Lectures and assignments (Part 1)

You are expected to do the reading and to know how to work the problems
listed.  These problems will not be collected.  The homework to be
collected is listed on the homepage under the date it is due.


Lecture 1 (1/18): Direction fields, Examples of equations and solutions.
 Chapter 1.1, 1.2 Do at least p 15-17# 1,2,7,9.

Lecture 2 (1/20):  Linear verus non-linear equations; first order linear
equations. You are responsible for the theory.  Chapter 1.3, 2.1 Do at
least:p24# 1-6: p 39-40 1,2,11,17,27:


Lecture 3  (1/25) More on first order linear equations, Separable equations,
Applications (partI).  Chapter 2.2, 2.3 Do at least  p47-48 #1,3 p59-60 
#2,3,5.

Lecture 4  (1/27) Homework 1 due.  Lecture:  Model problems using first
order ODE. p 60-64  #7-10 12,18 a), 19 a),b) 20, 21.

Lecture 5  (2/1) Autonomous equations, equilibrium points, linear
approximations  and population dynamics (2.5). Do at least P 88, 1-6
p90-91 #20,21,22,23

Lecture 6 (2/3) Second Homework due  Review for first exam. First exam
covers 1.1-1.3 2.1-2.5

First exam  (2/8)

Lecture 7 (2/10) Third homework due.  Lecture: Second order linear
differential equations.  Section 3.1 and 3.2. Do at least p 142 1-6,
9-12, 19,22,27 p151-152, 1-4, 21,22,23,24.

Lecture 8  (2/15) Complex numbers and exponentials, Section 3.3 and
3.4  p 164 1-6, 7-12, 17-20.

Lecture 9  (2/17) N-th order equations (4.1), linear independence and the
Wronskian test (4.1, 4.2 and 3.3)p 151 1-6, p 158 1-6 p 222 11-15. p 230
11-20.

Lecture 10  (2/22) The method of undetermined coefficients (3.6) P 184
 # 1-10.  

Lecture 11 (2/24)Phase planes (page 357) Mechanical and Electrical
Vibrations (3.8).p 203, 1-10, p 360 1-6.  Fourth homework due.

Lecture 12  (3/1)Repeated roots and resonance  (3.5 and 3.9)p 172 1-14,
p 214 5-8, 15,17.

Lecture 13  (3/3)  Systems of ordinary differential equations (7.1)
(5th homework due)  p 360 1-6.

Lecture 14  (3/8)  Matrices and linear algebra (7.2)p 372-373 1-15,21,22.

Lecture 15  (3/10) Eigenvalues (7.3) p 383 1-3,6-10, 15-21.

Lecture 16  (3/22) Linear equations with constant coefficients (7.5)p 398
1-6, 9,10, 15-18.

Lecture 17   (3/24) Complex eigenvalues (7.6) p 410 1-8 9, 10.

Lecture 18  (3/29)Review for second exam

Second exam will be on March  31:  This will cover Chapters 3.1-3.4, 3.6,
4.1 - 4.3, 7.1-7.6. For the matrix section of the course you need only
know how to do the computations for 2x2 matrices and for very simple 3x3
and 4x4 matrices.

Lecture 19 (4/5)  Phase plane, linear systems and examples of autonomous
systems.  Chapters 9.1, 9.2, 9.4 Problems 493 13-17 p 502 5-14.

Lecture 20 (4/7)Chapters 9.3, 9.4  Examples of 2x2 non-linear systems: competiton
and preditor-prey equations.  Page 525 1-6 (parts a and b...after the next
lecture you should be able to do c). Page 534 1-5 (parts a and b...after
the next lecture, you should do part c).

Lecture 21 (4/12)  Linearization again. Chapter 9.3  p 511 1-16.

Lecture 22 (4/14)  Power series solutions 5.1, 5.2  p 249 9-16, p 259 1-10.

Lecture 23 (4/16)  Introduction to Fourier Series  10.2 p 585 1-9, 13-18.

Lecture 24  (4/19)  More on Fourier Series  10.3  pp 591-2 1-6, 13, 14, 17.

Lecture 25  (4/21)  Even and Odd functions  10.4  p600 1-6, 15-26. 

Lecture 26  (4/26)  Separation of Variables  10.5  p610-611  1-12  p620 1-8.

Lecture 27  (4/28)  Guitar Strings  10.7 p 633-634 9,13

Make-up Exam  (5/3) This will cover material from Chapters 5.1, 5.2, 9.1
 9.2, 9.3 9.4 9.4 10.2, 10.4, 10.5 10.6. Include in your review the
problems in Prolem Set 11.

Lecture 28 (5/5) Review of Material for the Final