Exams
45
Midterm: Revision
Math 5486
Welcome!
Chapter 1: Initial Value Problems
1
Intro to Math 5486
2
Theory of IVPs
3
Euler’s Method
4
Higher Order Methods
5
Runge-Kutta Methods
6
Multistep Methods
7
Zero Stability
Chapter 2: Iterative Methods in Matrix Analysis
8
Jacobi & Gauss-Seidel Methods
9
Relaxation Methods
10
Conjugate Gradient
11
Krylov Subspace Methods
Chapter 3: Boundary Value Problems
12
Finite Differences
13
Convergence of Finite Differences
14
M Matrices and Stability in ∞-norm
15
Discrete Fourier Transform and Stability in 2-norm
16
Galerkin Method and Finite Elements
17
FEM: Error Estimates
Chapter 4: Partial Differential Equations
18
Transport and Heat Equations
19
Convergence of FDs for Heat Equation
20
Wave Equation
Problem Classes
21
P1: Chapter 1
22
P1: Hints
23
P2: Chapter 2
24
P2: Hints
25
P3: Chapter 3
26
P3: Hints
Extras
27
Student Work
28
Poisson’s Equation in 2d
29
Metropolis-Hastings
30
P2 Finite Elements
Appendices
31
Taylor Remainder Theorem
32
Linear Algebra
Assignments
33
A1: Notebooks
34
A1: Solutions
35
A2: Systems of IVP
36
A2: Solutions
37
A3: Absolute Stability
38
A3: Solutions
39
A4: Sparse Arrays
40
A4: Solutions
41
A5: Fast Fourier Transform
42
A5: Solutions
43
A6: Transport Equation
44
A6: Solutions
Exams
45
Midterm: Revision
46
Midterm Exam
47
Final Exam - ideas
Admin
48
Syllabus
49
Schedule
50
Installing Julia & Jupyter
51
Topics for Presentations/Posters/Papers
Table of contents
45.1
Chapter 1: Initial Value Problems
45.2
Chapter 2: Iterative Methods
45.3
Chapter 3: Boundary Value Problems
45.4
Chapter 4: Partial Differential Equations
Other Links
Canvas
This notebook
Exams
45
Midterm: Revision
45
Midterm: Revision
List of resources
Published
May 1, 2026
Read the lecture notes,
Do the examples/exercises from the notes and problem classes
,
Review homework problems
Read the resources (referenced in the lecture notes),
….
45.1
Chapter 1: Initial Value Problems
45.2
Chapter 2: Iterative Methods
45.3
Chapter 3: Boundary Value Problems
45.4
Chapter 4: Partial Differential Equations
44
A6: Solutions
46
Midterm Exam