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 |