Maple Lab • Calculus & Algebra

Functions, plots, derivatives, integrals, and equation solving
Calculus & algebra track

This track shows how to use Maple on the exact objects that appear in UI calculus and algebra courses: functions, graphs, limits, derivatives, integrals, and algebraic equations.

📐 First- & second-year focus 📊 Graphs & visualisation 🧮 Symbolic & numeric solving
Topic C1
Functions and plots

A large part of calculus is about “what does this function look like?” Maple lets you answer that question quickly, as long as you define your functions clearly.

Standard pattern:

  • f := x -> x^2 + 2*x + 1;
  • f(0); f(1); f(2);
  • plot( f(x), x = -5..5 );
Example: visualising a piecewise function 
f := x -> piecewise( x < 0,  -x,
                     0 <= x and x <= 2, x^2,
                     x > 2, 2 );

plot( f(x), x = -3..4 );

This mirrors typical exam questions where one must sketch a piecewise definition by hand. Maple lets you verify whether your sketch is reasonable.

🎓 Common in UI courses: first-year calculus, real analysis warm-up
Topic C2
Differentiation and integration

Maple treats differentiation and integration as commands. You should learn how to:

  • • Differentiate functions defined using ->.
  • • Compute antiderivatives.
  • • Evaluate definite integrals.
Example: derivative and critical points 
f := x -> x^3 - 3*x;

df := diff( f(x), x );

# Critical points: solve f'(x) = 0
solve( df = 0, x );

Combine this with plot( f(x), x = -3..3 ); to compare algebraic critical points with the graph.

Example: definite integral and comparison 
int( x^2 * exp(-x), x = 0..infinity );

# Numerical approximation
evalf( int( x^2 * exp(-x), x = 0..infinity ) );

When Maple returns a special function or constant, you can still ask for a numerical value using evalf.

🎓 Connects directly to UI integration techniques & Gamma/Beta function ideas
Topic C3
Solving equations and inequalities

Maple distinguishes between exact (symbolic) and approximate (numeric) solving:

  • solve( x^2 - 5*x + 6 = 0, x );
  • fsolve( sin(x) = x/2, x );
Example: intersection of two curves 
f := x -> exp(-x);
g := x -> x^2 - 1;

eq := f(x) = g(x);
sol := fsolve( eq, x, -2..2 );

plot( [f(x), g(x)], x = -2..2 );

This is the Maple analogue of solving “where do these curves meet?” questions.

🎓 Useful for assignment checking and contest preparation

Connecting this track to UI courses

Below are some example ways to tie Maple sessions to specific UI courses. The codes here are placeholders for the real course codes you will use in practice.

Calculus I companion

Level 100 • Weekly worksheet
  • Week 1: domain and range via plots.
  • Week 2: tangent lines and derivative plots.
  • Week 3: basic definite integrals.

Calculus II companion

Level 200 • Selected weeks
  • Improper integrals and convergence checks.
  • Polar and parametric plots.
  • Series experiments with partial sums.

Algebra & functions lab

Level 200–300 • Problem-solving focus
  • Equation solving with solve and fsolve.
  • Visual checks of algebraic identities.
  • Exploring simple inequalities via plots.
A typical Maple study session
Template for students
  • • Pick one worked example from your lecture notes.
  • • Recreate it in Maple using a clear function definition and plot.
  • • Change one detail (coefficient, interval, parameter) and see what changes.
  • • Add a short text paragraph above the commands explaining what you discovered.
Mini worksheet structure

You can build each Maple worksheet as a one-page story:

  • 1. Title & your name.
  • 2. Warm-up: two or three quick commands (arithmetic, simple functions).
  • 3. Main example 1: function definition, derivative, graph.
  • 4. Main example 2: definite integral and numeric comparison.
  • 5. One short “challenge” question that you plan to refine later.
For tutors

During a Maple–calculus lab, the most valuable thing you can do is connect commands to the exact theorem or technique that was used in class that week.

  • • Show where Maple agrees with hand calculations.
  • • Point out when Maple returns something more general than what you did by hand.
  • • Discuss how to interpret any strange output.
Maple is a tool, not an oracle. Encourage students to predict the answer before running the command, then treat Maple as a way to check and deepen their reasoning.