146C
146C
Office Hours: Monday 1-3pm at Skye 281 and 5-6pm over zoom (link on canvas) or by appt
Email: nchie005@ucr.edu
Please feel free to contact me over email with any questions or concerns. If any typos or errors are found in notes please let me know, so I can add a comment of the mistake.
Discussion Section:
Week 1 (Apr 4) - Notes + worksheet and worksheet solutions
Summary:
Partial derivatives
Gradient
Divergence
Directional derivatives
Practice with integration
Week 2 (Apr 11) - Notes
Summary:
Gronwall Inequality differential and integral version
Stability of solutions
Transport equation
Some key remarks not in notes:
Adding zero and triangle inequality
Moving absolute values from outside integrals inside integrals and Lipschitz condition
Fundamental theorem of calculus
Office hours (Apr 14): Notes
Error in notes for this week. Below is the correct outline of solving a transport equation of the form:
a u_t + bu_x = 0 with initial condition u(0,x) = u_0(x)
To solve, divide the PDE by a to get u_t + (b/a)u_x = 0 with initial condition u(0,x) = u_x(0). Solving this equation provides a solution to the original PDE.
Week 3 (Apr 18) - Notes + Worksheet and worksheet solutions
Summary:
Fixing error in notes last week
Review of how to solve ODE with integrating factor method.
Review of how to solve ODE using separation of variables.
Week 4 (Apr 25) - Notes
Summary:
Steps to solve general transport equation.
Walk through an example solution of the general transport equation.
Week 5 (May 2) - Midterm Review
Summary:
How to solve constant coefficient transport equation.
How to solve general transport equation.
How to solve homogenous heat equation with dirichlet boundary conditions.
How to solve non-homogenous heat equation with dirichlet boundary conditions.
How to solve homogenous heat equation without dirichlet boundary conditions.
Week 6 (May 9) - This day we will be working on the take home exam.
Week 7 (May 16) - Substitute today, so worked on homework problems.
Week 8 (May 23) - Notes
Summary:
How to solve heat equation with Neumann boundary conditions.
How to solve homogenous heat equation without Neumann boundary conditions
How to solve wave equation
Remark that the methods are all analogous to the Dirichlet case, which is why the notes are quite bare.
Week 9 (May 30) - Worked on HW and provided extra hints
Week 10 (June 6) - Final review
Small typo, but the integals for f_n should be from 0 to L rather than 0 to t.
Summary:
How to solve transport equations.
How to solve heat equations with Dirichlet data.
How to solve heat equations with Neumann data.
How to solve wave equation with Neumann data.
Example of principle of superposition.