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 620-180 Intermediate Mathematics

Note

  1. This subject is exactly equivalent to [98]620-142. It will run once only. It is required for some students during the transition to the new first year course structure which has been introduced for 1999.

  2. Students may gain credit for only one of 620-180, 620-142, [98]620-111, [98]620-121, [98]620-142. Passing 620-180 excludes subsequent credit for any of 620-141, 620-161, 620-162.

Credit Points

12.5

Coordinator

Dr A Owczarek

Prerequisites

620-141; or both of 620-161, 620-162; or special permission of the Director of First Year Studies.

Semester

1 (view timetable)

Contact

36 lectures (three per week), 12 one-hour tutorials (one per week) and 36 hours problem solving

Subject Description

This subject introduces the different types of numbers, intuitive notions of limits as used in continuity, differentiation and integration and the notion of integral as area. It also develops the fundamental ideas in the calculus of functions of several variables. Students should develop the ability to manipulate complex numbers and to use them to solve problems; to approximate and estimate; to solve problems involving contours of surfaces; and to find extrema of functions and to find volumes using differentiation and integration. This subject demonstrates the role of proof and logical reasoning in mathematics, the role of limits in both the differential and integral calculus. It shows the uses of complex numbers and vectors and the practical uses of calculus.

Foundations: sets, integers, mathematical induction; real numbers; complex numbers, polar form, de Moivre's theorem, complex exponential. Calculus: functions of one real variable (including limits and continuity), Mean Value Theorem and applications, Newton's method for root-finding, approximate integration, Taylor polynomials. Multivariable calculus: Functions of several variables, level curves, heights; partial derivatives, commutation of mixed partial derivatives; total derivative, gradient vector, directional derivatives and applications; chain rule; Hessian matrix, maxima and minima of functions of several variables; introduction to double and triple integrals and applications.

Assessment

Up to 24 pages of written assignments, a three-hour end-of-semester written examination and class tests totalling not more than 1.5 hours.

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Status:                   Official 1999
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