## 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.