Multivariable Calculus

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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 … For more content click the Read More button below.

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.

Syllabus

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.

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.

Enrolment restrictions

Available to undergraduate students only. Not available to students who have completed MTH403

Pre-requisite

Incompatible