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Course10910412440 lectures

Calculus of One Real Variable

Prof. Joydeep Dutta · IIT Kanpur

Start with lecture 1 At NPTEL

About

This course intend to develop a thorough understanding of the fundamental aspects of calculus of single variable which is fundamental tool in Sciences, Engineering and Economics.

Intended audience: First year engineering, science and economics students with mathematics as main course.Prerequisites : Basic mathematics till 12th standard

Lectures

Week 1

  1. Introduction to Numbers YouTube
  2. Countability and Uncountability YouTube
  3. Examples of Irrational numbers YouTube
  4. Functions YouTube
  5. Limits of Functions-I YouTube

Week 2

  1. Limit of Functions- II YouTube
  2. Continuous Functions YouTube
  3. Intermediate Value Theorem YouTube
  4. Maximum Value Theorem YouTube
  5. Supremum and Infimum YouTube

Week 3

  1. Derivative of a Function YouTube
  2. Rules of Differentiation YouTube
  3. Maxima and Minima YouTube
  4. Rolle's Theorem and Lagrange Mean Value Theorem (MVT) YouTube
  5. Monotonic Functions and Inverse Functions YouTube

Week 4

  1. Newton’s Method for solving Equations YouTube
  2. Optimization Problems YouTube
  3. Integration-I : In the style of Newton and Leibnitz YouTube
  4. Integration-II : In the spirit of Newton and Leibnitz YouTube
  5. Integration-III : Newton and Leibnitz Style YouTube

Week 5

  1. Integration theory of Riemann-I YouTube
  2. Integration theory of Riemann-II YouTube
  3. Integration Rule YouTube
  4. Fundamental Theorem of Calculus (in Riemann style) YouTube
  5. The Kurzweil-Henstock Integral (K-H Integral) YouTube

Week 6

  1. Calculating Indefinite Integrals YouTube
  2. Improper Integral-I YouTube
  3. Improper Integral-II YouTube
  4. Application of Definite Integral-I YouTube
  5. Application of definite Integral-II YouTube

Week 7

  1. Application of definite Integral-III YouTube
  2. Application of definite Integral-III YouTube
  3. Numerical Integration-I YouTube
  4. Numerical Integration-II YouTube
  5. Sequences YouTube

Week 8

  1. Sequence (continued) YouTube
  2. Infinite Series YouTube
  3. infinite series (continued) YouTube
  4. Taylor's Theorem, other issues and end of the course-I YouTube
  5. Taylor's Theorem, other issues and end of the course-II YouTube

Syllabus and materials

At NPTEL, as the course publishes them.

Credits and licence

Institution
IIT Kanpur
Department
Mathematics
Teacher
Prof. Joydeep Dutta
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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