# Welcome to the Calculus Bible!

The Calculus Bible is a guide to the Advanced Placement tests in AB and BC Calculus. It can serve as a review packet before quizzes or tests and is also a great review of the entire year's matieral before the AP.

Combined, the two cover:

• functions (domain, range, asymptotes, and fundamental properties)
• graphs you must know
• the derivative (definition, formulas, theorems, etc.)
• applications of the derivative (slope of a curve, slope of the normal line, curve sketching, max-min word problems, related rates, motion along a line, etc.)
• antiderivatives (the definition and applications)
• techniques of integration (including u-substituion, the inverse chain rule, and integration by parts)
• approximations of the definite integral
• the definite integral as area
• applications of the integral (motion along a line, mean value of a function, area between two curves, and volume of a solid of revolution)
• advanced techniques of integration (reduction formulas, power formualas, etc.)
• trigonometric substitutions
• partial fractions
• improper integrals
• further applications of the definite integral (volumes of known cross-sections, length of a plane curve, and work)
• parametrically-defined equations (definition, derivative, and length of the plane curve)
• polar functions (lines, circles, and rectangular hyperbolas)
• limacons
• lemniscates
• spirals
• roses
• sequences and series (convergence and tests for convergence)
• function approximations by infinite series