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Quick Facts
| Medium Of Instructions | Mode Of Learning | Mode Of Delivery |
|---|---|---|
| English | Self Study | Video and Text Based |
Course Overview
The course of Differential Calculus offered by the Swayam platform is beneficial for every student. This course is offered under the guidance of MHRD [Ministry of Human Resource Development].
This course is an undergraduate-level course in which the duration of the course is 15 weeks and it is divided into 36 sessions. After completion of this course, students will gain 4 credits and a certificate of completion. The students who are pursuing their careers in the science stream or are planning to pursue it or are curious to dive into the depth of mathematics should take this course for understanding the core of Differential Calculus.
Every student can avail themselves the benefits of this course by applying the understanding of Differential Calculus to their degree programmes or in their quantitative learning and even in the basic principles of their academic learning. After completion of this course, you will achieve another big milestone in the field of mathematics and science. Proper learning and understanding of this course by the students can benefit them in their professional lives and can help them in understanding applications of the world as well as of the universe.
The Highlights
- Government-approved course under MHRD [Ministry of Human Resource Development].
- Duration is 15 weeks
- Enrolled candidates will gain 4 credits.
- The course is divided into 36 sessions.
- Certificate of completion will be provided after paying according to the guidelines of Swayam platform.
- 100% online programme
Programme Offerings
- Modules
- Books
- references
- Online lectures
Courses and Certificate Fees
| Certificate Availability | Certificate Providing Authority |
|---|---|
| yes | Mahatma Gandhi College, Iritty |
Eligibility Criteria
Certification qualifying details
Candidates who have enrolled themselves for this course will be awarded a ``Course Completion’’ certificate after paying according to the guidelines of the Swayam platform. The certificate will be provided on the basis of a minimum 30 percent Course Assessment and 70 percent of End-Term Proctored Exam.
The enrolled candidate has to gain 4 credits in order to receive the course completion certificate. The certificate will be signed under the name of Dr. Bijumon Ramalayathil who has 19 years of teaching experience and is the Associate Professor as well as Post Graduate Department of Mathematics. He is the course coordinator of a number of courses on the Swayam platform.
What you will learn
After successful completion of the course Differential, Calculus candidates will be able to gain important insights on-
- The candidates will study and learn about Rolle's theorem, mean value theorems through examples.
- They will study the concepts of tangents and normals.
- They will be familiarized with methods of finding curvature, asymptotes, and singular points.
- They will familiarise themselves with the functions of several variables.
- They will be able to study sequence and series in calculus.
- A detailed study on Taylor’s theorems, Taylor’s series, and Maclaurin’s series through examples.
- Study Euler’s theorem on homogeneous functions and some of its mathematical applications.
- Familiarize with the concept of limit and continuity
- Learn through examples of successive differentiation and Leibniz’s theorem.
- Learn methods of tracing curves in cartesian, parametric, and polar forms.
Who it is for
Admission Details
The admission procedure for the Differential Calculus course is direct and simple. You have to follow the below-mentioned steps and enroll yourself in this program.
Step 1: Visit the homepage of the Swayam platform.
Step 2: Click on the URL https://onlinecourses.swayam2.ac.in/cec20_ma22/preview
Step 4: Click the Sign-In/ Register option to start your enrolling procedure.
Step 5: Select your desired course.
Step 6: Fill in your complete details.
Step 7: After your enrolling procedure is complete you can then avail of the lessons.
The Syllabus
- Functions
- Inverse of Functions and Inverse Trigonometric Functions
- Limit of Functions – An Intuitive Approach
- Computing Limits - Limit laws
- The Precise Definition of Limit
- Continuity
- Tangent Lines and Rate of Change
- The Derivative of a Function
- Techniques of differentiation and the Chain Rule
- Derivatives of trigonometric and inverse trigonometric functions
- Implicit Differentiation, Tangents and Normals and Logarithmic Differentiation
- Successive Differentiation, nth derivative of standard functions and Leibniz Theorem
- I – Local Linear Approximation of Functions of One Variable
- II - Differentials
- Increasing and Decreasing Functions and Concavity
- Extreme Values of Functions
- Extreme Values of Functions on Unbounded Intervals and Limit at Infinity
- The Rolles and mean value theorems
- Asymptotes
- Curve tracing in Cartesian Coordinates
- L’ Hospitals rule
- Sequences
- Techniques for Finding Limit of Sequences
- Infinite series
- Tests for Convergence of Series
- Alternating Series and Absolute Convergence of Series
- Power series and Radius of Converge
- Taylor and Maclaurin series of Functions
- Parametric Equations
- Differentiable Parametrized Curves, Second Derivative of Parametrized Curves
- Polar Coordinates
- Graphing Polar Curves
- I: Tracing of Cardiods and Families of Roses
- II: Tangent Lines to Polar Curves
- I: Curvature and Evolutes of Curves in Parametric Equations
- II: Formula for Radius of Curvature of Cartesian Equations;
- III: Centre of Curvature and Circle of Curvature of Cartesian Curves
- Curvature and Evolutes of Curves in Parametric Equations
- II: Curvature in Polar coordinates
- Functions of Several Variables
- Limits and Continuity of Functions of Several Variables
- Partial Derivatives
- Partial Derivatives of Higher Order
- Differentiability
- I: The Chain Rule of functions of more than one variable
- II: Euler's theorem on homogeneous functions
Evaluation process
Exam certification required for this course is a minimum of 30 percent for course assessment and 70 percent for an end-term proctored exam. After paying according to the guidelines of the Swayam platform you can avail the course completion certificate.