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September 23, 2023

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Description

Mathematics I. Instructor: Prof S. K. Ray, Department of Mathematics and Statistics, IIT Kanpur.

1. Calculus of Functions of One Variable
Real numbers, Functions, Sequences, Limit and Continuity, Differentiation : review, successive differentiation, chain rule and Leibnitz theorem, Rolle's and Mean Value Theorems, Maxima/ Minima, Curve sketching, Linear and quadratic approximations, Error estimates, Taylor's theorem, Newton and Picard methods, The Riemann integral, Approximate integration, Natural logarithm, Exponential function, Relative growth rates, L'Hospital's rule geometric applications of integrals, Infinite series, Tests of convergence, Absolute and conditional convergence, Taylor and maclaurin series.

2. Calculus of Functions of Several Variables
Scalar fields, Limit and continuity, Partial derivatives, Chain rules, Implicit differentiation, Directional derivatives, Total differential, Tangent planes and normals, Maxima, Minima and Saddle Points, Constrained maxima and minima, Double Integrals, Applications to Areas and Volumes, Change of variables.

3. Vector Calculus
Vector fields, divergence and curl, Line integrals, Green's theorem, Surface integrals, Divergence theorem, Stoke's theorem and application. (from nptel.ac.in)

Course Curriculum

  • Real Numbers Unlimited
  • Lecture 02 – Sequences I Unlimited
  • Lecture 03 – Sequences II Unlimited
  • Lecture 04 – Sequences III Unlimited
  • Lecture 05 – Continuous Functions Unlimited
  • Lecture 06 – Properties of Continuous Functions Unlimited
  • Lecture 07 – Uniform Continuity Unlimited
  • Lecture 08 – Differentiable Functions Unlimited
  • Lecture 09 – Mean Value Theorem (One Variable) Unlimited
  • Lecture 10 – Maxima/ Minima (One Variable) Unlimited
  • Lecture 11 – Taylor’s Theorem Unlimited
  • Lecture 12 – Curve Sketching Unlimited
  • Lecture 13 – Infinite Series I Unlimited
  • Lecture 14 – Infinite Series II Unlimited
  • Lecture 15 – Test of Convergence Unlimited
  • Lecture 16 – Power Series Unlimited
  • Lecture 17 – Riemann Integral Unlimited
  • Lecture 18 – Riemann Integrable Function Unlimited
  • Lecture 19 – Applications of Riemann Integral Unlimited
  • Lecture 20 – Length of a Curve Unlimited
  • Lecture 21 – Line Integrals Unlimited
  • Lecture 22 – Functions of Several Variables Unlimited
  • Lecture 23 – Differentiation Unlimited
  • Lecture 24 – Derivatives Unlimited
  • Lecture 25 – Mean Value Theorem (Multivariables) Unlimited
  • Lecture 26 – Maxima/ Minima (Multivariables) Unlimited
  • Lecture 27 – Method of Lagrange Multipliers Unlimited
  • Lecture 28 – Multiple Integrals Unlimited
  • Lecture 29 – Surface Integrals Unlimited
  • Lecture 30 – Green’s Theorem Unlimited
  • Lecture 31 – Stokes’ Theorem Unlimited
  • Lecture 32 – Gauss’ Divergence Theorem Unlimited

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