This course intend to develop a thorough
understanding of the fundamental aspects of calculus of single
variable which is fundamental tool in Sciences, Engineering and
Economics.

Modules

Topics

1

Introduction to
Numbers,Countability and Uncountability Examples of
Irrational numbers,Functions,Limits of Functions-I

2

Limit of Functions-II,Continuous
Functions,Intermediate Value Theorem,Maximum Value
Theorem,Supremum & Infimum

3

Uniformly Continuous
Function,Derivative of a Function,Rules of
Differentiation,Derivatives maxima & minima,Rolle TMs
Theorem and Lagrange MVT(Mean-Value Theorem)

4

Monotonic Functions and Inverse
Functions,Newton TMs Method for solving
Equations,Optimization Problems,Integration,Basic Theorems
of Integration

5

Indefinite Integrals,Integration
by Parts,Integration of Rational Functions,Trapezoidal Rule
for evaluating definite integral,Simpson TMs Rule for
evaluating definite integral

6

Applications of Definite
Integral-I,Applications of Definite Integral-II,Applications
of Definite Integral-III,Applications of Definite
Integral-IV,Transcendental Functions-I

Infinite series and their
convergence,Tests for Convergence of a series,Absolute and
conditional convergence,Power Series,Historical Development
of the Calculus

B.E/B.Tech,B.Sc,

1. Calculus by M Spivak 2.Calculus by Thomos and Finney.

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