NAMSSN UI Chapter

A Maple worksheet is made of input regions (where you type commands) and output regions (where Maple shows results). Lines end with a semicolon ; or a colon :.

• 2 + 3;
• 3^4; (powers)
• sqrt(2);

Basic rule: press the Enter key (not just a new line) to execute an input region.

A good worksheet has clear text blocks and tidy command blocks. You can type explanations in plain text, then insert input regions for Maple to execute.

In this module you practise:

• • Creating a title and section headings.
• • Separating text from commands.
• • Saving and reopening .mw files safely.

Maple has built-in help. A few commands:

• ?int — open help for the integral command.
• ?LinearAlgebra — help for linear algebra commands.
• restart; — clear all definitions and start fresh.

In Maple, a function is often written as f := x -> expression;.

• f := x -> sin(x) + x^2;
• f(0); f(1); f(2);
• plot( f(x), x = -2..2 );

Maple commands for calculus:

• diff( f(x), x ); — derivative of f.
• int( x^2, x ); — indefinite integral.
• int( exp(-x^2), x = -infinity..infinity ); — definite integral.

Two essential commands:

• solve( x^2 - 5*x + 6 = 0, x );
• fsolve( sin(x) = x/2, x ); (numerical solutions)

Start by loading the package: with(LinearAlgebra):

with(LinearAlgebra):

A := Matrix([[1,2],[3,4]]);
B := Matrix([[0,1],[1,0]]);

A + B;
A . B;
Determinant(A);

A compact way to explore eigenvalues:

• Eigenvalues(A);
• Eigenvectors(A);
• JordanForm(A, output = 'P,J');

A first test problem:

de  := diff(y(x), x) = y(x);
sol := dsolve(de, y(x));

# With an initial condition y(0) = 1
sol_ic := dsolve({de, y(0) = 1}, y(x));

Use DEplot (from DEtools) and plot to see how solutions behave. Typical tasks:

• • Plot families of solutions for several initial conditions.
• • Plot a slope field for a first-order ODE.

The ambition of Module 3 is to design worksheets that map directly to UI courses: MAT 2xx, MAT 3xx, ODE–Integration Bee practice sheets, and project notes.

You decide:

• • Which examples to include from each week’s lectures.
• • How to structure your worksheet (sections, warm-ups, main examples, challenges).
• • How to annotate results so that Maple output is easy to read later.

Long-term goal: a living library of Maple worksheets for UI mathematics, built and maintained by NAMSSN students.