PRACTICE PROBLEMS

 1 The Real Number System 2 Convergence of a Sequence, Monotone Sequences 3 Cauchy Criterion, Bolzano - Weierstrass Theorem 4 Continuity and Limits 5 Existence of Maxima/Minima, Intermediate Value Property 6 Differentiability, Rolle's Theorem 7 Mean Value Theorem, Cauchy Mean Value Theorem, L'Hospital Rule 8 Fixed Point Iteration Method, Newton's Method 9 Tests for maxima and minima, Curve sketching 10 Taylor's Theorem 11 Series: Definition, Necessary and sufficient conditions, absolute convergence 12 Comparison, Limit comparison and Cauchy condensation tests 13 Ratio and Root tests, Leibniz's Test 14 Power Series, Taylor Series 15 Integration, Riemann's Criterion for integrability (Part I) 16 Integration, Riemann's Criterion for integrability (Part II) 17 Fundamental Theorems of Calculus, Riemann Sum 18 Improper Integrals Uniform Continuity (Not for Examination) 19 Area of a region between curves; Polar Coordinates 20 Area in Polar Co-ordinates, Volume of a Solid by Slicing 21 Washer and Shell Methods, Length of a plane curve 22 Areas of Surfaces of Revolution; Pappus's Theorems 23 Review of vectors, equations of lines and planes, Quadric Surfaces 24 Calculus of Vector Valued Functions I: Parametric curves 25 Calculus of Vector Valued Functions II: Tangent, Normal and Curvature 26 Functions of several variables : Sequences, continuity and partial derivatives 27 Functions of several variables : Differentiabilty and Chain Rule 28 Directional derivative, gradient and tangent plane 29 Mixed Partial Derivatives, Mean Value Theorem and Extended Mean Value theorem 30 Maxima, Minima, Second Derivative Test 31 Method of Lagrange Multipliers 32 Double integral 33 Change of variables in double integrals, Polar coordinates 34 Triple integral, Change of variables, Cylindrical and Spherical coordinates 35 Parametric surfaces, surface area and surface integrals 36 Line integrals 37 Green's  Theorem 38 Stokes' Theorem 39 Divergence Theorem