Functions, limits, derivatives, curve sketching, Mean Value Theorem, trigonometric functions, related rates, linear and quadratic approximations, maximum-minimum problems.

3 hours lecture, 2 hours recitation.

This course is not regularly offered, and exists primarily to give credit to students entering the University with half a semester placement in calculus. Such students are placed into 21-121.

21-121
Integration and Differential Equations
Fall and Spring: 10 units

Definite and indefinite integrals; inverse functions, logarithmic, exponential, and hyperbolic functions; applications of integration, integration by substitution and by parts. 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.

3 hours lecture, 2 hours recitation.

Prerequisite: 21-115.

Includes the second half of 21-120 and the first half of 21-122 and is offered to achieve flexible placement of entering students.

21-123
Calculus of Approximation
Fall and Spring first minis: 5 units

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: 21-121.

This mini course includes the second half of 21-122 and is offered primarily to allow flexible placement of students entering the University.

Suggestions of what a student starting calculus should know.