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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 useful for all Math majors, and for students who want to proceed to study more advanced topics in mathematics.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.
Students successfully completing this course should:• be proficient in the basic techniques of multivariable calculus.• be able to use calculus methods to solve standard applied problems and to apply their understanding of multivariate geometry to express and solve vector calculus problems.• Have developed problem solving skills both as part of a team and as an individual.
This course will provide students with an opportunity to develop the Graduate Attributes specified below:
Critically competent in a core academic discipline of their award
Students know and can critically evaluate and, where applicable, apply this knowledge to topics/issues within their majoring subject.
MATH103 or MATH199 or EMTH119
MATH261, MATH264, EMTH202, EMTH204, EMTH210
Felipe Voloch
Ngin-Tee Koh
Stewart, James; Calculus : early transcendentals ; Eighth edition; Cengage Learning, 2016 (Earlier editions of the text are also suitable).
Library portal LEARN
Domestic fee $897.00
International fee $5,188.00
* 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 .