PRACTICE PROBLEMS

              1

 The Real Number System

PDF

              2

 Convergence of a Sequence, Monotone Sequences

PDF

              3

 Cauchy Criterion, Bolzano - Weierstrass Theorem

PDF

              4

 Continuity and Limits

PDF

              5

 Existence of Maxima/Minima, Intermediate Value Property

PDF

              6

 Differentiability, Rolle's Theorem

PDF

              7

 Mean Value Theorem, Cauchy Mean Value Theorem, L'Hospital Rule

PDF

              8

 Fixed Point Iteration Method, Newton's Method

PDF

              9

 Tests for maxima and minima, Curve sketching

PDF Figures

             10

 Taylor's Theorem

PDF

              11

 Series: Definition, Necessary and sufficient conditions, absolute convergence

PDF

              12

 Comparison, Limit comparison and Cauchy condensation tests

PDF

            13

 Ratio and Root tests, Leibniz's Test

PDF

            14

 Power Series, Taylor Series

PDF

             15

 Integration, Riemann's Criterion for integrability (Part I)

PDF

             16

 Integration, Riemann's Criterion for integrability (Part II)

PDF

             17

 Fundamental Theorems of Calculus, Riemann Sum

PDF

             18

 Improper Integrals

PDF Figures

 

 Uniform Continuity (Not for Examination)

 

            19

Area of a region between curves; Polar Coordinates

PDF Figures

            20

Area in Polar Co-ordinates, Volume of a Solid by Slicing

PDF Figures

            21

Washer and Shell Methods, Length of a plane curve

PDF Figures

            22

 Areas of Surfaces of Revolution; Pappus's Theorems

PDF

           23

 Review of vectors, equations of lines and planes, Quadric Surfaces

PDF Figures

           24

 Calculus of Vector Valued Functions I: Parametric curves

PDF Figures

           25

 Calculus of Vector Valued Functions II: Tangent, Normal and Curvature

PDF

           26

 Functions of several variables : Sequences, continuity and partial derivatives

PDF

           27

Functions of several variables : Differentiabilty and Chain Rule

PDF

           28

 Directional derivative, gradient and tangent plane

PDF

           29

Mixed Partial Derivatives, Mean Value Theorem and Extended Mean Value theorem

PDF

           30

Maxima, Minima, Second Derivative Test

PDF

           31

Method of Lagrange Multipliers

PDF

           32

Double integral

PDF Figures

           33

 Change of variables in double integrals, Polar coordinates

PDF Figures

           34

 Triple integral, Change of variables, Cylindrical and Spherical coordinates

PDF Figures

           35

 Parametric surfaces, surface area and surface integrals

PDF

           36

 Line integrals

PDF

           37

 Green's  Theorem

PDF 

           38

 Stokes' Theorem

PDF

           39

 Divergence Theorem

PDF