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SYLLABUS
MATH 101 
Introduction to Differential Calculus 
(3+0) credithours 
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) credithours 
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 131 
Foundations of Mathematics 
(3+1) credithours 
Introduction to logic, methods of proof, mathematical induction. Sets, operations, on sets, cartesian product, binary relation, partition of a set, equivalence relation, equivalence classes, mappings, equivalence of sets, finite sets, countable sets, cardinal numbers. Binary operations, morphisms. Definition and examples of groups, definition and examples of rings and fields. 
Prerequisite: 101M 



