MATH201-16S1 (C) Semester One 2016

Multivariable Calculus

15 points

Details:
 Start Date: Monday, 22 February 2016 End Date: Sunday, 26 June 2016
Withdrawal Dates
Last Day to withdraw from this course:
• Without financial penalty (full fee refund): Friday, 4 March 2016
• Without academic penalty (including no fee refund): Friday, 20 May 2016

Description

This course deals with techniques in multivariable calculus and linear algebra 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 Taylor series; 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 an appropriate combination of calculus and matrix methods, MAPLE and MATLAB 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

Assessment

Assessment Due Date Percentage
Assignments 20%
Test 1 16%
Test 2 16%
Final Examination 48%

Textbooks / Resources

Required Texts

Anton, Howard. , Bivens, Irl., Davis, Stephen; Calculus : early transcendentals ; 9th ed; John Wiley, 2009 (or 10th edition).

Indicative Fees

Domestic fee \$720.00

International fee \$3,450.00

* 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 .

All MATH201 Occurrences

• MATH201-16S1 (C) Semester One 2016