MATH201-19S1 (C) Semester One 2019

Multivariable Calculus

15 points
18 Feb 2019 - 23 Jun 2019

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

Pre-requisites

Restrictions

MATH261, MATH264, EMTH202, EMTH204, EMTH210

Timetable 2019

Students must attend one activity from each section.

Lecture A
Activity Day Time Location Weeks
01 Wednesday 11:00 - 12:00 A3 Lecture Theatre 18 Feb - 7 Apr
29 Apr - 2 Jun
Lecture B
Activity Day Time Location Weeks
01 Friday 11:00 - 12:00 C3 Lecture Theatre 18 Feb - 7 Apr
29 Apr - 2 Jun
Lecture C
Activity Day Time Location Weeks
01 Monday 08:00 - 09:00 E9 Lecture Theatre 18 Feb - 7 Apr
29 Apr - 2 Jun
Tutorial A
Activity Day Time Location Weeks
01 Thursday 11:00 - 12:00 Jack Erskine 240 25 Feb - 7 Apr
29 Apr - 2 Jun
02 Thursday 15:00 - 16:00 Ernest Rutherford 260 25 Feb - 7 Apr
29 Apr - 2 Jun
03 Friday 12:00 - 13:00 Jack Erskine 240 25 Feb - 7 Apr
29 Apr - 2 Jun
04 Thursday 08:00 - 09:00 Ernest Rutherford 225 25 Feb - 7 Apr
29 Apr - 2 Jun
05 Monday 12:00 - 13:00 Jack Erskine 239 25 Feb - 7 Apr
29 Apr - 2 Jun
06 Monday 10:00 - 11:00 Jack Erskine 441 25 Feb - 7 Apr
29 Apr - 2 Jun

Examination and Formal Tests

Test A
Activity Day Time Location Weeks
01 Thursday 18:30 - 19:30 K1 Lecture Theatre 1 Apr - 7 Apr

Course Coordinator / Lecturer

Michael Plank

Lecturer

Michael Langton

Assessment

Assessment Due Date Percentage 
Homework assignments 25%
Test 25%
Final examination 50%

Textbooks / Resources

Recommended Reading

Stewart, James,1941-; Calculus :early transcendentals; Eighth edition; Cengage Learning, 2016.

Indicative Fees

Domestic fee $764.00

International fee $4,000.00

* 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

  • MATH201-19S1 (C) Semester One 2019