The University of Southampton
Courses

# MATH1060 Multivariable Calculus

## Module Overview

This module introduces the main ideas and techniques of differential and integral calculus of functions of two or more variables.

### Aims and Objectives

#### Module Aims

This module aims to introduce the student to the main ideas and techniques of differential and integral calculus.

#### Learning Outcomes

##### Learning Outcomes

Having successfully completed this module you will be able to:

• evaluate and interpret derivatives of functions of two or more variables
• classify critical points of two variable functions and interpret them geometrically
• use line integrals to calculate areas of certain regions
• set up and evaluate double and triple integrals over simple regions
• adapt integration problems to different coordinate systems when appropriate and evaluate them

### Syllabus

Differentiable calculus of functions of several variables: • Sketching functions of two variables. • Limits of multivariable functions. • Partial derivatives, Gradient, Directional Derivative. • Tangent plane, Maximum and minimum points. • Change of variables and the chain rule, Jacobian. • Second and higher partial derivatives, chain rule for second derivatives. • Critical points and their classification. • Lagrange Multipliers. • Multivariable Taylor Series Integral calculus of functions of two or three variables: • Double and repeated integrals, including change of order in a repeated integral. • General change of variables in a double integral. • Polar coordinates, cylindrical polar coordinates, spherical polar coordinates. • Triple integrals in various coordinates. Line integrals: • Evaluation of simple line integrals • The Fundamental Theorem of line integrals • Green’s Theorem

### Learning and Teaching

#### Teaching and learning methods

Lectures, problem classes, workshops, private study

TypeHours
Independent Study96
Teaching54
Total study time150

#### Resources & Reading list

ADAMS R.A.. Calculus - A Complete course.

WREDE R. & SPIEGEL, M.R. Advanced Calculus.

### Assessment

#### Summative

MethodPercentage contribution
Class Test 10%
Homework Exercises 20%
Written exam  (2 hours) 70%

#### Referral

MethodPercentage contribution
Written exam 100%

#### Repeat Information

Repeat type: Internal & External