MATH 109

Real numbers,inequalities.

Functions and operations on functions

Limits,trigonometric limits,vertical asymptoptes and horizontal asymptotes.

Derivatives:definition and rules of derivation.Derivatives of usual functions.

Increasing functions,decreasing functions and the first derivative test.

Concavity,convexity,points of inflections and the second derivative test.

Graphing functions.

Logarithmic and exponential functions.

Primitives and the computation of definite integrals.

The substitution method,integrating rational functions and integration by parts.

Functions of many variables,extrema problems.

First ordre separable and linear differential equations.