Partial Differential Equations (MA3016)

Autumn 2023        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.
Thursday
Friday

Week

October

 

5 (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

 

12 (notes)

1.1: What is a PDE?

13 (notes) (notes)

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

2

 

19 (notes)

2.1: The Wave Equation

20

2.1: The Wave Equation

3

 

26 (notes)

2.2: Causality and Energy

27 (notes) (notes)

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

4

 

November

 

2 (notes) (notes)

2.3: The Diffusion Equation

3 (notes) (notes)

2.5: Comparison of Waves and Diffusions
1.6: Types of Second-Order Equations

5

 

9  (notes) (notes)

1.5: Well-Posed Problems
4.1: Separation of Variables, The Dirichlet Condition

10 (notes) (notes)

4.1: The Dirichlet Condition
4.2: The Neumann Condition

6

 

16

4.2: The Neumann Condition

17  (notes)

5.1: Coefficients of a Fourier Series

7

 

23  (notes)

5.2: Even, Odd, Periodic and Complex Functions

24  (notes)

5.3: Orthogonality and General Fourier Series

8

 

December

 

30  (notes)

5.4: Completeness

1

5.4: Completeness

6.1: Laplace's Equation

9

 

7  (notes)

6.1: Laplace's Equation

8 (notes) (notes)

6.2: Rectangles and Cubes

6.3: Poisson's Formula

10

 

14  (notes)

6.3: Poisson's Formula

15  (notes)

EXAMPLES

11

 

January

 

 

11

OFFICE HOURS by appointment

12

OFFICE HOURS by appointment

12

MOCK            EXAM 22/23    EXAM 22/23 SOLUTIONS


FINAL EXAM

23 January 2024