Mathematical Analysis

By Mansoor P | MES College of Engineering Kuttippuram, Kerala

Learners enrolled: 635

Mathematics is an inevitable subject and it has significant role in many real life problems. In order to formulate and solve many engineering problems, one has to relate the problems with various Mathematical concepts. A thorough understanding of mathematics is an essential one to do such problems easily. In this course, I would like to discuss some basic concepts of mathematics under the following titles.

1. Real Analysis

2. Complex analysis

3. Vector analysis

This is a 10 week course comprising 40 modules, assignments and tests under the above mentioned topics.

The course is helpful to those students they are doing BSc Mathematics degree course under various universities of India.

This course will help students from science stream for the systematic study of the basic concepts of metric space, complex analysis and vector analysis. By completing this course, the students will have a legible understanding of basic concepts of metric space, complex analysis and vector analysis which will be useful in many situations.

Summary

Course Status :	Completed
Course Type :	Core
Language for course content :	English
Duration :	12 weeks
Category :
Credit Points :	4
Level :	Undergraduate
Start Date :	04 Jan 2021
End Date :	31 Mar 2021
Exam Date :

Page Visits

Course layout

Week 1

Day 1 Metric Space- open and closed sets

Day 2 Boundedness, compactness and connectedness

Day 3 Complete sets, dense sets and compact sets

Day 4 Sequences in metric spaces

Day 5 Interaction

Week 2

Day 1 limit and continuity

Day 2 Isometry Mappings and Homeomorphisms

Day 3 Extension Theorems

Day 4 Equivalent Metrics and Subspaces

Day 5 Interaction
Day 6 Assignment

Week 3

Day 1 Reimann Integral I

Day 2 Reimann Integral II

Day 3 Continuity of real valued functions
Day 4 Interaction
Day 5 Assignment

Week 4

Day 1 Partial differentiation

Day 2 Partial differentiation- Young’s theorem and Schwarz’s theorem

Day 3 Partial differentiation- Implicit, Homogeneous and Composite functions

Day 4 Interaction
Day 5 Assignment

Week 5

Day 1 Infinite series

Day 2 Series of arbitrary terms
Day 3 Interaction

Day 4 Assignment

Week 6

Day 1 Tests for positive term series

Day 2 Double sequences and series

Day 3 Convergence of double Series
Day 4 Interaction
Day 5 Assignment

Week 7

Day 1 Fourier series

Day 2 Fourier series of functions having period 2C

Day 3 Fourier series for even and odd periodic functions

Day 4 Half Range Fourier Series Expansions
Day 5 Interaction
Day 6 Assignment

Week 8

Day 1 Power series solution of ordinary differential equations

Day 2 Bessel functions

Day 3 Legendre polynomials

Day 4 Sturm-Liouville problem and Orthogonality properties of Bessel functions and Legendre polymonials
Day 5 Interaction
Day 6 Assignment

Week 9
Day 1 Derivative of complex valued functions

Day 2 Cauchy Riemann equations

Day 3 Continuous functions

Day 4 Mobius Transformation
Day 5 Interaction
Day 6 Assignment

Week 10

Day 1 Vector analysis I

Day 2 Vector analysis II

Day 3 Differentiation of vector valued function

Day 4 Gradient, divergent and curl
Day 5 Interaction
Day 6 Assignment

Week 11

Day 1 Line integral of vector valued functions

Day 2 Independence of path

Day 3 Surface integral

Day 4 Greens theorem
Day 5 Interaction

Week 12

Day 1 Volume integral and divergence theorem

Day 2 Stokes theorem
Day 3 Interaction

Day 4 Assignment

Books and references

1. M. Apostol, Calculus (Vol. I), John Wiley and Sons (Asia) P. Ltd., 2002.

2. R.G. Bartle and D. R Sherbert, Introduction to Real Analysis, John Wiley and Sons (Asia) P. Ltd., 2000.

3. E. Fischer, Intermediate Real Analysis, Springer Verlag, 1983.

4. K.A. Ross, Elementary Analysis- The Theory of Calculus Series- Undergraduate Texts in Mathematics, Springer Verlag, 2003.

5.James Ward Brown and Ruel V. Churchill, Complex Variables and Applications, 8th Ed., McGraw – Hill International Edition, 2009.

6. Joseph Bak and Donald J. Newman, Complex analysis, 2nd Ed., Undergraduate Texts in Mathematics, Springer-Verlag New York, Inc., New York, 1997.

7. G.B. Thomas and R.L. Finney, Calculus, 9th Ed., Pearson Education, Delhi, 2005.

8. H. Anton, I. Bivens and S. Davis, Calculus, John Wiley and Sons (Asia) P. Ltd. 2002.

9. P.C. Matthew’s, Vector Calculus, Springer Verlag London Limited, 1998

Instructor bio

MANSOOR P

Assistant Professor, Department of Mathematics, MES College of Engineering Kuttippuram, Trikkanapuram P.O., Malappuram D.T., Kerala, India 679582, easyganitham@gmail.com, 09037250791

Academic qualification

M.Phil in Mathematics, MSc. Mathematics, BSc. Mathematics

Other Merits:

Pursuing PhD. in Mathematics with Bharathiar University Coimbatore. (Thesis submitted, viva-voce to be completed)

Served as Course coordinator for the MOOC on Calculus under SWAYAM platform.

Developed and presented a number of e-content modules in Mathematics for CEC, MHRD India.

Delivered a number of lectures in Mathematics for DTH Swayamprabha Channel 8 of MHRD at University of Calicut.

Acted as Course Chairman for first year Mathematics courses at the college.

Acted as Question paper setter and scrutinizer for various courses of APJ Abdul Kalam Kerala Technological University.

Published research articles in reputed International Journals.

Presented papers in International and Regional Seminars.