2023-2025 Catalog

MATH 126 Intro to Multivariable Calculus

Covers multiple-dimensional coordinate systems, vector geometry in three dimensions, functions of multiple variables and their multiple representations, partial derivatives, and their applicatins including optimization and motion. Includes an introduction to multivariable integral calculus. Prerequisite: C or better in MATH 125 (NS, QS)




  1. Evaluate functions of two or more variables describe by a table, equation, or graph.
  2. Use various coordinate system (e.g. rectangular, polar cylindrical) and concert among them.
  3. Create and interpret pictorial representation of functions of two variables, such a graphs, contour diagrams and cross-sections by hand and using a graphing utility.
  4. Find formulas for linear functions with given properties, create and interpret their graphical representations and use linear approximation
  5. Apply and interpret the operation of vector algebra, including addition, scalar multiplication, dot and cross product.
  6. Use and interpret the geometric definitions of partial and directional derivatives, the gradient, tangent planes ( and their equations) as they relate to graphs and surfaces; explain the connection between these derivatives and the graph, contour diagram and cross-section of a function.
  7. Interpret the carious derivatives multivariable function as rates of change.
  8. Use and interpret the geometric definition of the integral as a limit of Riemann sums.
  9. Apply the geometric understanding of multiple integrals to practical situations, such as computing average values, areas, volumes and total amount from a density.