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Differential Calculus

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Mahatma Gandhi College, Iritty, Keezhur PO, Kannur Dt – 670...
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SwayamCourses from Swayam
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For Rs. 1000
Intermediate

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Checklist

Certification

You will get a certificate on completing this course.

University

The course is not from a very prestigious university.

Price

This course costs very less.

Why should you choose this course?

Description

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.

Syllabus

COURSE LAYOUTWeek 11. Functions2. Inverse of Functions and Inverse Trigonometric Functions3. Limit of Functions – An Intuitive Approach Week 24. Computing Limits - Limit laws5. The Precise Definition of Limit 6. Continuity Week 3 7. Tangent Lines and Rate of Change 8. The Derivative of a Function 9. Techniques of differentiation and the Chain Rule Week 410. Derivatives of trigonometric and inverse trigonometric functions11. Implicit Differentiation, Tangents and Normals and Logarithmic Differentiation 12. Successive Differentiation, nth derivative of standard functions and Leibniz Theorem Week 513.I – Local Linear Approximation of Functions of One Variable II - Differentials14. Increasing and Decreasing Functions and Concavity 15. Extreme Values of Functions Week 616. Extreme Values of Functions on Unbounded Intervals and Limit at Infinity 17. The Rolles and mean value theorems 18. AsymptotesWeek 719. Curve tracing in Cartesian Coordinates 20. L’ Hospitals rule 21. Sequences Week 822. Techniques for Finding Limit of Sequences 23. Infinite series 24. Tests for Convergence of Series Week 925. Alternating Series and Absolute Convergence of Series 26. Power series and Radius of Converge27. Taylor and Maclaurin series of Functions Week 1028. Parametric Equations 29. Differentiable Parametrized Curves, Second Derivative of Parametrized Curves30. Polar Coordinates Week 1131. Graphing Polar Curves32.I: Tracing of Cardiods and Families of RosesII: Tangent Lines to Polar Curves33.I: Curvature and Evolutes of Curves in Parametric EquationsII: Formula for Radius of Curvature of Cartesian Equations;III: Centre of Curvature and Circle of Curvature of Cartesian CurvesWeek 1234I: Curvature and Evolutes of Curves in Parametric EquationsII: Curvature in Polar coordinates35. Functions of Several Variables36. Limits and Continuity of Functions of Several VariablesWeek 1337. Partial Derivatives38. Partial Derivatives of Higher Order 39. DifferentiabilityWeek 1440.I: The Chain Rule of functions of more than one variableII: Euler's theorem on homogeneous functions

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