6 Calculus Preparatory Programs

The Calculus Course addresses a variety of topics centered around the theme of "calculus with infinite processes", largely the content of BC-level AP Calculus that isn't in the AB-level syllabus. It is needed throughout probability and statistics at all levels, as well as to understand approximation procedures that arise in all quantitative fields (including economics and computer graphics). 

Logarithmic, exponential, and trigonometric functions. Sequences and series; Taylor's series with the remainder. Methods of integration. Calculus I and II together constitute an introduction to calculus of a function of a single real variable.

Extends concepts and techniques of calculus and develops further applications. Topics include higher dimensional calculus, applications of vector analysis, uniform convergence of series, complex series, improper integrals, gamma and beta functions, Stirling's formula, and Fourier series and transform.

Limits; derivatives; differentiation of algebraic and transcendental functions. Applications to maxima, minima, and convexity of functions. The definite integral; the fundamental theorem of integral calculus.

Differentiation and integration of functions of one variable. Same topics as CAS MA 123, but with less emphasis on mathematical generality and more on applications. Especially suitable for students concentrating in the biological and social sciences.

Introduction to software design, programming techniques, data structures, and software engineering principles. The course is structured bottom up, beginning with basic hardware followed by an understanding of machine language that controls the hardware and the assembly language that organizes that control.