Math 13x Series - Accelerated (Honors) Calculus
This is a three quarter series which covers the material of Math 124, Math 125, Math 126, Math 207, Math 208, and prepares students for mathematical reasoning as in Math 300. See the page on Honors Mathematics for course equivalencies and registration information if you are considering taking this series. Note that the honors series is transitioning to a new syllabus in 2027-2028 which will involve changes to content, name, and equivalencies so please pay attention.
Textbook
- Calculus - One and Several Variables (Tenth Edition) by Salas, Hille, and Etgen
- Textbooks for linear algebra and differential equations topics vary by instructor
Suggested Syllabus
Math 134
- The real number system and introduction to proof writing
- Definition of the limit and limit theorems
- Definition of the derivative and differentiability
- Applications of differentiation
- Definition of the integral and the Fundamental Theorem of Calculus
- Techniques and applications of integration
- Improper integrals
- Taylor polynomials and series
Math 135
- First order differential equations - separable and linear
- Applications of first order differential equations
- Techniques for second and higher order differential equations
- The Laplace transform
- Applications of second order differential equations
- 3D space and vectors
- Calculus of vector functions in space
Math 136
- Vector spaces,linear transformations and matrices
- Basis, dimension, subspaces
- Eigenvalues, eigenvectors and diagonalization
- Inner product spaces
- Selected applications of linear algebra
- Functions of two or more variables
- Limits, differentiability, and the gradient
- Partial derivatives and applications