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Course11110516060 lectures

Advanced Calculus for Engineers

Prof. Jitendra Kumar and Prof. Somesh Kumar · IIT Kharagpur

Start with lecture 1 At NPTEL

About

This course is about basic mathematics, which is a fundamental and essential component of all undergraduate studies in sciences and engineering. This course consists of topics in differential, integral, and vector calculus with applications to various engineering problems. This course will cover calculus of two or more variables in detail. Knowledge of ordinary differential equations are part of this course. Students will learn how to perform double and triple integrals. Topic in vector calculus includesline and surface integrals, Green, Gauss and Stokes theorem.

Prerequisites: Higher SecondaryINTENDED AUDIENCE: All branches of science and engineering

Lectures

Week 1 :

  1. Lecture 01 : Rolle’s Theorem YouTube
  2. Lecture 02 : Mean Value Theorem YouTube
  3. Lecture 03 : Taylor’s Formula (Single Variable) YouTube
  4. Lecture 04 : Indeterminate Forms – Part 01 YouTube
  5. Lecture 05 : Indeterminate Forms – Part 02 YouTube

Week 2 :

  1. Lecture 06 : Introduction to Limit YouTube
  2. Lecture 07 : Evaluation of Limit YouTube
  3. Lecture 08 : Continuity YouTube
  4. Lecture 09 : First Order Partial Derivatives YouTube
  5. Lecture 10 : Higher Order Partial Derivatives YouTube

Week 3 :

  1. Lecture 11 : Differentiability – Part 1 YouTube
  2. Lecture 12 : Differentiability – Part 2 YouTube
  3. Lecture 13 : Differentiability – Part 3 YouTube
  4. Lecture 14 : Differentiability – Part 4 YouTube
  5. Lecture 15 : Composite & Homogeneous Functions YouTube

Week 4 :

  1. Lecture 16 : Taylor’s Theorem (Multivariable) YouTube
  2. Lecture 17 : Maxima & Minima – Part 1 YouTube
  3. Lecture 18 : Maxima & Minima – Part 2 YouTube
  4. Lecture 19 : Maxima & Minima – Part 3 YouTube
  5. Lecture 20 : Maxima & Minima – Part 4 YouTube

Week 5 :

  1. Lecture 21 : Formation of Differential Equations YouTube
  2. Lecture 22 : First Order and First Degree DE YouTube
  3. Lecture 23 : Exact Differential Equations YouTube
  4. Lecture 24 : Integrating Factor YouTube
  5. Lecture 25 : Linear Differential Equations YouTube

Week 6

  1. Lecture 26 : Introduction to Higher Order DEs YouTube
  2. Lecture 27 : Complementary Function YouTube
  3. Lecture 28 : Particular Integral YouTube
  4. Lecture 29 : Cauchy-Euler Equations YouTube
  5. Lecture 30 : Method of Variation of Parameters YouTube

Week 7 :

  1. Lecture 31 : Improper Integral – Part 1 YouTube
  2. Lecture 32 : Improper Integral – Part 2 YouTube
  3. Lecture 33 : Improper Integral – Part 3 YouTube
  4. Lecture 34 : Improper Integral – Part 4 YouTube
  5. Lecture 35 : Beta & Gamma Function – Part 1 YouTube

Week 8 :

  1. Lecture 36 : Beta & Gamma Function – Part 2 YouTube
  2. Lecture 37 : Differentiation under the Integral Sign YouTube
  3. Lecture 38 : Double Integrals – Part 1 YouTube
  4. Lecture 39 : Double Integrals – Part 2 YouTube
  5. Lecture 40 : Double Integrals – Part 3 YouTube

Week 9 :

  1. Lecture 41 : Double Integrals – Part 4 YouTube
  2. Lecture 42 : Double Integrals – Part 5 YouTube
  3. Lecture 43 : Double Integrals – Part 6 YouTube
  4. Lecture 44 : Triple Integrals – Part 1 YouTube
  5. Lecture 45 : Triple Integrals – Part 2 YouTube

Week 10 :

  1. Lecture 46 : Vector Functions YouTube
  2. Lecture 47 : Vector and Scalar Fields YouTube
  3. Lecture 48 : Divergence and Curl of a Vector Field YouTube
  4. Lecture 49 : Line Integrals YouTube
  5. Lecture 50 : Conservative Vector Fields YouTube

Week 11 :

  1. Lecture 51 : Green’s Theorem YouTube
  2. Lecture 52 : Surface Integral (Part - 1) YouTube
  3. Lecture 53 : Surface Integrals (Part - 2) YouTube
  4. Lecture 54 : Stokes’ Theorem YouTube
  5. Lecture 55 : Divergence Theorem YouTube

Week 12 :

  1. Lecture 56 : Application of Derivatives YouTube
  2. Lecture 57 : Application of Derivatives-Continued YouTube
  3. Lecture 58 : Properties of Gradient, Divergence and Curl YouTube
  4. Lecture 59 : Properties of Gradient, Divergence and Curl-Continued YouTube
  5. Lecture 60 : Curl and Integrals YouTube

Syllabus and materials

At NPTEL, as the course publishes them.

Credits and licence

Institution
IIT Kharagpur
Department
Mathematics
Taught by
Prof. Jitendra Kumar, Prof. Somesh Kumar
Level
Undergraduate
Language
English
Subjects
Mathematics
Source
NPTEL
Licence
CC BY-NC-SA, as NPTEL states it. Non-commercial use only. NPTEL's terms
Attribution
NPTEL states: "Distributed under Creative Commons Attribution-ShareAlike / CC BY - NC - SA", beside a BY-NC-SA badge.
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