Math 126 - Introduction to PDEs - Fall 2014
Instructor:    Jason Murphy   (for contact info click here)

Lecture:   MWF 3:10–4pm in   9 Evans    160 Dwinelle     Barrows 20

Office hours:   Tues. 2–3:30pm and Fri. 1:30–3pm in 857 Evans

RRR week office hours:   Monday, Tuesday, Wednesday from 1–3pm in Moffitt 102

Piazza:   For discussion boards etc. you can find a Piazza signup link here.

Course control number:    54227

Prerequisites:    Math 53, Math 54

Textbook:   Partial Differential Equations, An Introduction, Walter Strauss
Additional reference:   Partial Differential Equations, Lawrence C. Evans

Both of these books are on reserve in the Mathematics Statistics Library.

Syllabus:    The official course description includes the following topics: waves and diffusion,
initial value problems for hyperbolic and parabolic equations, boundary value problems for
elliptic equations, Green's functions, maximum principles, a priori bounds, Fourier transform.

We will cover these topics and more. A rough outline is as follows: Grading:   Grades will be determined using the following: Your grade will be computed by using the best of the following schemes: Course policies:   It is your responsibility to know the policies stated below. Contact info: The best way to reach me is by email — murphy (at) math (dot) berkeley (dot) edu.
Please check the course webpage for information before writing.

Class notes:   I will maintain some notes here, which will supplement the material presented in class.
It may be better not to print the notes, as they will be updated often and early versions may contain typos.

Class schedule:    The following table will be updated throughout the semester.

Date   Lecture   Topics   References   Remarks  
8/29 1 Introduction (derivation of some common PDE) 
9/3 2 Background (calculus, topology)   Strauss A.1, A.3  
Evans C.2, C.3
9/5 3  Background (convolution, distributions)  Strauss 12.1 
9/8 4  Laplace/Poisson (fundamental solution)  Strauss 6.1, 7.2,  
Evans 2.2.1
9/10 5  Laplace/Poisson (Green's functions)  Strauss 7.3
Evans 2.2.4		 Homework 1 Due 
9/12 6  Laplace/Poisson (Green's functions, mean value property)  Strauss 7.4, 7.1  
Evans 2.2.4, 2.2.2   		 
9/15 7   Laplace/Poisson (maximum principle, uniqueness)  Strauss 6.1, 7.1
Evans 2.2.3 (a)  		  
9/17 8   Heat Equation (fundamental solution)   Strauss 2.4
Evans 2.3.1  		 Homework 2 Due  
9/19 9  Heat Equation (mean value property)   Evans 2.3.2    
9/22 10   Heat Equation (maximum principle, uniqueness)   Strauss 2.3
Evans 2.3.3  		  
9/24 11  Wave Equation (fundamental solution in 1d)  Strauss 2.1, 2.2
Evans 2.4.1  		 Homework 3 Due 
9/26 12  Wave Equation (solution in 3d)  Strauss 9.1, 9.2
Evans 2.4.1 		  
9/29 13  Wave Equation (solution in 2d) Strauss 9.1
Evans 2.4.1, 2.4.3 		  
10/1 14  Wave Equation (energy methods)  Evans 2.4.3   
10/3   Review    Homework 4 Due  
10/6   Midterm 1     Midterm 1 
10/8 15  Separation of variables, Fourier series  Strauss 1.4, 4.1, 4.2    
10/10 16   Separation of variables, Fourier series   Strauss 5.1, 5.2, 5.3, 5.4   
10/13 17   Separation of variables, Fourier series   Strauss 5.1, 5.2, 5.3, 5.4   
10/15 18  Fourier transform   Strauss 12.3
Evans 4.3.1 		 Homework 5 Due 
10/17 19  Fourier transform   Strauss 12.3
Evans 4.3.1 		  
10/20 20  Fourier transform   Strauss 12.3, 12.4
Evans 4.3.1 		  
10/22 21   Tempered distributions   Strauss 12.1, 12.3  Homework 6 Due 
10/24 22  Duhamel's principle   Strauss 3.4    
10/27 23   Method of characteristics  Evans 3.2    
10/29 24   Method of characteristics
Scalar conservation laws 		 Evans 3.2, 3.4,
Strauss 14.1  		 Homework 7 Due  
10/31 25  Scalar conservation laws  Evans 3.4,
Strauss 14.1 		  
11/3 26  Calculus of variations  Strauss 7.1, 11.1, 14.3
Evans 8.1  		  
11/5 27  Calculus of variations  Strauss 7.1, 11.1, 14.3
Evans 8.1  		  
11/7   Review     Homework 8 Due 
11/10   Midterm 2     Midterm 2 
11/12 28   Numerical methods   Strauss 8.1, 8.2   
11/14 29   Numerical methods   Strauss 8.3, 8.5    
11/17 30  Classical mechanics      
11/19 31   Quantum mechanics   Strauss 9.4, 9.5  Homework 9 Due 
11/21 32   Quantum mechanics   Strauss 9.4, 9.5   
11/24 33   Quantum mechanics  Strauss 10.3, 10.6   
11/26 34   Quantum mechanics  Strauss 10.3, 10.6  Homework 10 Due 
12/1 35   Electromagnetism   Strauss 13.1   
12/3 36  Elementary particles   Strauss 13.5    
12/5   Conclusion and review     
12/8   RRR Office hours    Moffitt 102, 1–3pm
Homework 11 Due  
12/9   RRR Office hours    Moffitt 102, 1–3pm
12/10   RRR Office hours    Moffitt 102, 1–3pm


Homework assignments: Exam review problems:

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