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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. One of the pre-requisites for MATH2003, MATH2011, MATH2014, MATH3033, MATH2038, MATH2039, MATH2045 and MATH2040

Aims and Objectives

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

Pre-requisites: MATH1048 AND MATH1059


Costs associated with this module

Students are responsible for meeting the cost of essential textbooks, and of producing such essays, assignments, laboratory reports and dissertations as are required to fulfil the academic requirements for each programme of study.

In addition to this, students registered for this module typically also have to pay for:

Books and Stationery equipment

Recommended texts for this module may be available in limited supply in the University Library and students may wish to purchase reading texts as appropriate.

Please also ensure you read the section on additional costs in the University’s Fees, Charges and Expenses Regulations in the University Calendar available at

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