MATH201-12S1 (C)
Mathematics 2
This is a semester one course worth 15 points.
Message of the Day
Posted by Rua Murray on February 1 2012, 12:01 pm
Course materials will be posted on LEARN, and all important announcements will be posted there. The link "Course information for Math201" (above) contains some details about the course (and does not require LEARN access).
All timetable information should be obtained from the "Official details" link (to the CIS).
The textbooks are
* Required: Anton's Calculus (as for first year)
* Highly recommended: Poole, Linear Algebra (also used for Math203 in Semester 2)
--Rua
Course Information
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
Text
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).
Enquiries
Dr Rua Murray
Room 604 Erskine Building
Phone Extension 4867
Homepage