Introduction to Calculus II

Indefinite integral, definite integral, fundamental theorem of calculus, method of substitution, area between two curves. Inverse functions and their derivatives, exponential and logarithmic functions, inverse trigonometric functions. Indeterminate forms and l'Hôpital's Rule. Geometric series, compound interest, exponential growth and decay. Techniques of integration (integration by parts, rationalizing substitution, partial fractions), improper integrals. Differential equations (separable and first-order linear equations) and initial-value problems. Three-dimensional coordinate system, functions of several variables, partial derivatives, the chain rule. Maximum and minimum values, the second partials test, the method of Lagrange Multipliers. Double integrals.