MATH 165: Linear Algebra with Differential Equations

Note: If this course is being taught this semester, more information can be found at the course home page.

Cross Listed



MATH 162 or MATH 143 or MATH 172

This course is required for many majors in engineering and the sciences, including mathematics. See Comparing the Calculus Sequences.

Usually Math 164 (multidimensional calculus) is taken before Math 165 since its subject matter is more closely related to Math 162. However, Math 164 and 165 can be take in either order; Math 164 is NOT a prerequisite for Math 165.


Math 165 spends about two thirds of the semester covering basic linear alegbra and one third of the semester on differential equations. Applications to physical, engineering, and life sciences.

Topics covered

Matrix algebra and inverses, Gaussian elimiation and solving systems of linear equations, determinants, vector spaces, linear dependence, bases, dimension, eigenvalue problems. First order differential equations including separable equations and linear equations. Linear nth order differential equations with constant coefficients, undetermined coefficients, first order linear homogenous systems of differential equations. Applications of differential equations to physical, engineering, and life sciences.

See Comparing the Calculus Sequences.

Math 165 is a prerequisite for many courses including:

  • MATH 208 is an introductory course in Operations Research and linear optimization methods.

  • MATH 235 is a more advanced course in linear algebra with an emphasis on abstract vector spaces and proofs.

  • MATH 263 is an upper level course in ordinary differential equations which deals more with the qualitative behavior of the solutions to differential equations. This is important in many applications, where the exact solution of the differential equation cannot be calculated.

  • MATH 281 deals with partial differential equations, which are important in mathematics and in physical applications.