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Differential Equations
and Linear Algebra

by Kiryl Tsishchanka

SYLLABUS
GRADE CALCULATOR
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Tests

Weeks Dates Sections Handouts Recommended Homework
1
Jan 17, 19 Section 1.1 Introduction

Section 1.2 First-order linear differential equations
1-14
Section 1.4 Separable equations
1-5, 6-12 (solve the given initial-value problem only)
2
Jan 24 Section 1.9
Exact equations, and why we cannot solve very many differential equations
3-11
Section 1.10 The existence-uniqueness theorem; Picard iteration
1-15
Jan 26 Section 2.1
Algebraic properties of solutions
1, 2
3
Jan 31 Section 2.2
Linear equations with constant coefficients
1-8 (part 1), 1-6, 8, 9 (part 2), 1-4, 6, 7 (part 3)
Feb 2 Section 2.3
The nonhomogeneous equation
1-3
4
Feb 7 Section 2.4
The method of variation of parameters
1-8
Feb 9 Section 2.5
The method of judicious guessing
1-16
5
Feb 14 Section 2.8
Series solutions
1-8
Feb 16 Section 3.1
Algebraic properties of solutions of linear systems
1-15
6
Feb 21 Sections 1.1, 1.2, 1.4, 1.9, 1.10, 2.1-2.5, 2.8
MIDTERM 1

Feb 23
Section 3.2
Vector spaces
1-12
7
Feb 28 Section 3.3
Dimension of a vector space
1-11
Mar 2
Section 3.4 Applications of linear algebra to differential equations
1-9
8
Mar 7 Section 3.5
The theory of determinants
3-8, 10-15
Mar 9
Section 3.6 Solutions of simultaneous linear equations 1-4, 9-14, 17-20
9
Mar 13-18 Spring break
10
Mar 21 Section 3.7
Linear transformations
1-13, 19-21
Mar 23 Section 3.8
The eigenvalue-eigenvector method of finding solutions
1-12
11
Mar 28 Section 3.9
Complex roots
1-8
Mar 30
Section 3.10
Equal roots
1-8
12
Apr 4 Section 3.11
Fundamental matrix solutions; eAt
1-11
Apr 6
Sections 3.1-3.9 MIDTERM 2

13
Apr 11 Section 4.1
Introduction
1-8
Section 4.2
Stability of linear systems
1-10
Apr 13 Section 4.4
The phase-plane
1-3, 5-14
14
Apr 18 Section 4.7
Phase portraits of linear systems
1-9
Apr 20 Section 5.1
Two point boundary-value problems
1-9
15
Apr 25 Section 5.2
Introduction to partial differential equations

Apr 27 Section 5.3
The heat equation; separation of variables
1-7
16
 May 2
Section 5.4
Fourier series
1-13
May 4
Section 5.5
Even and odd functions
1-11
Section 5.6
Return to the heat equation
1,2
17
May 11 (Thu) 9:00-12:00 noon
Cumulative FINAL EXAM