MTH 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



MTH 162 or MTH 143 or MTH 172

This course is a prerequisite or co-requisite for

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

Usually MTH 164 (multidimensional calculus) is taken before MTH 165 (linear algebra with differential equations) since its subject matter is more closely related to MTH 162. However MTH 164 and MTH 165 can be taken in either order; MTH 164 is NOT a prerequisite for MTH 165.


MTH 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.

MTH 165 is a prerequisite for many courses including: