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Quick Facts
| Medium Of Instructions | Mode Of Learning | Mode Of Delivery |
|---|---|---|
| English | Self Study | Video and Text Based |
Course Overview
Mathematics is a subject that plays a significant role in human life and existence and can solve many complex real-life problems. Mathematical concepts have the power to explain the mysteries and complexities of the universe. The Mathematical Analysis online course is an attempt to provide a thorough understanding of some complex mathematical concepts to science stream students.
The Mathematical Analysis programme consists of 40 modules, tests and assignments and is a 10-week- long core course. This is a comprehensive course provided by Swayam in association with MES College of Engineering Kuttippuram of Kerala. Over the course of 10 weeks, you will learn some basic and some complex mathematical concepts which will prove most useful for students pursuing B.Sc in Maths degree from any university.
The Highlights
- Online learning medium
- Final exam
- Course assignments
- Student interaction
- Undergraduate level programme
Programme Offerings
- References mentioned
- UG/PG level programme
- Proctored examination
- assignments
- 10-week training
Courses and Certificate Fees
| Certificate Availability |
|---|
| no |
What you will learn
Once you have completed all the modules for Mathematical Analysis online programme, you will acquire familiarity with the following mathematical concepts:
- Vector analysis
- Real Analysis
- Extension Theorems
- Complex analysis
- Reimann Integral
- Infinite series
- Partial differentiation
Who it is for
While the Mathematical Analysis programme will benefit most students from science stream, it is most suitable for students studying B.Sc in Mathematics.
Admission Details
Step 1: If you wish to participate in the Mathematical Analysis certification, register on Swayam website.
Step 2: Now, click on this link to visit the course page- https://onlinecourses.swayam2.ac.in/cec21_ma05/preview
Step 3: Click on the icon that says ‘JOIN’ and you will be redirected to another page.
Step 4: Now, use your Google, Facebook or Microsoft credentials to sign in to your Swayam account.
Application Details
You must use your Google, Facebook, or Microsoft profile to register for this course. Enter a username, strong password and an active email ID to sign up for the account and use the same details to log in every time.
The Syllabus
- Metric Space- open and closed sets
- Boundedness, compactness and connectedness
- Complete sets, dense sets and compact sets
- Sequences in metric spaces
- Interaction
- limit and continuity
- Isometry Mappings and Homeomorphisms
- Extension Theorems
- Equivalent Metrics and Subspaces
- Interaction
- Assignment
- Reimann Integral I
- Reimann Integral II
- Continuity of real valued functions
- Interaction
- Assignment
- Partial differentiation
- Partial differentiation- Young’s theorem and Schwarz’s theorem
- Partial differentiation- Implicit, Homogeneous and Composite functions
- Interaction
- Assignment
- Infinite series
- Series of arbitrary terms
- Interaction
- Assignment
- Tests for positive term series
- Double sequences and series
- Convergence of double Series
- Interaction
- Assignment
- Fourier series
- Fourier series of functions having period 2C
- Fourier series for even and odd periodic functions
- Half Range Fourier Series Expansions
- Interaction
- Assignment
- Power series solution of ordinary differential equations
- Bessel functions
- Legendre polynomials
- Sturm-Liouville problem and Orthogonality properties of Bessel functions and Legendre polymonials
- Interaction
- Assignment
- Derivative of complex valued functions
- Cauchy Riemann equations
- Continuous functions
- Mobius Transformation
- Interaction
- Assignment
- Vector analysis I
- Vector analysis II
- Differentiation of vector valued function
- Gradient, divergent and curl
- Interaction
- Assignment
- Line integral of vector valued functions
- Independence of path
- Surface integral
- Greens theorem
- Interaction
- Volume integral and divergence theorem
- Stokes theorem
- Interaction
- Assignment
Instructors
MESCE Kuttippuram Frequently Asked Questions (FAQ's)
Yes, interaction sessions will be held every week where students can interact with each other and the instructor.
You can find a list of references on the course page under the section titled ‘Books and References’.
The course will be taught by Mansoor P, who is an Assistant Professor in the Department of Mathematics, MES College of Engineering.
This course has been designed by MES College of Engineering Kuttippuram, Kerala and is offered by Swayam learning platform.