Single-Variable Calculus

This comprehensive course explores the fundamental topics of differential and integral calculus of a single variable, including limits, continuity, rates of change, differentiation, integration, introductory differential equations, infinite sequences and series, convergence and divergence of series, power series, and Taylor series and polynomials and their applications. Throughout the course, students will approach calculus using analytic, graphical, algorithmic, and numerical points of view, with an emphasis on rigorous problem-solving and high-level development of the mathematical content. Additionally, students will consider the historical development of calculus, and will form connections between the classical theory and modern applications of calculus. This course serves as a challenging and engaging course in single-variable calculus, and prepares students for more advanced work in mathematics. OM045 firmly situates calculus in the broader narrative of mathematical exploration, and fosters connections between students' previous coursework in mathematics, the discovery of calculus and the analysis of functions, and higher-level mathematics.