## 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 q_{0}=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].