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.

The authors study the Wiener process and Itô integrals in some detail, with a focus on results needed for the Black–Scholes option pricing model. After developing the required martingale properties of this process, the construction of the integral and the Itô formula (proved in detail) become the centrepiece, both for theory and applications, and to provide concrete examples of stochastic differential equations used in finance.