Inequalities and their solutions: Real numbers and real line, intervals, absolute values and its properties, solution of inequalities. Function and graphs: Domain and range of a function. Operations with functions: sum, product, quotient and composition. Graphs and shifting of graphs. Limits and continuity: Informal definition of limits, Rules for finding limits, and formal definition of limits, One sided and two-sided limits, Infinite limits, Continuity, Theorems on continuity, Continuous extension to a point. Derivatives and their applications: Definition, techniques of differentiation. Graphing f/ from estimated values, one sided vs two sided derivatives, derivatives as a rate of change, related rates, linearization and differentials. Extreme values of functions, The Mean Value Theorem, Increasing and decreasing functions, the first derivative test for local extreme values, graphing with y/ and y//, concavity, asymptotes and dominant terms, optimization problems, indeterminate forms. L ’Hospital’s rule. Complex Number System: Complex numbers, arithmetic operations in complex numbers, Argand diagrams, roots.

This course will be helpful to improve the knowledge of limit, continuity, differential in real number system and elementary knowledge of complex number system.

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Book Title : Calculus and Analytical Geometry

Author : G. B. Thomas Jr. and R. L. Finney

Edition :

Publisher : 11th Edition, Addison Wesley Publishing Company, 2005

Book Title : Calculus

Author : H. Anton, I. Bevens and Davis

Edition :

Publisher : 8th Edition, John Wiley & Sons, 2005

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