Multivariable Calculus

Synopsis

MTH316 Multivariable Calculus will introduce students to the Calculus of functions of several variables. Students will be exposed to computational techniques in evaluating limits and partial derivatives, multiple integrals as well as evaluating line and surface integrals using Green’s theorem, Stokes’ theorem and Divergence theorem. Applications of Lagrange multipliers to optimization and applications of integration such as dynamics, electromagnetism and thermodynamics will also be emphasized.

Level: 3
Credit Units: 5
Presentation Pattern: EVERY JAN

Topics

Limits and Continuity
Partial differentiation
Differentiable functions
Chain Rule
Taylor’s formula
Lagrange multipliers
Multiple integrals
Change of order of integration
Jacobian matrix
Change of variables in multiple integrals
Line integrals
Surface integrals

Learning Outcome

Show that a given multivariable function is continuous/discontinuous or differentiable/not differentiable at specific points.
Apply Lagrange multipliers and/or derivative test to find relative extremum of multivariable functions.
Calculate the gradient or directional derivative of a multivariable function in a given direction.
Determine the existence of limits of multivariable functions and value of these limits if they exist.
Use Green’s Theorem, Divergence Theorem or Stoke’s Theorem for given line integrals and/or surface integrals.
Compute multiple integrals or integrals of vector valued functions of several variables.

Part-time Programmes / CET Courses

Singapore University of Social Sciences

Multivariable Calculus