The University of Southampton

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


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

Independent Study96
Total study time150

Resources & Reading list

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

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



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


MethodPercentage contribution
Written exam 100%

Repeat Information

Repeat type: Internal & External

Linked modules


To study this module, you will need to have studied the following module(s):

MATH1048Linear Algebra I
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