## Maple examples for MA 166H

Lab 1 - Volumes of solids, 3D graphs in Maple

·  Part 1 (.mws) In this exercise we learn how to plot 3D functions using Maple.

Lab 2 - Baseball pitches, Assignment3D graphs in Maple

·  Part 1 (.mws) In this exercise we learn how to plot 3D functions using Maple.

Assignment: 1. Research and write a 2-3 page double-spaced paper on the Physics and Calculus of your favorite pitch (curveball, knuckleball, etc).

2. Study the p. 483, EE1 case when q0=p/4, using the worksheet above. Pick best two w’s.

Lab 3 – Introduction of Excel to Calculus

Probabilistic behavior ( .xls) Exploratory exercise EE1 in Section 5.7 is examined using Excel.

Dynamic systems behavior ( .xls) An Excel example describing different behavior of a dynamical system.

Assignment: 1. Do EE1 on p. 505 with the functions (a) f(x)=27x^2(1-x)/4 ; and (b) f(x)=sin(3.14 x). Plot a phase portrait using Excel. What conclusions can you draw?

Lab 4 – Using rules for integration in Maple (no assignment)

·  Part 1 (.mws)

Lab 5 – Integration and CAS

·  Part 1 (.mws) In this exercise we study integration using Maple.

Assignment 6.5:   1. W1 (a short essay on how to set up a symbolic integration software);

2. Problems 29-36 (in 29 use only the HW problems) .

Lab 6 – Differential Equations with Maple

·  Part 1 (.mws) In this exercise we study differential equations using Maple.

Assignment:          1. Verify your homework problems from Section 7.2: 16, 18, 28, 29, 36;

2. Use directional field plots (dfieldplot command) to solve: 7.3: 23, 32, 33, 37-40;

Lab 7 – More Differential Equations with Maple, Systems of Differential equations

·  Part 1 (.mws) In this exercise we study numerical methods (Euler method) for solving differential equations using Maple.

·  Part 2 (.mws) Systems of differential equations.

Assignment:          1. Verify your homework problems from Section 7.3: 15, 16, 17;

2. Program the Improved Euler’s method from EE 1 on p. 599;

·  Lab 8 - Sequences and Series

·  Part 1 ( .mws) Sequences and series using Maple.

·  Lab 9 - Sequences and Series

·  Part 1 ( .mws)  Convergence of series and error estimates.

Assignment: 8.5 19, 24, 28, 41;

1. For these problems establish convergence using Maple’s limit command.

2. Find the sums of the series within 0.0001. Indicate clearly which approach you are using: integral test error (book and/or modified version), comparison test error, or alternating series test error. What is N in each case?                      `

·  Lab 10 – Taylor Series (no assignment)

·  Part 1 (.mws) In this exercise we study the Taylor series representations.

Lab 11 – Fourier Series

·  Part 1 ( .mws)  In this worksheet we study the Fourier series. We define piecewise functions, find Fourier coefficients and a Fourier sections. Finally we plot the function and the Fourier section on the same coordinate system.

Assignment: For the following three piecewise functions find the Fourier series coefficients and plot the Fourier section with N=10 and the corresponding function on the same plot.      1. F(x) = x^2 on [-4,0] and x+x^3 on [0,4].

2. G(x)=2|x| on [-Pi..Pi].

3. H(x)=exp(x) on [-2,0] and exp(-x) on [0,2].