Course overview
The mathematics required to describe most "real life" systems involves functions of more than one variable, so the differential and integral calculus developed in a first course in Calculus must be extended to functions of more variables. In this course, the key results of one-variable calculus are extended to higher dimensions: differentiation, integration, and the link between them provided by the Fundamental Theorem of Calculus are all generalised. The machinery developed can be applied to another generalisation of one-variable Calculus, namely to complex calculus, and the course also provides an introduction to this subject. The material covered in this course forms the basis for mathematical analysis and application across an extremely broad range of areas, essential for anyone studying the hard sciences, engineering, or mathematical economics/finance.
Topics covered are: introduction to multivariable calculus; differentiation of scalar- and vector-valued functions; higher-order derivatives, extrema, Lagrange multipliers and the implicit function theorem; integration over regions, volumes, paths and surfaces; Green's, Stokes' and Gauss's theorems; differential forms; curvilinear coordinates; an introduction to complex numbers and functions; complex differentiation; complex integration and Cauchy's theorems; and conformal mappings.
Course learning outcomes
- Demonstrate understanding of the basic concepts of calculus involving more than one real variable
- Demonstrate understanding of the basic concepts of calculus for one complex variable
- Be able to state and apply the major results in the course
- Apply the theory in the course to solve a variety of problems at an appropriate level of difficulty
- Demonstrate skills in communicating mathematics orally and in writing
Fee calculator
To display course fees, please select your status and program below:
We’re updating this Fee Calculator. It currently shows fees for programs only. Please check the relevant program for full fee details.
Study Abroad student tuition fees are available here.
Only some Postgraduate Coursework programs are available as Commonwealth Supported. Please check your program for specific fee information.
The Student Contribution amount displayed below is for students commencing a new program from 2021 onwards. If you are continuing in a program you commenced prior to 1 January 2021, or are commencing an Honours degree relating to an undergraduate degree you commenced prior to 1 January 2021, you may be charged a different Student Contribution amount from the amount displayed below. Please check the Student Contribution bands for continuing students here. If you are an international student, or a domestic student studying in a full fee paying place, and are continuing study that you commenced in 2025 or earlier, your fees will be available here before enrolments open for 2026.