# Math 126 Week 3 Assignment Pro

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

__Instructor:__**MWF 3:10–4pm in Barrows 20**

__Lecture:__**Tues. 2–3:30pm and Fri. 1:30–3pm in 857 Evans**

__Office hours:__**Monday, Tuesday, Wednesday from 1–3pm in Moffitt 102**

__RRR week office hours:__**For discussion boards etc. you can find a Piazza signup link here.**

__Piazza:__**54227**

__Course control number:__**Math 53, Math 54**

__Prerequisites:__

__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.

**The official course description includes the following topics: waves and diffusion,**

__Syllabus:__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:

- Introduction/background
- Laplace/heat/wave equations
- Methods
- Topics/applications

**Grades will be determined using the following:**

__Grading:__- Homework - eleven assignments, lowest score dropped
- Midterm 1 - in class, Monday October 6
- Midterm 2 - in class, Monday November 10
- Final exam - Tuesday, December 16 at 7pm

- Homework (20%), Midterm 1 (20%), Midterm 2 (20%), Final (40%)
- Homework (20%), Midterm 1 (20%), Final (60%)
- Homework (20%), Midterm 2 (20%), Final (60%)
- Homework (20%), Final (80%)

**It is your responsibility to know the policies stated below.**

__Course policies:__- You cannot pass this course without taking the final exam.
- Any conflicts due to religious creed or extra-curricular activities must be addressed

by the end of week two (September 12, 2014). - No make-up exams will be given for missed midterms.
- You are free to collaborate on homework assignments and/or seek outside sources;

however, in order to receive credit you must write up solutions in your own words and

cite any sources you use. (Read this handout for a discussion of academic honesty.) - Questions or complaints regarding the grading of an assignment or midterm must be

addressed within two weeks of the date the assignment or midterm is returned to the class. - Late homework assignments will not be accepted.

**The best way to reach me is by email — murphy (at) math (dot) berkeley (dot) edu.**

__Contact info:__Please check the course webpage for information before writing.

**I will maintain some notes here, which will supplement the material presented in class.**

__Class notes:__It may be better not to print the notes, as they will be updated often and early versions may contain typos.

**The following table will be updated throughout the semester.**

__Class schedule:__ 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:__- Homework 1 - due Wednesday, 09/10
- Homework 2 - due Wednesday, 09/17
- Homework 3 - due Wednesday, 09/24
- Homework 4 - due Friday, 10/03
- Homework 5 - due Wednesday, 10/15
- Homework 6 - due Wednesday, 10/22
- Homework 7 - due Wednesday, 10/29
- Homework 8 - due Friday, 11/07
- Homework 9 - due Wednesday, 11/19
- Homework 10 - due Wednesday, 11/26
- Homework 11 - due Monday, 12/08

__Exam review problems:__Back

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