MATH201-20S1 (C) Semester One 2020

# Multivariable Calculus

15 points

Details:
 Start Date: Monday, 17 February 2020 End Date: Sunday, 21 June 2020
Withdrawal Dates
Last Day to withdraw from this course:
• Without financial penalty (full fee refund): Friday, 28 February 2020
• Without academic penalty (including no fee refund): Friday, 29 May 2020

## Description

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 forms the final part of the core mathematics sequence MATH102 - MATH103 - MATH201. It covers techniques in multivariable calculus and vector calculus and interesting applications in many areas of science, commerce and engineering. It is required for all Math majors, and is the foundation 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.

## Learning Outcomes

• 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.

## Restrictions

MATH261, MATH264, EMTH202, EMTH204, EMTH210

## Timetable 2020

Students must attend one activity from each section.

Activity Day Time Location Weeks Lecture A 01 Tuesday 14:00 - 15:00 - (24/3, 21/4)Online Delivery (28/4-26/5)A2 Lecture Theatre (18/2-17/3) 17 Feb - 29 Mar 20 Apr - 31 May Lecture B 01 Wednesday 12:00 - 13:00 - (25/3, 22/4)Online Delivery (29/4-27/5)Meremere 108 Lecture Theatre (19/2-18/3) 17 Feb - 29 Mar 20 Apr - 31 May Lecture C 01 Monday 15:00 - 16:00 - (23/3, 20/4)Online Delivery (4/5-25/5)K1 Lecture Theatre (17/2-16/3) 17 Feb - 29 Mar 20 Apr - 26 Apr 4 May - 31 May Tutorial A 01 Thursday 17:00 - 18:00 24 Feb - 22 Mar 20 Apr - 26 Apr 02 Wednesday 10:00 - 11:00 24 Feb - 29 Mar 03 Thursday 13:00 - 14:00 24 Feb - 22 Mar 04 Tuesday 10:00 - 11:00 24 Feb - 29 Mar 05 Tuesday 15:00 - 16:00 24 Feb - 29 Mar 06 Thursday 14:00 - 15:00 24 Feb - 22 Mar 07 Friday 13:00 - 14:00 24 Feb - 22 Mar

## Examination and Formal Tests

Activity Day Time Location Test A 01 Thursday 12:00 - 00:00 20 Apr - 26 Apr

## Indicative Fees

Domestic fee \$780.00

International fee \$4,250.00

* Fees include New Zealand GST and do not include any programme level discount or additional course related expenses.

For further information see Mathematics and Statistics.

## All MATH201 Occurrences

• MATH201-20S1 (C) Semester One 2020