20100-55 Mathematical Methods for Physical Sciences II

Spring 2007



Instructor

Dr. Thomas M. Fiore

Email

fiore"at"math.uchicago.edu

Office hours

Mondays 1:30-2:30, Wednesdays 3:00-4:00, and by appointment. All office hours are in Room 318, Eckhart Hall.

Class Meeting Times

MWF 12:30-1:20, Room 016, Albert Pick Hall for International Studies, 5828 S. University Ave.


Textbooks

Elementary Differential Equations and Boundary Value Problems: Eighth Edition,
by William E. Boyce and Richard DiPrima,
Complex Variables: Second Edition,
by Stephen D. Fisher.

Exams

In-Class Exam I: Wednesday, April 11th Solutions
In-Class Exam II: Friday, May 4th Solutions
Final: Thursday, June 7th, 4-6, in Stuart 101

Syllabus

pdf

Topics Covered

Direction fields, classification of differential equations, integrating factors, separable equations, modeling, linear versus nonlinear equations, population dynamics, exact equations, Euler's method, existence and uniqueness theorem, Picard's Iteration Method, difference equations, second order homogeneous equations with constant coefficients, fundamental solution sets, Wronskians, linear independence, characteristic equation and solutions, method of undetermined coefficients, variation of parameters, vibrations, higher order equations, power series review, power series solutions near an ordinary point, power series solutions near a regular singular point, Laplace transform and initial value problems, step functions, equations with discontinuous forcing functions, Dirac delta-function, convolution, geometry of the complex plane (circles and lines), triangle inequality, open subsets, curves, complex functions, complex sequences, complex power series, complex exponential and trigonometric functions, line integrals, Green's Theorem, analytic and harmonic functions, Cauchy-Riemann equations, Cauchy's Theorem, Cauchy's Formula, isolated singularities, Residue Theorem, and applications to definite integrals.


Homework: Homework is due at the beginning of class on Wednesdays. All exercises are in Boyce and DiPrima, until we use Fisher later in the quarter. Use Mathematica or MatLab for the exercises marked with a "mouse symbol" in the text, and hand in the printouts.

Due

Homework Assignment

Practice for Final
(will not be collected)

6.4 Pages 337-339: 1, 5 (you may draw the forcing function by hand)
Practice Problem Set.
Redo old problems and practice new ones.

April 4th

Read Chapter 1
Pages 7-10: Problems 1,2,3,7,9,11,15-21,26,28 (for problems with "mouse symbol" see above)
Pages 15-19: Problems 1,3,5,8,9,15
Pages 24-26: Problems 1-9,15,19,21,25
Pages 39-41: Problems 1,11,13,16,20,27
Scanned copy of problems: pdf

April 11th

Read Sections 2.1-2.9, 3.1-3.6
Pages 47-49: Problems 1,7,18
Pages 59-68: Problems 4,9
Pages 75-77: Problems 1,2,4,7
Pages 88-94: Problems 1,15
Pages 99-101: Problems 1,2,3,13
Pages 107-109: Problem 1
Pages 117-119: Problems 3,9
Pages 129-130: Problems 1,2,8
Scanned copy of problems Part (a): pdf
Scanned copy of problems Part (b): pdf
Scanned copy of Answers Chap 1-3: pdf

April 18th

Read Sections 3.7-4.2
Pages 142-143: Problems 1,10,20
Pages 151-152: Problems 1,8,9,22,23
Pages 158-159: Problems 1,5,10
Pages 164-166: Problems 1,6,7,17
Pages 172-175: Problems 1,11,16
Scanned copy of problems: pdf
Scanned copy of Answers Chap 1-3: pdf

April 25th

Read Sections 4.3-5.2
Pages 184-186: Problems 3,7,14
Pages 190-192: Problems 3,15
Pages 203-206: Problems 1,6
Pages 214-216: Problems 1,5
Pages 222-224: Problems 1,7,8
Pages 230-232: Problems 1,11,18

May 2nd

Read Sections 5.3-5.8
Pages 235-237: Problems 1,16
Pages 240-241: Problem 3
Pages 249-250: Problems 4,12,24
Pages 259-260: Problems 7,8,17
Pages 265-267: Problems 2,6,10
Pages 271-272: Problems 2,6

May 9th

Read Chapter 1 of Fisher Complex Variables
Pages 278-279: Problems 4,15
Pages 284-285: Problems 1,9
Pages 292-293: Problems 3,5,15

May 16th

Read Chapter 2 of Fisher Complex Variables (leave out 2.1.1 and 2.3.1.)
Pages below refer to Fisher.
1.1 Pages 9-10: Problems 1,5(abcd),6(abc)
1.2 Pages 20-21: Problems 1,3,23
1.4 Pages 41-43: Problems 1,2,36
1.5 Pages 53-56: Problems 3,5,6,19
1.6 Pages 73-76: Problems 1,6
Some Solutions to 1.4 and 1.5

May 23rd

Read Chapter 2.5 and 2.6 of Fisher Complex Variables.
Read 6.1 and 6.2 of Boyce and DiPrima
Pages below refer to Fisher.
2.1 Pages 84-85: Problems 1(ab),3,4,20(a)
2.2 Pages 103-106: Problems 1,2,9
2.3 Pages 116-119: Problems 1,2,5 Solution to Page 116 Problem 5
2.4 Pages 133-135: Problems 1,2,9

May 30th

Read 6.3-6.6 of Boyce and DiPrima
Pages below refer to Fisher.
2.5 Pages 150-153: Problems 1, 5, 7
2.6 Pages 167-170: Problems 1
Pages below refer to Boyce and DiPrima.
6.1 Pages 312-314: 1, 5, 7
6.2 Pages 322-325: 1, 8, 11
6.3 Pages 329-332: 1, 13

Practice for Final
(will not be collected)

6.4 Pages 337-339: 1, 5 (you may draw the forcing function by hand)
Practice Problem Set.
Redo old problems and practice new ones.

 

Remark: The code for this site goes back to Miklos Abert – who got it from someone else.