### Discrete Mathematics (MATH163)

Discrete mathematics is the first non-calculus course for mathematics, computer science and engineering majors. This course introduces mathematical tools and techniques used to study discrete processes as opposed to continuous processes. Topics covered include such discrete concepts as basic set theory, functions, relations, recurrences, counting principles, fundamentals of propositional calculus and Boolean algebra, graphs and trees. The course also introduces proof techniques of mathematics including proof by induction, proof by truth table, proof by Venn diagram, pigeonhole principle, etc. This course is indeed prerequisite for logic design, operational research and other advance level courses in combinatorics, abstract algebra, mathematical modeling, geometry and topology.

### Calculus I

Limits and continuity. Derivatives, Rules of differentiation, Higher order derivatives, Chain rule. Related rates. Rolle's and the mean value theorem. Critical Points. Asymptotes. Curve sketching. Integrals, Fundamental Theorem, Techniques of integraion, Definite integrals. Application to geometry and science. Indeterminate forms. L'Hospital's Rule. Improper integrals. Polar Coordinates.

### Calculus II

Power series,Taylor Polynomials, Taylor Series, Maclaurin series, Lines and planes, Functions of Several Variables, Limits and Continuity, Partial Differentiation, Chain Rule, Tangent plane, Critical points, Global and Local Extrema, Directional Derivatives, Gradient, Divergence and Curl, Multiple integrals with applications, Triple integrals with applications, Triple integrals in Cylindrical and Spherical coordinates, Line-, Surface- and Volume Integrals, Independence of path, Green’s Theorem, Conservative Vector Fields, Divergence Theorem, Stoke’s Theorem.