![]() The Derivative 185 Continuous Functions 188 Increasing and Decreasing Functions 191 Darboux's Theorem 194 Rolle's Theorem 195 Lagrange's Mean Value Theorem 196 Cauchy's Mean Value Theorem 198 Higher Order Derivatives 206ġ. Uniform Continuity 179įUNCTIONS OF A SINGLE VARIABLE (II) 1. Functions Continuous on Closed Intervals 4. ![]() Positive Term Series 114 Comparison Tests for Positive Term Series Cauchy's Root Test 124 D'Alembert's Ratio Test 125 Raabe's Test 127 Logarithmic Test 131 Integral Test 132 Gauss's Test 135 Series with Arbitrary Terms 139 Rearrangement of Terms 148įUNCTIONS OF A SINGLE VARIABLE (I) 1. Cauchy's General Principle of Convergence 73 7. Non-Convergent Sequences (Definitions) 68 6. Absolute Value of a Real Number 27 Chapter 2 Introduction 1 Field Structure and Order Structure 11 Bounded and Unbounded Sets: Supremum, Infimum 16 4 Completeness in the Set of Real Numbers 5. Khalsa College University of Delhi Delhi, IndiaĬontents Preface to the Second Edition Preface to the First Edition Chapter 1 ![]() Malik Savita Arora Department of Mathematics S.G.T.B.
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