Function theory: limits, continuity, implicitely defined functions, review of

inverse function theory.

Differentiation: Definition of the derivative, examples; the derivative of a

sum, difference, product, and quotient of two functions; derivatives of

polynomials, the trigonometric functions, logs, exponentials, and the

inverse trigonometric functions; higher-order derivatives, first-order

separable differential equations.

Applications of the derivative: Local maxima and minima, the second-

derivative test; global maxima and minima; maximization on a closed

interval; curve sketching.

The definite integral: Definition of  the integral, examples; The

Fundamental Theorem of Calculus; antiderivatives; u-du substitutions;

integration by parts; changes of variable for the definite integral.

                 

Applications of the integral: Volumes by cross sections and cylindrical

shells; arc-length; surface areas of revolution.