MTH218 Multivariable Calculus (8)

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.

Availability

Session 1 (30)
Online
Orange 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

HD/FL

One session

School

School of Computing and Mathematics

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

This subject will cover the following topics:
• 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.