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This course deals with techniques in multivariable calculus and vector calculus which have applications in many areas of science, commerce and engineering. It is also preparation for many courses in advanced mathematics.
This course covers techniques in multivariable calculus and vector calculus and interesting applications in many areas of science, commerce and engineering. It is strongly recommended to anyone who is considering majoring in mathematics or another subject that involves a high level of numeracy. Topics covered: geometry of multivariable functions, partial derivatives, linearisation, multivariate chain rule, implicit function theorem; multivariate optimisation, sufficient conditions for optimality, Lagrange multipliers for optimisation problems; iterated integrals, polar coordinates; Jacobian determinants; parametric curves, tangent vectors, line integrals, work integrals; div, grad, curl; surface integrals; volume integrals; Green's Theorem; Stokes Theorem; Divergence Theorem; physical applications.
At the end of the course, students will:Be proficient in the basic techniques of multivariable calculus: linearization, use of chain rule, multivariable integration (in several coordinate systems), evaluation of line integrals, work integrals, surface and volume integrals.Apply their understanding of multivariate geometry to express and solve vector calculus problems using suitable notation and theorems.Be able to use calculus methods to solve standard applied problems.Have developed problem solving skills both as part of a team and as an individual.Have developed written and oral communication skills, emphasizing the ability to explain what the mathematics means.
MATH103 or MATH199 or EMTH119
MATH261, MATH264, EMTH202, EMTH204, EMTH210
Students must attend one activity from each section.
General information for students
Domestic fee $788.00
International fee $4,438.00
* All fees are inclusive of NZ GST or any equivalent overseas tax, and do not include any programme level discount or additional course-related expenses.
For further information see
Mathematics and Statistics