Laboratory assignments

(a) Open the Introduction and read it with your lab partner.

(b) Open the Index and look at it. Click on a topic, then figure out a way to get back to the Index.

(c) Open Chapter 1 and work through each section, executing all of the Maple commands and doing what the text tells you to do.

(d) Use the things you have learned in Chapter 1 to make a Maple worksheet that presents the following problem in text and equations, discusses how to solve it, then uses Maple commands to solve it.

(e) A charged disk of radius and uniform charge density produces an electric field along the -axis (where the -axis is the line perpendicular to the disk through its center) given by the integral expression

Find a simple algebraic expression for , then use e-6 , e-12 , and mm to make a plot of from to .

(f) In Example 15.13 of Serway the Venturi tube is discussed. Bernoulli's equation

and the equation of continuity

are solved simultaneously to obtain the following formula
for :

Use Maple's solve command to obtain this result.

Chapters 2 and 9 (labs 3-4)

(a) Go to Chapter 9 and study the symbolic algebra commands listed there, running the examples as you go. Don't work through the long exercise at the end, but just try to become familiar with the commands and what they do. As you work the other problems in this course you will probably refer to this chapter often as you try to talk Maple into giving you results in the form you want.

(b) Work through the sections of Chapter 2 from x-y Plotting to Plotting Data, skipping the advanced topics. Work the following problems and show your work to your TA.

2.1, 2.2, 2.3, 2.6, 2.7, 2.8, and the Plotting Data example.

(c) Work through the sections of Chapter 2 from Parametric Plots to 3-D Plotting and do the following problems:

2.10, 2.12, 2.13, 2.14, 2.16, 2.18, 2.20, 2.24, and work through and experiment with the commands in the 3D Plotting section. Especially become familiar with the items available on the toolbar at the top of the plot frame.

(d) Not required, but a good idea: If you have time, do the advanced material on wave
packets in the section on animations
and do problems 2.21-23.

CHECKPOINT 1:

Chapters 1 and 2 must be finished now; no late work accepted after the end of the 4th laboratory period.

Chapter 3 (labs 5-7)

(a) Work through Limits, Differentiation, and part of Integration in Chapter 3, up through Elementary Integrals. Show your TA your work on Problems 3.1, 3.2, 3.3, 3.4, 3.5, 3.6, 3.7, 3.8, and 3.11.

(b) Work through the rest of Integration in Chapter 3, and show to your TA Problems 3.12, 3.13, 3.14, 3.16, and 3.17.

(c) Work through Series Expansions and Sums. Do Problems 3.19, 3.20, 3.21, 3.22, 3.23, 3.24, 3.25, and 3.26.

Chapter 4 (lab 8)

Work through Chapter 4 on Complex Analysis, doing Problems 4.1, 4.2, 4.3, 4.4, 4.5, 4.7, 4.8, 4.11, 4.12, and 4.13.

Chapter 5 (lab 9)

Work through Chapter 5 on Linear Algebra, doing Problems 5.1, 5.2, 5.3, 5.4, 5.5, and 5.6.

CHECKPOINT 2:

Chapters 3-5 must be finished now; no late work accepted after the end of the 9th laboratory period.

Chapter 6 (lab 10)

(a) Work through Chapter 6 on Solving Equations, doing problems 6.1, 6.2, 6.4, and 6.5.

(b) Find all of the zeros of the Bessel function derivative between 0 and 100.
Load them into a column vector . You can do this problem very compactly by using the seq command with fsolves inside it, remembering that the zeros of Bessel functions are separated by about . A plot of the derivative expression will immediately show you that there is a root at , but Maple will have trouble finding it because of the that appears in the derivative formula. Just load this simple root by hand and let Maple find the rest.