Lectures Notes: Ordinary Differential Equations

Class Policies

 Midterm 1: Wednesday February 19, 2025. Time: 8:00-9:00 p.m. Location: HAMP 1252

 Miderm 2: Tuesday April 8, 2025. Time: 8:00-9:00 p.m. Location: LWSN B151

 Office Hours: Wednesday 1:30-2:30 p.m. or by appointment

 

Section 1.1: Direction Fields 

Section 1.2: Solutions of some differential equations

Section 1.3: Linear versus nonlinear ordinary differential equations

Section 2.1: Method of integrating factors to solve first order liner ODE

Section 2.2: Separable equations and homegeneous equations

Section 2.3: Modeling with first order differential equations

Section 2.3: Modeling with first order differential equations (Continuation)

Section 2.4: Existence theorems for first order linear and nonlinear equations

Section 2.5: Analysis of autonomous equations

Section 2.6: Method of exact equations

Section 2.7: Method of the tangent line (Euler's method)

Section 3.1: Second order linear homogeneous equations with constant coefficients

Section 3.2: Solutions of linear homogeneous second order equations: the Wronskian

Section 3.3: Complex roots of characteristic equation

Section 3.4: Repeated roots; method of reduction of order

Section 3.5: Non-homogeneous equations and the method of undetermined coefficients

Section 3.5: Non-homogeneous equations and the method of undetermined coefficients (continuation)

Section 3.6: Variation of Parameters

Section 3.7: Mechanical and electrical vibrations

Section 3.8: Forced Vibrations

Sections 4.1 and 4.2: Higher order, liner ODE

Section 4.3: Method of undetermined coefficients for higher order, liner, constant coefficents, non-homegeneous equations

Section 6.1: Definition of Laplace Transform

Section 6.2: Solution of initial value problems

Section 6.3: Step functions

Section 6.4: More examples of differential equation of discontinuous forcing term

Section 6.5: Impulse functions

Section 6.6: The convolution integral

Section 7.1: Introduction to systems of first order linear equations

Section 7.2: Review of matrices

Sections 7.3 and 7.5: Eigenvalues and eigenvectors. System of equations: case 1 (different and real eigenvalues

Section 7.6: Case 2: Complex eigenvalues

Section 7.8: Case 3: Repeated eigenvalues

Section 7.9: Case 3: Non-homogeneous systems

HW 1: Due on Friday January 24

1.1: 1, 11, 16, 18

1.2: 1(a), 7, 8, 12

1.3: 1, 2, 3, 4, 8, 10, 12, 14

2.1: 2, 13, 21

HW 2: Due on Friday January 31

2.1: 22, 23

2.2: 1, 4, 9, 11, 22, 27, 29

2.3: 2, 3, 11, 13

HW 3: Due on Friday February 7

2.4: 1, 3, 7, 8, 18, 23

2.5: 2, 4, 9

2.6: 1, 2, 5

HW 4: Due on Friday February 14

2.6: 7, 14, 15, 19

2.7: 12, 15

HW 5: Due on Monday February 24

3.1: 1, 15, 16, 17, 21

3.2: 4, 8, 10, 11, 13, 14, 16, 20, 22

HW 6: Due on Friday February 28

3.3: 3, 5, 14, 18, 23

3.4: 4, 15, 19, 24, 25

Hw 7: Due on Friday March 7

3.5: 1, 3, 5, 13, 16(a), 18(a), 19(a), 21(a)

3.6: 2, 8, 11, 13

HW 8: Due on Sunday March 23

3.7: 3, 4, 9, 13

3.8: 4, 5(a), 13

4.1: 3, 4, 11

4.2: 9, 13, 16, 17, 23

4.3: 1, 3, 7 , 10, 11, 12

HW 9: Due on Friday March 28

6.1: 1, 2, 4(a), 4(b)

6.2: 1, 3, 5, 7, 9

HW 10: Due on Friday April 4

6.3: 1, 3, 5, 9, 12, 14, 15

6.4: 1, 6, 7

6.5: 1, 3