Learn · NPTEL

Course11110414440 lectures

Basic Calculus 1 and 2

Prof. Parasar Mohanty · IIT Kanpur

Start with lecture 1 At NPTEL

Lectures

Week 1: Real number system and Limits

  1. Lecture 1: Real numbers and Archimedean property Video
  2. Lecture 2: Supremum and Decimal representation of Reals Video
  3. Lecture 3: Functions Video
  4. Lecture 4: Functions continued and Limits Video
  5. Lecture 5: Limits continued. Video

Week 2: Continuity and Differentiation of functions

  1. Lecture 6: Limits (continued) and Continuity Video
  2. Lecture 7: Continuity and Intermediate Value Property Video
  3. Lecture 8: Differentiation Video
  4. Lecture 9: Chain Rule Video
  5. Lecture 10: Nth derivative of a function Video

Week 3: Plotting graph of functions

  1. Lecture 11: Local extrema and Rolle's theorem Video
  2. Lecture 12: Mean value theorem and Monotone functions Video
  3. Lecture 13: Local extremum tests Video
  4. Lecture 14: Concavity and points of inflection Video
  5. Lecture 15: Asymptotes and plotting graph of functions. Video

Week 4: L'Hospital Rule and Integration

  1. Lecture 16: Optimization and L'Hospital Rule Video
  2. Lecture 17: L'Hospital Rule continued and Cauchy Mean value theorem Video
  3. Lecture 18: Approximation of Roots Video
  4. Lecture 19: Antiderivative and Riemann Integration Video
  5. Lecture 20: Riemann's criterion for Integrability Video

Week 5: Integration and its numerical methods

  1. Lecture 21: Integration and its properties Video
  2. Lecture 22: Area and Mean value theorem for integrals Video
  3. Lecture 23: Fundamental theorem of Calculus Video
  4. Lecture 24: Integration by parts and Trapezoidal rule Video
  5. Lecture 25: Simpson's rule and Substitution in integrals Video

Week 6: Applications of Integration

  1. Lecture 26: Area between curves Video
  2. Lecture 27: Arc Length and Parametric curves Video
  3. Lecture 28: Polar Co-ordinates Video
  4. Lecture 29: Area of curves in polar coordinates Video
  5. Lesson 30: Volume of solids Video

Week 7: Improper Integrals, Sequences and Series

  1. Lecture 31: Improper Integrals Video
  2. Lecture 32: Sequences Video
  3. Lecture 33: Algebra of sequences and Sandwich theorem Video
  4. Lecture 34: Subsequences Video
  5. Lecture 35: Series Video

Week 8: Series and its convergence

  1. Lecture 36: Comparison tests for Series Video
  2. Lecture 37: Ratio and Root test for series Video
  3. Lecture 38: Integral test and Leibniz test for series Video
  4. Lecture 39: Revision I Video
  5. Lecture 40: Revision II Video

Syllabus and materials

At NPTEL, as the course publishes them.

Credits and licence

Institution
IIT Kanpur
Department
Mathematics
Teacher
Prof. Parasar Mohanty
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.
Who can watch
NPTEL gives no rating. Invisible Network shows it to Tweens profiles and older, judged from what the source says about it. How courses are placed