Ordinary and Partial Differential Equations
Duke University

Instructor: Yuhao Hu

Email: yh89 at math dot duke dot edu

Office: 110 Phytotron

Office Hours: WF 4:00-5:00pm

Office Hour Location: 201 Physics

Lectures: MWF 08:45-9:35am at Bio Sciences 113

Textbook: W. E. Boyce and R. C. DiPrima, Elementary Differential Equations and Boundary Value Problems (10th edition)

Syllabus: Here is the course syllabus.

Overview

First and second order ordinary differential equations with applications, Laplace transforms, series solutions and qualitative behavior, Fourier series, partial differential equations, boundary value problems, Sturm-Liouville theory.

Homework

Unless announced otherwise, homework is due at the beginning of classes on Mondays.

HW 1 HW 2 HW 3 HW 4 HW 5 HW 6 HW 7 HW 8 HW 9 HW 10

HW 11 HW 12

Exams

The final exam will be on Thursday, Dec. 15, from 9:00am to noon. The midterm exams are during class on Wednesday, Oct. 5 and Monday, Nov. 21.

Midterm I Solutions Midterm II Solutions

Notes

Lecture 1       Lecture 2       Lecture 3       Lecture 4       Lecture 5       Lecture 6       Lecture 7       Lecture 8

Lecture 9       Lecture 10     Lecture 11     Lecture 12     Lecture 13     Lecture 14     Lecture 15     Lecture 16

Lecture 17     Lecture 18     Lecture 19     Lecture 20     Lecture 21     Lecture 22     Lecture 23     Lecture 24

Lecture 25     Lecture 26     Lecture 27     Lecture 28     Lecture 29     Lecture 30     Lecture 31     Lecture 32

Lecture 33     Review Guide

Schedule

Lecture	Date	Topics	Note
1	Aug 29	Introduction, Linear Equations, Integrating Factors
2	Aug 31	Separable Equations
3	Sept 2	Modeling with First Order Equations Linear & Nonlinear Equations: Difference
4	Sept 5	Autonomous Equations, Population Dynamics	HW1 Due
5	Sept 7	Exact Equations, Integrating Factors
6	Sept 9	Euler's Method	Drop/Add Ends
7	Sept 12	Constant Coeff. Homogeneous Equations Solving Linear Homogeneous Equations, Wronskian Complex Roots; Characteristic Equation	HW2 Due
8	Sept 14	Reduction of Order; Undetermined Coefficients
9	Sept 16	Variation of Parameters
10	Sept 19	Power Series I	HW3 Due
11	Sept 21	Power Series II
12	Sept 23	Series Solutions Near an Ordinary Point I
13	Sept 26	Series Solutions Near an Ordinary Point II	HW4 Due
14	Sept 28	Euler Equations; Regular Singular Points
15	Sept 30	Euler Equations (cont.) Laplace Transform
16	Oct 3	Laplace Transform (cont.) Solving Initial Value Problems	HW5 Due
Midterm I	Oct 5
Fall break	Oct 7-11
17	Oct 12	Step Functions
18	Oct 14	DE with Discontinuous Forcing Terms
19	Oct 17	Impulse Functions
20	Oct 19	The Convolution Integral	HW6 Due
21	Oct 21	Two-Point BVP
22	Oct 24	Fourier Series
23	Oct 26	Fourier Convergence Theorem Even and Odd Functions	HW7 Due
24	Oct 28	Separation of Variables
25	Oct 31	Heat Conduction in a Rod
26	Nov 2	More Heat Conduction Problems	HW8 Due
27	Nov 4	Wave Equations: Vibrating String
28	Nov 7	Laplace's Equation
29	Nov 9	Two-Point BVP: Occurence	HW9 Due
30	Nov 11	Sturm-Liouville BVP	Last Day to Withdraw
31	Nov 14	Sturm-Liouville BVP (cont.)
32	Nov 16	TBD
33	Nov 18	TBD	HW10 Due
Midterm II	Nov 21
Break	Nov 22-27		Thanksgiving Recess
34	Nov 28	Non-homogeneous BVP
35	Nov 30	Non-homogeneous BVP (cont.)
36	Dec 2	TBD
37	Dec 5	TBD	HW11 Due
38	Dec 7	TBD
39	Dec 9	TBD
Final Exam	Dec 15

Ordinary and Partial Differential Equations Duke University