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Course Contents

Real number system, absolute values, inequalities, Functions, graphing of some basic functions, basic concept of limits, some useful limits, continuity, continuity of combinations of functions. Properties of continuous functions. Derivatives of algebraic, trigonometric and transcendental functions implicit differentiation. Differentials, Related rates, Higher derivatives, Leibnitz’s theorem (statement only), Extreme values, Concavity, Singular points. Asymptotes Statements of Rolle’s theorem, Mean value theorems and their applications, Increasing and decreasing functions.Indeterminate forms, L’ Hospital rule. Antiderivatives, definite and indefinite integrals, definite integral as limit of sum, fundamental theorem of integral calculus, properties of definite integral, reduction formulae, Walli’s sine and cosine formulae, product formulae, Improper integrals.


Course Learning Outcomes

This course includes all necessary contents, which are required in the different subjects,e.g. Physics, Chemistry, Economics, Statistics at master and higher level. It is also useful in Engineering and Banking.


Absolute values inequalities

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Quadratic inequalities

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Aboute functions(Finding domain and range of function)

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About domain and sketching graph

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Piece-wise functions and its graph

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Composition of two functions

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About domain and range of function

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limit of function

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Finding limit of functions

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Finding limit of functions(Part 2)

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finding delta of limit

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FInding limit graphically

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continuity

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continuity (part 2)

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continuity (part 3)

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mean value theorem

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Rolle's theorem

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differentiation

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Book Title : Calculus and Analytic Geometry
Author : 2. G.B. Thomas Jr. and R.L. Finney
Edition :
Publisher : Addision Wasely publishing company







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