Lecture note

Hand-written lecture notes will be posted here and available during the quarter.

Contents:

1. ODE Theory
   • Introduction: Week 1
   • Initial value problems (IVPs): Week 1 ~ Week 4
   • Boundary value problems (BVPs): Week 4
2. PDE Theory
   • Introduction: Week 5
   • Parabolic PDEs: Week 5 ~ Week 7
   • Hyperbolic PDEs: Week 7 ~ Week 8
   • Elliptic PDEs: Week 8 ~ Week 9
   • Spectral Methods: Week 10

• Review sheet

Week 1

• Lecture note 1
• Lecture note 2
• Lecture note 3

• Example: the Euler’s Methods
  • Example 1:
  • Example 2:

Week 2

• Lecture note 4
• Lecture note 5
• Lecture note 6

Week 3

• Lecture note 7
• Lecture note 8
• Lecture note 9

Week 4

• Lecture note 10 with typo corrections
• Lecture note 11
• Lecture note 11 – hand written note

Week 5

• Two-point BVPs for ODEs
  • The shooting method
  • The finite difference method

• Lecture note 12
• Lecture note 12 – hand written note with typo corrections
• Lecture note 13

Week 6

• Lecture note 14
• Lecture note 15
• Lecture note 16

Week 7

• Lecture note 17
• Lecture note 18
• Lecture note 19
• Lecture note 20

Week 8

• Lecture note 21
• Lecture note 22
• Lecture note 23

Week 9

• Lecture note on Direct Solvers
• Lecture note 24
• Lecture note 25
• Lecture note 26

Week 10

• Lecture note 27
  • This lecture note is based on the book, Spectral Methods for Time-Dependent Problems, by Hesthaven, Gottlieb, and Gottlieb.
  • Also see the reading materials under /References/SpectralMethods in your git repo.