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"$