- Math425 – Syllabus 2020
- Part of the notes and problems are taken from:
- Lecture 1 – ODEs review
- Lecture 2 – The method of characteristics
- Lecture 3 – The Coordinate Method. Fundamental PDEs I
- Lecture 4 – Fundamentals PDEs II
- Lecture 5 – The Wave Equation without boundaries
- Lecture 6 – The heat equation I (maximum principle)
- Lecture 7 – The heat equation II (The solution)
- Lecture 8 – The heat equation III (half-line and sources)
- Lecture 9 – Method of Separation of Variables I
- Lecture 10 – Fourier Series I (The Coefficients)
- Lecture 11 – Fourier Series II (Orthogonality)
- Lecture 12 – Fourier Series III (Statement of Convergence Theorems)
- Lecture 13 – Fourier Series IV (L2 Theory, completeness)
- Lecture 14 – Fourier Series V (Pointwise and Uniform Convergence Proof)
- Lecture 14 – Pointwise proof summary
- Lecture 15 – Nonhomgeneous Problems (Method of Eigenfunction Expansion)
- Lecture 16 – Laplace Equation
- Lecture 17 – Harmonic Functions
- Wave Equation on a Circle – Method of Frobenious
- Lecture 18 – Fourier transform and linear PDEs
- Lecture 19 – Heisenberg’s uncertainty principle
- Homework1
- Homework2
- Homework3
- Homework4
- Homework5
- Homework6
- Homework7
- Homework8
- Homework9
- Homework10
- Math 425 – Spring 2020 – Midterm1 – Practice exam
- Math 425 – Spring 2020 – Midterm1 – Practice exam – Solutions
- Math 425 – Spring 2020 – Midterm1
- Math 425 – Spring 2020 – Midterm1 – Solutions
- Homework8 – Practice Midterm 2 – Solutions
- Math 425 – Midterm 2 – Spring 2020
- Math 425 – Spring 2020 – Midterm2 – Solutions
- Math 425 – Spring 2020 – Final Exam Part II
Eduardo García-Juárez 