620-142 Intermediate Mathematics B

Note

Students may only gain credit for one of 620-111, 620-121, 620-142 or the 1997 Handbook subjects 618-111, 618-121, 618-142. Passing 620-142 excludes subsequent credit for any of 620-141, 620-161, 620-162.

Credit Points

Coordinator

Prerequisites

620-141 (1997 Handbook: 618-141), or both of 620-161, 620-162 (1997 Handbook: 618-161, 618162) or special permission of the Director of First Year Studies

Semester

Contact

Subject Description

Students completing this subject should comprehend

• some of the nature of the different types of numbers they use;
• the intuitive notion of limits as used in continuity, differentiation and integration;
• the notion of integral as area;
• the fundamental ideas in the calculus of functions of several variables;

have developed the ability to

• manipulate complex numbers and to use them to solve problems;
• approximate and estimate;
• solve problems involving contours of surfaces;
• find extrema of functions and to find volumes using differentiation and integration;

and appreciate

• the role of proof and logical reasoning in mathematics;
• the use of complex numbers;
• the role of limits in both the differential and integral calculus;
• the practical uses of calculus;
• the importance of the general concept of a vector.

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; coordinate transformations, Jacobi matrix and determinant; 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.