A topic is chosen which involves the student in an area of current interest in mathematics. Students must prove a significant number of theorems on their own. For over 2500 years, these three ideas formed the foundation of the Calculus, one of the greatest creations of mankind. The course focuses on the confluence of two seemingly disparate notions, slope and area, in one of the surprising theorems of our civilization, The Fundamental Theorem of Calculus. The study is done at a deep level and in a visual way but without most of the notation, which sometimes inhibits a humane understanding of this beautiful subject.
Students learn how to use their imaginations and to use language precisely and efficiently.
Calculus I. Limits, derivatives, applications of derivatives, integration, logarithm and exponential functions. Fall and Spring. L'Hopital's Rule, inverse trigonometric and hyperbolic functions, methods of integration, analytic geometry, applications of integrals, sequences and series. Fall and Spring. The study of the completeness property, sequences, limits, tangency, derivatives, area, and integration.