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Course: Elements of Mathematics II
Level: Postgraduate
Time: Currently not offered
Syllabus
Past Exams


Syllabus: Relations and Functions: Ordered pairs, Definition of a relation, domain and range of a relation. Functions as a special kind of relation from one set to another, domain and range of a function, real valued functions of the real variable, graphs of standard functions. One to one and onto functions, inverse of a function, composite functions.
Calculus: Limit of a function. Continuous functions. Definition of a derivative, its relation with the slope of a tangent of the curve. Derivatives of products and quotients of functions, derivatives of polynomial and trigonometric functions, derivatives of composite functions, chain rule, Rolles and Mean Value Theorems (without proof). Applications in determining rates of change and maxima/minima. Integration as an inverse process of differentiation. Integration of a variety of functions by substitution, by partial fractions and by parts. Definite integrals as limits of a sum. Fundamental Theorem of Integral Calculus (without proof), basic properties, applications in finding areas under simple curves.

Reference Texts:


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Past Exams
Midterm
16.pdf 17.pdf
Semestral
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Supplementary and Back Paper

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[Indian Statistical Institute]