- Syllabus
- Part of the notes and problems are taken from:
- Lecture 1 – ODEs review
- Lecture 1 (handwritten) – ODEs review
- Lecture 2 – First-order PDE
- Lecture 2 (handwritten) – First-order PDE
- Lecture 3 – First-order PDE and transport equation
- Lecture 3 (handwritten) – First-order PDE and transport equation
- Lecture 4 – Wave, heat and laplace equations
- Lecture 5 – The Wave equation (typed)
- Lecture 5 – The Wave equation
- Lecture 5 (handwritten) – The Wave equation
- Lecture 6 – The heat equation I (typed)
- Lecture 6 (handwritten) – The heat equation I (Maximum Principle)
- Lecture 7 – The heat equation II (The solution)
- Lecture 7 (handwritten) – The Heat Equation II (The solution)
- Lecture 8 – Review for Midterm 1
- Lecture 10 – Heat equation, interpretation of the solution
- Lecture 11 – Heat equation on the half-line
- Lecture 12 – Inhomogeneous heat and wave equations
- Lecture 13 – Separation of variables I (typed)
- Lecture 13 – Separation of variables I
- Lecture 14 – Separation of variables II
- Lecture 15 – Fourier series
- Lecture 16 – Sturn-Liouville theory – Orthogonality of Fourier series
- Lecture 17 – Convergence of Fourier series
- Lecture 18 – Bessel’s inequality, Parseval’s equality, Dirichlet kernel
- Lecture 19 – Pointwise, uniform convergence proofs
- Lecture 20 – Laplace on rectangles and circles, Poisson formula
- Lecture 21 – Harmonic functions. Fourier Transform
- Lecture 22 – Fourier transform and (linear) PDE
- Lecture 23 – Heisenberg’s principle and Calculus of Variations
- Lecture 24 – Calculus of Variations and FEM
- Lecture 25 – Review
- Problems from previous exams
- Midterm 1 – Practice exam
- Midterm 1 – Practice exam – Solutions
- Midterm 1
- Midterm 1 – Solutions
- Midterm 2 – Previous years practice exam
- Midterm 2 – Previous years exam
- Midterm 2 – Practice exam
- Midterm 2 – Practice exam – Solutions
- Math 425 – Final exam – Practice exam
- Math 425 – Final exam – Practice exam – Solutions
Eduardo García-Juárez 