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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 : Ongoing
Course Type : Core
Duration : 12 weeks
Start Date : 04 Jan 2021
End Date : 31 Mar 2021
Exam Date :
Category :
Level : Undergraduate



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. 



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