Partial Differential Equations (MA3016)

Autumn 2022        Instructor: Dr Jonathan Ben-Artzi

Timeline

The table below shows what we expect to cover each class during the semester. The section numbers (such as 1.3 appearing at the very top) refer to sections in the book. Clicking on the week number to the right will take you to that week's homework assignment. All homework is to be handed-in in class on Thursdays.
Monday
Thursday

Week

October

 

3 (notes)

1.3: Where do Partial Differential Equations (PDEs) come from?

6

1.3: Where do PDEs come from?
A.1-A.4: Functions, series, differentiation, integration and differential equations

1

 

10 (notes)

1.1: What is a PDE?

13 (notes) (notes)

1.2: First-Order Linear Equations
1.4: Initial and Boundary Conditions

2

 

17 (notes)

2.1: The Wave Equation

20

2.1: The Wave Equation

3

 

24 (notes)

2.2: Causality and Energy

27 (notes) (notes)

2.4: Diffusion on the Whole Line
2.3: The Diffusion Equation

4

 

November

 

31 (notes)

2.3: The Diffusion Equation

3 (notes) (notes) (notes)

2.5: Comparison of Waves and Diffusions
1.5: Well-Posed Problems
1.6: Types of Second-Order Equations

5

 

7  (notes)

4.1: Separation of Variables, The Dirichlet Condition

10 (notes) (notes)

4.1: The Dirichlet Condition
4.2: The Neumann Condition

6

 

14

EXAMPLES

17  (notes)

5.1: Coefficients of a Fourier Series

7

 

21  (notes)

5.2: Even, Odd, Periodic and Complex Functions

24  (notes)

5.3: Orthogonality and General Fourier Series

5.4: Completeness

8

 

December

 

28  (notes)

5.4: Completeness

1

5.4: Completeness

6.1: Laplace's Equation

9

 

5  (notes)

6.1: Laplace's Equation

8 (notes) (notes)

6.2: Rectangles and Cubes

6.3: Poisson's Formula

10

 

12  (notes)

6.3: Poisson's Formula

15  (notes)

EXAMPLES

11

 

January

 

 

9

OFFICE HOURS by appointment

12

OFFICE HOURS by appointment

12

FINAL EXAM

9-11 am, 26 January 2023


Mock exam