Functions, limits, derivatives, curve sketching, Mean Value Theorem, trigonometric functions, related rates, linear and quadratic approximations, maximum-minimum problems. Definite and indefinite integrals; inverse functions, logarithmic, exponential, and hyperbolic functions; applications of integration, integration by substitution and by parts.

3 hours lecture, 2 hours recitation.

21-122
Integration, Differential Equations, and Approximation
Fall and Spring: 10 units

Integration by trigonometric substitution and partial fractions; arclength; improper integrals; Simpson's and Trapezoidal Rules for numerical integration; separable differential equations, first order linear differential equations, homogeneous second order linear differential equations with constant coefficients. Indeterminate forms, Newton's method, Taylor's Theorem including a discussion of the remainder, sequences, series, power series.

3 hours lecture, 2 hours recitation.

Prerequisite: 21-120.

Suggestions of what a student starting calculus should know.