution for x + y = 2, x + y = 3 + [wxMaxima: comment end ] */ + + +/* [wxMaxima: input start ] */ +solve([x + y = 2, x + y = 3]); +/* [wxMaxima: input end ] */ + + +/* [wxMaxima: comment start ] +Q Find the solution for x + y = 2, 2x + 2y = 4 + [wxMaxima: comment end ] */ + + +/* [wxMaxima: input start ] */ +solve([x + y = 2, 2*x + 2*y = 4]); +/* [wxMaxima: input end ] */ + + +/* [wxMaxima: comment start ] +Q Find the solution for x + y + z = -1, x - y + z = 5, 2x + 2y +2z = -2 + [wxMaxima: comment end ] */ + + +/* [wxMaxima: input start ] */ +solve([x + y + z = -1, x - y + z = 5, 2*x + 2*y +2*z = -2]); +/* [wxMaxima: input end ] */ + + + +/* Old versions of Maxima abort on loading files that end in a comment. */ +"Created with wxMaxima 22.04.0"$ diff --git a/Questions/Maxima file/24-Sep-2020.wxm b/Questions/Maxima file/24-Sep-2020.wxm new file mode 100644 index 0000000..32a58ed --- /dev/null +++ b/Questions/Maxima file/24-Sep-2020.wxm @@ -0,0 +1,188 @@ +/* [wxMaxima batch file version 1] [ DO NOT EDIT BY HAND! ]*/ +/* [ Created with wxMaxima version 22.04.0 ] */ +/* [wxMaxima: title start ] +24-Sep-2020 + [wxMaxima: title end ] */ + + +/* [wxMaxima: comment start ] +Q Find the limit of f(x) = 1/x² at x = 0 and f(x) = 1/x^4 at ∞ + [wxMaxima: comment end ] */ + + +/* [wxMaxima: input start ] */ +f(x):= 1/x^2; +/* [wxMaxima: input end ] */ + + +/* [wxMaxima: input start ] */ +limit(f(x), x, 0); +/* [wxMaxima: input end ] */ + + +/* [wxMaxima: input start ] */ +f(x):= 1/x^4; +/* [wxMaxima: input end ] */ + + +/* [wxMaxima: input start ] */ +limit(f(x), x, ∞); +/* [wxMaxima: input end ] */ + + +/* [wxMaxima: comment start ] +Q Find the right and left hand limit of 1/x at x = 0 + [wxMaxima: comment end ] */ + + +/* [wxMaxima: input start ] */ +f(x):= 1/x; +/* [wxMaxima: input end ] */ + + +/* [wxMaxima: input start ] */ +limit(f(x), x, 0, minus); +/* [wxMaxima: input end ] */ + + +/* [wxMaxima: input start ] */ +limit(f(x), x, 0, plus); +/* [wxMaxima: input end ] */ + + +/* [wxMaxima: comment start ] +Q Find the right and left hand limit of |x/|x|| at x = 0 +and what can you conclude from it + [wxMaxima: comment end ] */ + + +/* [wxMaxima: input start ] */ +f(x):= abs(x/(abs(x))); +/* [wxMaxima: input end ] */ + + +/* [wxMaxima: input start ] */ +limit(f(x), x, 0, minus); +/* [wxMaxima: input end ] */ + + +/* [wxMaxima: input start ] */ +limit(f(x), x, 0, plus); +/* [wxMaxima: input end ] */ + + +/* [wxMaxima: input start ] */ +limit(f(x), x, 0); +/* [wxMaxima: input end ] */ + + +/* [wxMaxima: comment start ] +the limit of f(x) = |x/|x|| exist at x = 0 and it is 1 + [wxMaxima: comment end ] */ + + +/* [wxMaxima: comment start ] +Q Find points of maxima and minima for f(x) = 3x/(x²+1)² also find maximum and minimum value of f(x) and plot the graph of f(x) + [wxMaxima: comment end ] */ + + +/* [wxMaxima: input start ] */ +f(x):= 3*x/(x^2 + 1)^2; +/* [wxMaxima: input end ] */ + + +/* [wxMaxima: input start ] */ +wxplot2d(f(x), [x, -5, 5]); +/* [wxMaxima: input end ] */ + + +/* [wxMaxima: input start ] */ +solve(diff(f(x), x)=0, x); +/* [wxMaxima: input end ] */ + + +/* [wxMaxima: input start ] */ +d2f(x):= ''(diff(f(x), x, 2)); +/* [wxMaxima: input end ] */ + + +/* [wxMaxima: input start ] */ +d2f(-1/(sqrt(3))); +/* [wxMaxima: input end ] */ + + +/* [wxMaxima: input start ] */ +d2f(1/(sqrt(3))); +/* [wxMaxima: input end ] */ + + +/* [wxMaxima: comment start ] +f(x) is minimum at x = -1/sqrt(3) as f''(x) at x = -1/sqrt(3) is +ive and f(x) is maximum at x = 1/sqrt(3) as f''(x) at x = 1/sqrt(3) is - + [wxMaxima: comment end ] */ + + +/* [wxMaxima: input start ] */ +f(-1/sqrt(3)); +/* [wxMaxima: input end ] */ + + +/* [wxMaxima: input start ] */ +f(1/sqrt(3)); +/* [wxMaxima: input end ] */ + + +/* [wxMaxima: comment start ] +maximum value of f(x) is 3^(5/2)/16 and minimum value of f(x) is -3^(5/2)/16 + [wxMaxima: comment end ] */ + + +/* [wxMaxima: comment start ] +Q Find points of maxima and minima for f(x) = 1/(x - %e^x) also find maximum and minimum value of f(x) and plot the graph of f(x) + [wxMaxima: comment end ] */ + + +/* [wxMaxima: input start ] */ +f(x):= 1/(x - %e^x); +/* [wxMaxima: input end ] */ + + +/* [wxMaxima: input start ] */ +wxplot2d(f(x), [x, -2, 2]); +/* [wxMaxima: input end ] */ + + +/* [wxMaxima: input start ] */ +solve(diff(f(x), x) = 0, x); +/* [wxMaxima: input end ] */ + + +/* [wxMaxima: input start ] */ +d2f(x):= ''(diff(f(x), x, 2)); +/* [wxMaxima: input end ] */ + + +/* [wxMaxima: input start ] */ +d2f(-log(log(%e))/log(e)); +/* [wxMaxima: input end ] */ + + +/* [wxMaxima: comment start ] +f(x) is minimum at x = 1 as f''(x) +at x = 0 is 1 and there is no +maximum. + [wxMaxima: comment end ] */ + + +/* [wxMaxima: input start ] */ +f(0); +/* [wxMaxima: input end ] */ + + +/* [wxMaxima: comment start ] +minimum value of f(x) is -1 at x = 0. + [wxMaxima: comment end ] */ + + + +/* Old versions of Maxima abort on loading files that end in a comment. */ +"Created with wxMaxima 22.04.0"$ diff --git a/Questions/Maxima file/Eq.wxm b/Questions/Maxima file/Eq.wxm new file mode 100644 index 0000000..bc440f1 --- /dev/null +++ b/Questions/Maxima file/Eq.wxm @@ -0,0 +1,156 @@ +/* [wxMaxima batch file version 1] [ DO NOT EDIT BY HAND! ]*/ +/* [ Created with wxMaxima version 22.04.0 ] */ +/* [wxMaxima: title start ] +Extra Questions + [wxMaxima: title end ] */ + + +/* [wxMaxima: comment start ] +Question: Let f(x) = x^5 - 14 +(i) Find the zeros of f(x) +(ii) Plot the graph of of f(x) in the interval (-1, 1) +(iii) Find f'(x) and zeros of f'(x) +(iv) Find f''(x) and zeros of f''(x) +(v) Plot combined graph of f(x), f'(x) and f'''(x) +(vi) Find the fractors of f(x) + [wxMaxima: comment end ] */ + + +/* [wxMaxima: input start ] */ +f(x):=x^5 - 14; +/* [wxMaxima: input end ] */ + + +/* [wxMaxima: input start ] */ +solve(f(x)=0, x); +/* [wxMaxima: input end ] */ + + +/* [wxMaxima: input start ] */ +wxplot2d(f(x), [x, -1, 1]); +/* [wxMaxima: input end ] */ + + +/* [wxMaxima: input start ] */ +df(x):= diff(f(x), x); +/* [wxMaxima: input end ] */ + + +/* [wxMaxima: input start ] */ +df(x); +/* [wxMaxima: input end ] */ + + +/* [wxMaxima: input start ] */ +allroots(df(x)=0); +/* [wxMaxima: input end ] */ + + +/* [wxMaxima: input start ] */ +wxplot2d(df(x), [x, -1 , 1]); +/* [wxMaxima: input end ] */ + + +/* [wxMaxima: input start ] */ +d2f(x):=diff(df(x), x); +/* [wxMaxima: input end ] */ + + +/* [wxMaxima: input start ] */ +d2f(x); +/* [wxMaxima: input end ] */ + + +/* [wxMaxima: input start ] */ +%o19, x=2; +/* [wxMaxima: input end ] */ + + +/* [wxMaxima: input start ] */ +A: 12; +/* [wxMaxima: input end ] */ + + +/* [wxMaxima: input start ] */ +A; +/* [wxMaxima: input end ] */ + + +/* [wxMaxima: input start ] */ +allroots(d2f(x)=0); +/* [wxMaxima: input end ] */ + + +/* [wxMaxima: input start ] */ +wxplot2d([f(x), df(x), d2f(x)], [x, -1, 1]); +/* [wxMaxima: input end ] */ + + +/* [wxMaxima: input start ] */ +factorC(x^5 - 14); +/* [wxMaxima: input end ] */ + + +/* [wxMaxima: comment start ] +Question: Let f(x) = log(x) - 1 +(i) Find the zeros of f(x) +(ii) Plot the graph of of f(x) in the interval (0.3, 5) +(iii) Find f'(x) +(iv) Find f''(x) +(v) Plot combined graph of f(x), f'(x) and f'''(x) + [wxMaxima: comment end ] */ + + +/* [wxMaxima: input start ] */ +f(x):= log(x) - 1; +/* [wxMaxima: input end ] */ + + +/* [wxMaxima: input start ] */ +solve(f(x)=0, x); +/* [wxMaxima: input end ] */ + + +/* [wxMaxima: input start ] */ +wxplot2d(f(x), [x, 0.3, 5]); +/* [wxMaxima: input end ] */ + + +/* [wxMaxima: input start ] */ +df(x):=diff(f(x), x); +/* [wxMaxima: input end ] */ + + +/* [wxMaxima: input start ] */ +df(x); +/* [wxMaxima: input end ] */ + + +/* [wxMaxima: input start ] */ +wxplot2d(df(x), [x, 0.3, 5]); +/* [wxMaxima: input end ] */ + + +/* [wxMaxima: input start ] */ +d2f(x):= diff(df(x), x); +/* [wxMaxima: input end ] */ + + +/* [wxMaxima: input start ] */ +d2f(x); +/* [wxMaxima: input end ] */ + + +/* [wxMaxima: input start ] */ +wxplot2d(d2f(x), [x, 0.3, 5]); +/* [wxMaxima: input end ] */ + + +/* [wxMaxima: input start ] */ +wxplot2d([f(x), df(x), d2f(x)], [x, 0.3, 5]); +/* [wxMaxima: input end ] */ + + + +/* Old versions of Maxima abort on loading files that end in a comment. */ +"Created with wxMaxima 22.04.0"$