MATH201-12S1 (C) Semester One 2012

Mathematics 2

15 points

Details:
Start Date: Monday, 20 February 2012
End Date: Sunday, 24 June 2012
Withdrawal Dates
Last Day to withdraw from this course:
  • Without financial penalty (full fee refund): Sunday, 4 March 2012
  • Without academic penalty (including no fee refund): Sunday, 20 May 2012

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 linear algebra 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; parametrised curves, tangent vectors, line integrals, work integrals; theorems of vector calculus; subspaces associated to a matrix; rank and nullity; eigenvalues, eigenvectors and diagonalisation; matrix applications include Markov chains and age-structured population models; coupled systems of linear ordinary differential equations, (including solution via eigenvectors, analysis of asymptotic behaviour and geometric interpretation).

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
  • understand and apply the basic ideas of linear algebra: span and linear independence, rank of a matrix, eigenvalues and eigenvectors
  • 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

Prerequisites

MATH103 or MATH109 or MATH199 or EMTH119

Restrictions

MATH261, MATH264, EMTH202, EMTH204, EMTH210

Course Coordinator

Rua Murray

Assessment

Assessment Due Date Percentage 
Internal Assessment - TBA 40%
Final Examination 60%

Textbooks / Resources

Required Texts

Anton, Howard. , Bivens, Irl., Davis, Stephen; Calculus : early transcendentals ; 9th ed; John Wiley, 2009 (8th Edition also suitable).

Recommended Reading

Poole, David; Linear algebra : a modern introduction ; 3rd ed; Brooks/Cole :Cengage Learning, 2011 (Highly recommended).

Course links

MATH201 Homepage

Indicative Fees

Domestic fee $622.00

International fee $3,200.00

* 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

  • MATH201-12S1 (C) Semester One 2012
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