CAAM 336

Course info

Instructor: Charles Puelz
Teaching Assistant: Mae Markowski
Location and Time: online (zoom), Monday, Wednesday, Friday, 130-225pm
Office hours: Tuesday, 4-5pm (Mae) and Wednesday, 12-130pm and 230-3pm (Charles)
Recitation Session: online (zoom), Thursday, 4-5pm
Syllabus: syllabus.pdf

Schedule and notes

• 1/25: intro to 336 and classification of differential equations. ch 1. lecture-1-336.pdf
• 1/27: classification of differential equations continued. ch 1. lecture-2-336.pdf
• 1/29: derivation of the heat equation. section 2.1. lecture-3-336.pdf
• 2/1: finish derivation of heat equation. section 2.1. lecture-4-336.pdf
• 2/3: boundary conditions and vector spaces. section 3.1. lecture-5-336.pdf
• 2/5: subspaces and spans. section 3.1. lecture-6-336.pdf
• 2/8: linear independence and dimension. lecture-7-336.pdf
• 2/10: linear operators. lecture-8-336.pdf
• 2/12: range of linear operators. section 3.2.1. lecture-9-336.pdf
• 2/22: null space of linear operators. section 3.2.2. lecture-10-336.pdf
• 2/24: normed and inner product spaces. section 3.4.1. lecture-11-336.pdf
• 2/26: projections. section 3.4.1-3.4.2. lecture-12-336.pdf
• 3/3: projection theorem. section 3.4.2. lecture-13-336.pdf
• 3/5: the Gram-Schmit procedure. lecture-14-336.pdf
• 3/8: introduction to symmetric linear operators. section 5.2.1. lecture-15-336.pdf
• 3/10: eigenpairs for the heat equation. section 5.2.1. lecture-16-336.pdf
• 3/12: the spectral method. section 5.2.2., 5.3.1-5.3.3. lecture-17-336.pdf
• 3/15: spectral method examples. section 5.3.1-5.3.2. lecture-18-336.pdf
• 3/17: spectral method examples. sections 5.3.4 and 6.2.2. lecture-19-336.pdf
• 3/19: separation of variables. section 6.1.6. lecture-20-336.pdf
• 3/22: weak formulations. section 5.4. lecture-21-336.pdf
• 3/24: weak and strong solutions. section 5.4. lecture-22-336.pdf
• 3/29: Galerkin approximation. section 5.5. lecture-23-336.pdf
• 3/31: properties of the Galerkin approximation. section 5.5. lecture-24-336.pdf
• 4/2: Galerkin method examples. lecture-25-336.pdf
• 4/5: intro to the hat function basis. section 5.6. lecture-26-336.pdf
• 4/7: more on the hat function basis. section 5.6. lecture-27-336.pdf
• 4/9: finite element method example. section 5.6. lecture-28-336.pdf
• 4/12: more finite element method examples. lecture-29-336.pdf
• 4/14: FEM with inhomogenous Dirichlet boundary conditions. lecture-30-336.pdf
• 4/16: FEM with homogenous Neumann boundary conditions. lecture-31-336.pdf
• 4/19: FEM for heat equation. section 6.4. lecture-32-336.pdf
• 4/21: FEM for heat equation. section 6.4. lecture-33-336.pdf

Homeworks

• homework 1 and solutions for homework 1. due Feb 5th.
• homework 2 and solutions for homework 2. due Feb 12th.
• homework 3 and solutions for homework 3. due Feb 26th.
• homework 4 and solutions for homework 4. due Mar 3rd.
• homework 5 and solutions for homework 5. due Mar 8th.
• homework 6 and solutions for homework 6. due Mar 19th.
• homework 7 and solutions for homework 7. due Mar 29th.
• homework 8. due Apr 12th.
• homework 9. due Apr 19th.