MTH165: Linear Algebra with Differential Equations

* Course home page for this semester
Cross Listed:
Fall and Spring
MTH162 or MTH143 or MTH172
This course is a prerequisite or co-requisite for:
An introduction to the basic concepts of linear algebra: matrices, determinants, vector spaces and linear transformations, as well as to ordinary differential equations with an emphasis on linear differential equations, second order equations with constant coefficients and systems of differential equations. Applications to physical, engineering, and life sciences. This course differs from MTH163 in that it has more material on linear algebra (including a discussion of eigenvalues), and the only differential equations covered are linear ones with constant coefficients, along with systems thereof. For many students, taking MTH165 will eliminate the need to take MTH235 (linear algebra).
Topics covered:
Usually MTH164 (multidimensional calculus) is taken before MTH163 or MTH165 since its subject matter is more closely related to MTH162. However some engineering majors require MTH163 or MTH165 to be completed by the end of the fall semester of the sophomore year. MTH165 spends about two thirds of the semester covering basic linear alegbra up through eigenvalues and eigenvectors and one third of the semester on differential equations covering elementary methods, linear equations, systems with constant coefficients and phase plane analysis and stability.
Related courses:
  • MTH263 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.
  • MTH281 deals with partial differential equations, which are important in mathematics and in physical applications.
  • ME163 and MTH163 overlap subtantially with MTH165.
  • ME 201 discusses ordinary and partial differential equations. It covers material similar to that in MTH281.
  • ME401 discusses ordinary differential equations.
  • EE212 includes some work with Laplace transform methods of solving ODEs.
  • EE213 includes some work with Laplace transform methods of solving ODEs.
  • EE410 includes material on dynamical systems (as does MTH263).