MATH 101 Introduction to Differential Calculus (3+0) credit-hours.

Real numbers, inequalities, functions, injective function and its inverse. Limits, definition, continuity, properties of a continuous function on an interval. Differentiability, techniques of differentiation, critical points, absolute and local extrema, mean value theorem. Intervals of increase and decrease, first derivative and second derivative tests for local extrema, concavity and infection points, asymptote, curve sketching, applied extrema problems, related rates. Conic sections.

MATH 102 Introduction to Integral Calculus (3+0) credit-hours.

Perquisite: 101M

Definition of Riemann integral by Riemann sums, properties of the definite integral. Mean value theorem for the integral, the fundamental theorem of calculus, indefinite integral, integration by substitution. Logarithmic and exponential functions, hyperbolic and inverse hyperbolic functions. Techniques of integration: integration by parts, trigonometric substitutions, integrals involving quadratic expressions, partial fractions, miscellaneous substitutions. Numerical integration (the trapezoidal rule). L'Hospital's rule, improper integrals. Evaluation of area, volume of revolution, arc length. Sketching of some elementary curves in polar coordinates, evaluation of area in polar coordinates.

MATH 105 Differential Calculus (3+0) credit-hours.

Language of instruction: English

Real numbers, functions, Limits, continuity. Derivatives, differentials, chain rule, implicit differentiation. Higher order derivatives, local extrema, concavity, horizontal and vertical asymptotes, applications of extrema, related rates. Rolle's theorem, mean value theorem, inverse trigonometric functions. Conic sections.

MATH 140 Precalculus: Functions and Graphs (3+0) Credit-hours.

Language of instruction: English

Basic algebraic operations. Equations and inequalities. Graphs, Functions. Polynomial and rational functions. Exponential and Logarithmic functions. Trigonometric functions, Trigonometric identity and conditional equations. Systems of equations and inequalities. Sequence, induction, and probability.** **