Math 53 logoMath 53 logo

Math 53
Spring 2025

Home Textbook Schedule Homework Exams FAQ Roadmap Widgets

This schedule is tentative, and may be adjusted as necessary.

Week Date Chapter Homework Assignment
1 March 31
April 2
April 4
1: What is a differential equation?
2: First-order ODE's: autonomous, separable, and initial value problems
3: First-order ODE's: dynamic perspectives
Homework 1
(due April 9)
2 April 7
April 9
April 11
4: Stationary values, stability, and phase line
5: Complex numbers
6: Second-order linear ODE's and initial value problems
Homework 2
(due April 16)
3 April 14
April 16
April 18
7: Homogeneous linear ODE systems and eigenvectors
8: Further applications of eigenvalues to ODE's
9: Two-dimensional homogeneous linear ODE systems and eigenvalues
Homework 3
(due April 23)
4 April 21
April 23
April 25
10: Solving inhomogeneous first-order linear ODE's
11: Solving inhomogeneous second-order linear ODE's
12: Chaos, bifurcation, and sensitive dependence on initial conditions & parameters
Homework 4
(due April 30)
5 April 28
April 30
May 2
13: Non-linear ODE systems: the role of linearization
14: Monotone and conserved quantities
15: Power series methods
Homework 5
(due May 7)
6 May 5
May 7
May 9
16: Introduction to numerical methods
17: Runge-Kutta methods and stiff ODE's
18: Introduction to PDE's
Homework 6
(due May 14)
7 May 12
May 14
May 16
19: Separation of variables for the heat equation
20: Fourier series for periodic functions
21: Solving PDE's via separation of variables and Fourier series
Homework 7
(due May 21)
8 May 19
May 21
May 23
22: More applications of separation of variables and Fourier series
23: Exponential Fourier series and transform perspective
24: Introduction to the Fourier transform
Homework 8
(due May 28)
9 May 26
May 28
May 30
No Class: Memorial Day
25: Gaussians and the heat equation on a line
26: Convolution and the wave equation on a line
Homework 9
(due June 4)
10 June 2
June 4
27: Applications of the Fourier transform
Final Exam Review

Spring 2025 -- Department of Mathematics, Stanford University