MTH 164: Multidimensional Calculus

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.


This extends the calculus techniques to handle functions of more than one variable. It also concentrates increasingly on the geometric aspect of calculus, the ability to picture what the symbols stand for. This ability to picture the information contained in the equations is particularly important for applying calculus to problems in physics, engineering (e.g. hydrodynamics), computer graphics and in upper level mathematics subjects such as differential geometry (MTH 255).

Topics covered

Equations of lines and planes, quadric surfaces, space curves, partial derivatives, linear approximation, directional derivatives, extrema, lagrange multipliers, double/triple integrals including cylindrical and spherical coordinates. Line, surface, and volume integrals, divergence theorem, Stokes’ theorem.

See Comparing the Calculus Sequences.