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Differential Calculus in Several Variables. Instructor: Prof. Sudipta Dutta, Department of Mathematics and Statistics, IIT Kanpur.
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Description
This course provides an introduction to a differential calculus of several variables. Functions of several variables and examples; Continuity; Matrix of linear transformation; How to define differentiable functions; Chain rule; Mean value theorem; Higher order derivatives; Taylor's formula; Maximum and minimum for real valued functions; Implicit function theorem and applications. (from nptel.ac.in)
Course content
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- Lecture 01 – Introduction to Several Variables and Notion of Distance in Rn Unlimited
- Lecture 02 – Continuity and Compactness Unlimited
- Lecture 03 – Continuity and Connectedness Unlimited
- Lecture 04 – Derivatives: Possible Definition Unlimited
- Lecture 05 – Matrix of Linear Transformation Unlimited
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- Lecture 06 – Examples for Differentiable Function Unlimited
- Lecture 07 – Sufficient Condition of Differentiability Unlimited
- Lecture 08 – Chain Rule Unlimited
- Lecture 09 – Mean Value Theorem Unlimited
- Lecture 10 – Higher Order Derivatives Unlimited
- Lecture 11 – Taylor’s Formula Unlimited
- Lecture 12 – Maximum and Minimum Unlimited
- Lecture 13 – Second Derivative Test for Maximum, Minimum and Saddle Point Unlimited
- Lecture 14 – Practical Test based on Hessian Matrix Unlimited
- Lecture 15 – Specialization to Functions of Two Variables Unlimited
Instructor
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