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Differential Equations
and Linear Algebra

by Kiryl Tsishchanka

SYLLABUS
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Weeks Dates Sections Handouts Recommended Homework
1 June 8
Section 1.1 Introduction

Section 1.2 First-order linear differential equations
1-16 S1 S2
2 June 11, 13, 15 Section 1.4 Separable equations
1-5, 6-12 (solve the given initial-value problem only) S1 S2
Section 1.9
Exact equations, and why we cannot solve very many differential equations
3-11 S1 S2
Section 1.10 The existence-uniqueness theorem; Picard iteration
1-3, 4-15 S1 S2
3
June 18, 20, 22
Section 2.1
Algebraic properties of solutions
1-7 S1 S2
Section 2.2
Linear equations with constant coefficients
Page 140: 1-8; Page 144: 1-6, 8, 9; Page 149: 1-4, 6, 7 S1 S2
Section 2.3 The nonhomogeneous equation 1-3 S
Section 2.4 The method of variation of parameters 1-8 S
4
June 25, 27, 29
Section 2.5
The method of judicious guessing
1-16 S1 S2
Section 2.8
Series solutions
Page 197: 1-8; Page 203: 1-8 S1 S2
5
July 2
Section 3.1
Algebraic properties of solutions of linear systems
1-15 S1 S2
July 6
Sections 1.1, 1.2, 1.4, 1.9, 1.10, 2.1-2.5, 2.8 MIDTERM 1
6
July 9, 11, 13 Section 3.2 Vector spaces 1-12 S
Section 3.3
Dimension of a vector space
1-11 S1 S2
Section 3.4 Applications of linear algebra to differential equations
1-9 S
7
July 16, 18, 20 Section 3.5
The theory of determinants
3-8, 10-15 S
Section 3.6 Solutions of simultaneous linear equations 1-4, 9-14, 17-20 S
Section 3.7
Linear transformations
1-13, 19-21 S
8
July 23, 25, 27
Section 3.8
The eigenvalue-eigenvector method of finding solutions
1-12 S
Section 3.9
Complex roots
1-8 S
Section 3.10
Equal roots
1-8 S
Section 3.11
Fundamental matrix solutions; eAt
1-10 S
9
July 30
Sections 3.1-3.10 MIDTERM 2

Aug 1, 3 Section 4.1
Introduction 1-8
Section 4.2 Stability of linear systems 1-10
Section 4.4 The phase-plane 1-3, 5-14
10
Aug 6, 8, 10 Section 4.7 Phase portraits of linear systems 1-9
Section 5.1
Two point boundary-value problems 1-9 S
Section 5.2 Introduction to partial differential equations
Section 5.3 The heat equation; separation of variables 1-7 S
11
Aug 13, 15, 17
Section 5.4
Fourier series 1-13
Section 5.5 Even and odd functions 1-11
Section 5.6
Return to the heat equation
1, 2
12
Aug 18 (Sat) 9:00am-12:00pm
Cumulative FINAL EXAM