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Differential Equations
and Linear Algebra

by Kiryl Tsishchanka

SYLLABUS
(1:00-2:00pm)

SYLLABUS
(3:00-4:00pm)
GRADE CALCULATOR
WolframAlpha
Tests

Weeks Dates Sections Handouts Recommended Homework
1
Aug 30, Sep 1
Section 1.1 Introduction

Section 1.2 First-order linear differential equations
1-16
Section 1.4 Separable equations
1-5, 6-12 (solve the given initial-value problem only)
2
Sep 6, 8 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
3
Sep 11, 13, 15 Section 2.1
Algebraic properties of solutions
1-7
Section 2.2
Linear equations with constant coefficients
Page 140: 1-8; Page 144: 1-6, 8, 9; Page 149: 1-4, 6, 7
Section 2.3 The nonhomogeneous equation 1-3
4
Sep 18, 20, 22 Section 2.4
The method of variation of parameters
1-8
Section 2.5
The method of judicious guessing
1-16
5
Sep 25, 27, 29
Section 2.8
Series solutions
Page 197: 1-8; Page 203: 1-8
Section 3.1
Algebraic properties of solutions of linear systems
1-15
6
Oct 2
Sections 1.1, 1.2, 1.4, 1.9, 1.10, 2.1-2.5, 2.8
MIDTERM 1

Oct 4, 6
Section 3.2
Vector spaces
1-12
7
Oct 9, 11, 13
Section 3.3
Dimension of a vector space
1-11
Section 3.4 Applications of linear algebra to differential equations
1-9
8
Oct 16, 18, 20
Section 3.5
The theory of determinants
3-8, 10-15
Section 3.6 Solutions of simultaneous linear equations 1-4, 9-14, 17-20
9
Oct 23, 25, 27
Section 3.7
Linear transformations
1-13, 19-21
Section 3.8
The eigenvalue-eigenvector method of finding solutions
1-12
10
Oct 30, Nov 1, 3
Section 3.9
Complex roots
1-8
Section 3.10
Equal roots
1-8
11
Nov 6, 8
Section 3.11
Fundamental matrix solutions; eAt
1-11
Nov 10
Sections 3.1-3.10 MIDTERM 2

12
Nov 13, 15, 17 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
13
Nov 20 Section 4.7 Phase portraits of linear systems 1-9
Nov 22-25 Thanksgiving holidays
14
Nov 27, 29, Dec 1 Section 5.1
Two point boundary-value problems 1-9
Section 5.2 Introduction to partial differential equations
Section 5.3
The heat equation; separation of variables 1-7
15
Dec 4, 6, 8 Section 5.4
Fourier series 1-13
Section 5.5 Even and odd functions 1-11
16
Dec 11
Section 5.6
Return to the heat equation
1, 2
17
Dec 14 (Thu) 7:00-10:00pm
 
MWF 3:00-4:00pm group (54165)
Cumulative FINAL EXAM
Dec 18 (Mon) 7:00-10:00pm
 
MWF 1:00-2:00pm group (54155)