# Singapore University of Social Sciences

## Multivariable Calculus (MTH316)

### 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 January

### 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.