Differential Calculus

By Dr Bijumon Ramalayathil | Mahatma Gandhi College, Iritty Keezhur PO, Kannur Dt – 670 703, Kerala

Learners enrolled: 4741

The course entitled “Differential Calculus” deals with the basic aspects differential calculus. The contents of this course are inevitable for many branches of sciences. The students of Mathematics, Physics, Chemistry, Computer Science, Statistics, etc., are equally benefited with this course as a stepping stone to the broad areas of Calculus.

The objective of this course is to familiarize students with important concepts coming under the branch “Differential Calculus” and to develop strong foundations on these concepts. Upon successful completion of this course, the students are expected to:

1. Familiarize with the concept of Limit and Continuity (Both informal and ε- δ definition)

2. Learn through examples Successive differentiation and Leibniz’s theorem.

3. Study Rolle’s theorem, Mean Value theorems through examples.

4. Study the concepts tangents and normals.

5. Familiarize with methods of finding Curvature, Asymptotes and Singular points.

6. Learn methods of Tracing of curves in Cartesian, Parametric and Polar forms

7. A study on sequences and series

8. A detailed study on Taylor’s theorem, Taylor’s series and Maclaurin’s series through examples.

9. Familiarise with functions of several variable.

10.Study Euler’s theorem on homogeneous functions and some of its mathematical applications.

Summary

Course Status :	Completed
Course Type :	Core
Duration :	15 weeks
Category :	Mathematics
Credit Points :	4
Level :	Undergraduate
Start Date :	29 Jul 2019
End Date :	26 Oct 2019
Exam Date :

Page Visits

Course layout

Week 1 :

1.Functions

2.Inverse Functions and Inverse Trigonometric Functions

3.Limit of Functions – An Intuitive Approach

Week 2 :

4.Limit Laws

5.The Precise Definition of Limit

6.Continuity of Functions

Week 3 :

7.Tangent Lines and Rates of Change

8.The Derivative of a Function

9.Techniques of Differentiation and the Chain Rule

Week 4 :

10.Derivative of Trigonometric Functions

11. Implicit Differentiation, Tangents and Normals, Logarithmic Differentiation

12.Successive Differentiation and Leibniz theorem

Week 5 :

13.Extreme Values of Functions

14.Rolle’s Theorem and Mean Value Theorems

15.Increasing and Decreasing Functions and Concavity of Functions

Week 6 :

16.Limit at Infinity and Asymptotes

17.Curve Tracing in Cartesian Coordinates

18.Linearization and Differentials

Week 7 :

19.L’Hôpital’s Rule

20.Sequences

21.Techniques for Limit of Sequences

Week 8 :
22. Infinite Series

23.Tests for Convergence of Series

24.Alternating Series and Absolute Convergence of Series

Week 9 :

25.Power Series and Radius of Convergence

26.Taylor Series and Maclaurin Series of a Function

27.Parametric Representation of Curves and Tracing of Parametric Curves, Singular Points

Week 10 :

28.Polar Coordinates

29.Graphing in Polar Coordinates

30.Curvature of Functions – Cartesian, Parametric and Polar forms

Week 11 :
31. Functions of Several Variables

32.Limit and Continuity of Functions of Several Variables

33.Partial Derivatives

Week 12 :

34.Differentiability, Linearization, and Differentials

35.The Chain Rule

36.Euler’s theorem on homogeneous functions

Week 13 :

Deadline for Submitting Assignments

Books and references

1. H. Anton, I. Birens and S. Davis, Calculus, John Wiley and Sons, Inc., 2002.

2. G.B. Thomas and R.L. Finney, Calculus, Pearson Education, 2007.

Instructor bio

Dr. Bijumon Ramalayathil has 19 years of teaching experience both in UG and PG level. He was awarded PhD from University of Calicut in 2010. His area of interest is Functional Analysis. Presently he is the Associate Professor at Post Graduate Department of Mathematics, Mahatma Gandhi College, Iritty, Kerala. He is the course coordinator of a couple of MOOC courses on SWAYAM platform.