Ordinary and Partial Differential Equations
Duke University

Instructor: Yuhao Hu

Email: yh89 at math dot duke dot edu

Office: Physics 274G

Office Hours: MTh 12:00-2:00pm

Lectures: MTuWThF 09:30-10:45am at Physics 259

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 Tuesdays and Fridays. Sections related to each homework will be updated in the Schedule table blow.

Exams

The final exam will be on Thursday, June 25, from 9:00am to noon. The midterm exams are during class on Friday, May 29 and Friday, June 12.

Exam I Exam I Solutions

Exam II Exam II Solutions

Final Exam Final Exam Solutions

Practice Exams

Practice Exam I Practice Exam I Solutions

Practice Exam II Practice Exam 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

Final Check List

Schedule

Lecture	Date	Topics	Note
1	May 13	Introduction, Linear Equations, Integrating Factors
2	May 14	Separable Equations
3	May 15	Modeling with First Order Equations Linear & Nonlinear Equations: Difference Autonomous Equations, Population Dynamics	HW 1 [Sec 2.1, 2.2] due. Drop/Add ends.
4	May 18	Exact Equations, Integrating Factors Euler's Method
5	May 19	Constant Coefficient Homogeneous Equations Complex Roots, Characteristic Equations	HW 2 [Sec 2.3, 2.4, 2.5, 2.6] due.
6	May 20	Repeated Roots, Reduction of Order Non-homogeneous Equations, Undetermined Coeff.
7	May 21	Variation of Parameters
8	May 22	Power Series	HW 3 [Sec 2.7, 3.1, 3.3, 3.4, 3.5] due.
Break	May 25		Memorial Day holiday, no class.
9	May 26	Series Solutions Near an Ordinary Point I
10	May 27	Series Solutions Near an Ordinary Point II	HW 4 [Sec 3.6, 5.1] due.
11	May 28	Euler Equations, Regular Singular Points
Midterm I	May 29		In-class Exam [Lectures 1-7]
12	June 1	Laplace Transform
13	June 2	Solution of Initial Value Problems	HW 5 [Sec 5.2, 5.3, 5.4] due.
14	June 3	Step Functions DE with Discontinuous Forcing Functions
15	June 4	Impulse Functions The Convolution Integral
16	June 5	Two-Point Boundary Value Problems	HW 6 [Sec 6.1, 6.2, 6.3, 6.4] due.
17	June 8	Fourier Series
18	June 9	Fourier Convergence Theorem Even and Odd functions	HW 7 [Sec 6.5, 6.6, 10.1, 10.2] due.
19	June 10	Separation of Variables	Last day to withdraw.
20	June 11	Heat Conduction Problems
Midterm II	June 12		In-class Exam [Lectures 8-17]
21	June 15	Wave Equation, Vibrating Strings
22	June 16	Laplace's Equation	HW 8 [Sec 10.3, 10.4, 10.5, 10.6] due.
23	June 17	Two-Point BVP: Occurence
24	June 18	Sturm-Liouville BVP
25	June 19	Non-homogeneous BVP	HW 9 [Sec 10.7, 10.8, 11.1] due.
26	June 22	Review	HW 10 [Sec 11.2, 11.3] due(Optional).
Final	June 25		9:00am-noon

Ordinary and Partial Differential Equations Duke University