Lecture Notes of MTH101

Lecture 1

 The Real Number System PDF

Lecture 2

 Convergence of a Sequence, Monotone Sequences PDF

Lecture 3

 Cauchy Criterion, Bolzano - Weierstrass Theorem PDF

Lecture 4

 Continuity and Limits PDF

Lecture 5

 Existence of Maxima, Intermediate Value Property, Differentiabilty PDF

Lecture 6

 Rolle's Theorem, Mean Value Theorem PDF

Lecture 7

 Cauchy Mean Value Theorem, L'Hospital Rule PDF

Lecture 8

 Fixed Point Iteration Method, Newton's Method PDF

Lecture 9

 Sufficient Conditions for Local Maximum, Point of Inflection PDF

Lecture 10

 Taylor's Theorem PDF

Lecture 11-13

 Infinite Series, Convergence Tests, Leibniz's Theorem PDF

Lecture 14

 Power Series, Taylor Series PDF
 Lecture 15 - 16  Riemann Integration PDF
 Lecture 17  Fundamental Theorems of Calculus, Riemann Sum PDF
 Lecture 18  Improper Integrals PDF
   Uniform Continuity (Not for Examination) PDF
 Lecture 19 Area Between Two Curves; Polar Coordinates PDF
 Lecture 20 Area in Polar Coordinates,Volume of Solids PDF
 Lecture 21 Washer and Shell Methods, Length of a plane curve PDF
 Lecture 22  Areas of Surfaces of Revolution; Pappus's Theorems PDF
 Lecture 23  Review of vectors, equations of lines and planes; sequences in R^3 PDF
 Lecture 24  Calculus of Vector Valued Functions PDF
 Lecture 25  Principal Normal; Curvature PDF
 Lecture 26 -27  Functions of Several Variables : Continuity and Differentiability PDF
 Lecture 28  Directional Derivatives, Gradient, Tangent Plane PDF
 Lecture 29  Mixed derivative Theorem, MVT, Extended MVT PDF
 Lecture 30  Maxima, Minima, Second Derivative Test PDF
 Lecture 31  Lagrange Multiplier Method PDF
 Lecture 32  Double integrals PDF
 Lecture 33  Change of Variable in a Double Integral, Triple Integrals PDF
 Lecture 34  Change of Variables in a Triple Integral, Area of a Parametric Surface PDF
 Lecture 35  Surface Area, Surface Integrals PDF
 Lecture 36  Line Integrals, Green's Theorem PDF
 Lecture 37  Green's Theorem (contd.), curl, Divergence PDF
 Lecture 38   Stokes' Theorem PDF
 Lecture 39   The Divergence Theorem PDF