Lectures Notes: Ordinary Differential Equations
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 1.2: 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 6.1: Definition of Laplace Transform
Section 6.2: Solution of initial value problems
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
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
HW 11: Due on Friday April 18
6.5: 1, 3
6.6: 5, 9, 11
7.1: 5, 6
7.3: 15, 17, 26
7.5: 10, 11
HW 12: Due on Friday April 25
7.6: 1, 3, 21
7.8: 1, 3, 14
7.9: 1, 2, 3