S.N

Unit

Content of the topics

Learning objects

Teaching Guidelines

Methodology

Time (Hrs)

1

one

 Continuity, properties of continuous functions,
 Sequential Continuity,
 Uniform continuity,
 Chain rule of differentiability.
 Mean value theorems; Rolle’s Theorem and Lagrange’s mean value theorem and their geometrical interpretations.
 Taylor’s Theorem with various forms of remainders,
 Darboux intermediate value theorem for derivatives,
 Indeterminate forms.

Students will be able to
 Continuity, Sequential Continuity, properties of continuous functions,
 Uniform continuity least upper bound, greatest lower bound of a set,
 Mean value theorems; Rolle’s Theorem and Lagrange’s mean value theorem and their geometrical interpretations.
 Taylor’s Theorem
 Darboux intermediate value theorem for derivatives, Indeterminate forms.

Lecture should be effective so that student can grasp the topics easily.

 Lecture.
 Seminar.
 Discussion/Interaction with Students.
 Assignment.
 Discussion on Assignment.
 Evaluation of Assignment.

15

2

Two

 Limit and continuity of real valued functions of two variables.
 Partial differentiation.
 Total Differentials;
 Composite functions & implicit functions.
 Change of variables.
 Homogenous functions
 Euler’s theorem on homogeneous functions.
 Taylor’s theorem for functions of two variables

Students will be able to
 Limit and continuity of real valued functions of two variables. Partial differentiation.
 Homogeneous equations with constant coefficient,
 Differentials; Composite functions & implicit functions.
 Taylor’s theorem for functions of two variables

Lecture should be effective so that student can grasp the topics easily.

 Lecture.
 Seminar.
 Discussion/Interaction with Students.
 Assignment.
 Discussion on Assignment.
 Evaluation of Assignment

15

3

Three

 Differentiability of real valued functions of two variables.
 Schwarz and Young’s theorem.
 Implicit function theorem.
 Maxima, Minima and saddle points of two variables.
 Lagrange’s method of multipliers,
 Involutes, evolutes,
 Bertrand Curves.
 Surfaces: Tangent planes, one parameter family of surfaces, Envelopes.

To make students familiar with
 Differentiability of real valued functions of two variables. Schwarz and Young’s theorem.
 Implicit function theorem. Maxima, Minima and saddle points of two variables. Lagrange’smethod of multipliers, Involutes, evolutes,
 Bertrand Curves. Surfaces: Tangent planes, Envelopes.

Lecture should be effective so that student can grasp the topics easily.

 Lecture.
 Seminar.
 Discussion/Interaction with Students.
 Assignment.
 Discussion on Assignment.
 Evaluation of Assignment

15
