Page 67 - CatalogNEP-PS

All the Physics honours students will do a supervised Physics Project as an important culmination
of training in Physics learning and research. This project shall be a supervised collaborative work
in Theoretical Physics (Condensed Matter Physics, Nuclear Physics, Particle Physics),
Experimental Physics, Computational Physics. The project will aim to introduce student to the
basics and methodology of research in physics, which is done via theory, computation and
experiments either all together or separately by one of these approaches. It is intended to give
research exposure to students.
MATHEMATICS
(DISCIPLINE – B)

DISCIPLINE SPECIFIC COURSES:

Maths.111 Differential Calculus 3+1*

LEARNING OBJECTIVES:

The primary objective of this course is:
 To introduce the basic tools of calculus, also known as ‗science of variation‘.
 To provide a way of viewing and analysing the real-world problems.

LEARNING OUTCOMES:

This course will enable the students to understand:
 The notion of limits, continuity, and uniform continuity of functions.
 Geometrical properties of continuous functions on closed and bounded intervals.
 Applications of derivative, relative extrema, and mean value theorems.
 Higher order derivatives, Taylor‘s theorem, indeterminate forms, and tracing of curves.

THEORY (45 Hours)

UNIT – I: Limits and Continuity (15 Hours)
Limits of functions (ε - δ and sequential approach), Algebra of limits, Squeeze theorem, One-
sided limits, Infinite limits, and limits at infinity; Continuous functions and its properties on
closed and bounded intervals; Uniform continuity.

UNIT – II: Differentiability and Mean Value Theorems (15 Hours)
Differentiability of a real-valued function, Algebra of differentiable functions, Chain rule,
Relative extrema, Interior extremum theorem, Rolle‘s theorem, Mean-value theorem and its
applications, Intermediate value theorem for derivatives.
UNIT – III: (15 Hours)

Successive Differentiation, Taylor’s Theorem and Tracing of Plane Curves
Higher order derivatives and calculation of the nth derivative, Leibnitz‘s theorem; Taylor‘s

theorem, Taylor‘s series expansions of , , . Indeterminate forms, L‘Hospital‘s rule;
Concavity and inflexion points; Singular points, Asymptotes, Tracing graphs of rational functions
and polar equations; Functions of severable variables (upto three variables), Limit and continuity
of these variables.

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