Courses:

Spring 2025: Math 234a, Partial Differential Equations (syllabus)

                       Math 240a, Second Year Seminar (syllabus)

Fall 2024: Math 122a, Numerical Methods and Big Data (syllabus)

Spring 2024: Math 232a, Numerical Methods for Scientific Computing (syllabus)

                       Math 240a, Second Year Seminar

Fall 2023: Math 122a, Numerical Methods and Big Data

Spring 2023: Math 37a, Differential Equations (syllabus) 

Fall 2022: Math 122a, Numerical Methods and Big Data

                  Math 234a, Partial Differential Equations

Spring 2022: Math 40a, Intro to Applied Math (syllabus)

                       Math 162a, Numerical Methods for Scientific Computing

Spring 2021: Math 40a, Intro to Applied Math

Fall 2020: Math 37a, Differential Equations

Spring 2020: Math 162a, Numerical Methods for Scientific Computing

Fall 2019: Math 40a, Intro to Applied Math

Spring 2019: Math 40a, Intro to Applied Math

Fall 2018: Math 37a, Differential Equations

Lecture notes:

Math 37a (Differential Equations): 

First-order equations

• Foundations

• Qualitative techniques

• Bifurcations

• Nonlinear systems

• Initial value problems

• Existence and uniqueness

• Solving linear equations

• Integrating factors

Second-order equations 

• Harmonic oscillator

• Exponential solutions

• Damped harmonic oscillator

• Forced harmonic oscillator

• Beats and resonance

Systems of differential equations

• Linear systems introduction

• 3D linear systems

• Nonlinear models

• Linear independence and the Wronskian

Laplace transforms

• Laplace transforms introduction

• Discontinuous forcing

• Second-order equations

• Introduction to control theory

Math 122a (Numerical Methods and Big Data): 

• Foundations

• Linear Algebra Review

• Gaussian Elimination

• Least Squares

• Singular Value Decomposition

• Optimization

• Sparsity and Matrix Completion

• Clustering by K-means