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# MTH218 Multivariable Calculus (8)

### Abstract

 This subject extends the study of calculus to functions of several variables. Partial derivatives are reviewed and double and triple integrals introduced. The subject also covers vector calculus, which includes differential operators (gradient, divergence and curl) and line and surface integrals. Vector calculus culminates in higher dimensional versions of the Fundamental Theorem of Calculus: Green's Theorem, Stokes' Theorem and the Divergence Theorem.

### + Subject Availability Modes and Location

Session 1
DistanceOrange Campus
 Continuing students should consult the SAL for current offering details: MTH218 Where differences exist between the Handbook and the SAL, the SAL should be taken as containing the correct subject offering details.

### Subject information

One sessionHD/FLSchool of Computing and Mathematics

Prerequisite(s)
MTH102

### Learning Outcomes

 Upon successful completion of this subject, students should: be able to classify and graph conics and simple quadric surfaces; be able to calculate and graph level curves and surfaces; be able to calculate partial derivatives, directional derivatives, the gradient, tangent planes and differentials; be able to calculate double and triple integrals; be able to calculate line integrals and recognise a conservative field; be able to calculate divergence and curl of a vector field; be able to calculate surface integrals; be able to understand and use Green's Theorem, Stokes' Theorem and the Divergence Theorem.

### Syllabus

 The subject will cover the following topics: Conics and quadric surfaces. Functions of several variables. Partial derivatives, directional derivatives, gradient, linear approximation. Double and triple integrals. Vector fields. Line integrals, fundamental theorem. Divergence and Curl. Green's Theorem. Surface integral and flux of a vector field. Stokes' Theorem. Divergence Theorem.

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The information contained in the 2016 CSU Handbook was accurate at the date of publication: 06 September 2016. The University reserves the right to vary the information at any time without notice.