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Homework

05/31

Review of Calculus

Introduction to ODEs

Section 2.2,2.4,2.5 Sec1.3,#2,8,17,21

Sec2.1,#2,6,7,10,13,14

 Solution and Handout #1

06/02

Solution to Separable Equations

Linear Equations

Section 2.4,2.7,2.8 Sec 2.2 #3,10,15,22

Solution

06/07

Linear Equations

Existence and Uniqueness of ODEs

Section 4.1,4.2,4.3 Sec 2.4, #2,7,13,37

Sec 2.7, #1,2,6,9,26,30

Solution, Handout #2(about existence & uniqueness)

06/09

Second-order Equations and Systems Section 4.3,4.5 Sec 4.1 #4,7,9,12,13

Sec 4.2 #2,4,6

Solution

06/14

Linear, Homogeneous Equations with Constant Coefficients

Inhomogeneous Equations

Section 4.6 Sec 4.3 #2,10,18,21,22,24

Solution

06/16

Variation of Parameters

Review for the Exam #1

Section 7.1,7.2 Sec 4.5 #2,6,17,19,25

Sec 4.6 #3,5

Solution, Exam #1

06/21

Vectors and Matrices

Geometry of Systems of Linear Equations

Section 7.3,7.4 Sec 7.1 #34,36,42,44,51,53 and the extra problem assigned in class

Sec 7.2 #1,3,6, Solution

Solution of the Exam #1

06/23

Solving Systems of Equations

Properties of Solution Sets

Section 7.5,7.6 Sec 7.3 #14,16,17,23,24

Solution

06/28

Subspaces Section 8.1,8.2 Sec 7.4 # 4,8,10,17,20,24,29

Sec 7.5 #2,6,13,29

Solution

06/30

Determinants

Introduction to Systems

Qualitative Analysis

Section 8.4 Sec 7.6 #7,12,26

Sec 8.1 #7,12,20

Sec 8.3 #2,7

Solution, Handout #3, Exam #2

07/05

Linear Systems

Review for the Exam #2

Section 9.1,9.2 Sec 8.4 #2,13,16,29,30

Solution, Solution of Exam #2

07/07

Overview of the Technique

Planar Systems

Section 9.4,9.5 Sec 9.1 #10,12,21,23

Sec 9.2 #4,23,24,37,38,44

Solution

07/12

Higher Dimensional Systems

Exponential of a Matrix

Section 9.7,9.8 Sec 9.4 #7,21,27,40,48

Sec 9.5 #17,18,34

Solution

07/14

Higher Order Linear Equations

Inhomogeneous Systems

Section 10.1 Sec 9.7 #10,15,25,28,31,40

Solution

07/19

Linearization of Nonlinear Systems Sec 9.8 #1,7

Sec 10.1 #2,4

Solution

07/21

Review for the final exam Final Exam and its solution