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Calculus I

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Table of Contents
Chapter 1 Limits
1.1 Functions
1.1.1 Mapping
1.1.2 Function of Single Variable
1.1.3 Elementa ry Functions and Hyperbolic Functions
Exercise
1.2 The Concept ot Ljmits and its Properties
1.2.1 Limits of Sequence
1.2.2 Limits of Functions
1.2.3 Properties of Limits
Exercise
1.3 Rules for Finding Limits
1.3.1 Operation on Limits
1.3.2 Limits Theorem
1.3.3 Two Important Special Limits
Exercise
1.4 Infinitesimal and Infinite
1.4.1 Infinitesimal
1.4.2 Infinite
1.4.3 Compa rison between Infinitesimal
Exercise
1.5 Continuous Function
1.5.1 Continuity
1.5.2 Continuity of Elementa ry Functions
1.5.3 Discontinuity
1.5.4 Theo rems about Continuous Functions on a Closed InfervaI
Exercise
Chapter Review Exercise

Chapter 2 Differentiation
2.1 The Derivative
2.1.1 Two Prob Lems with one Theme
2.1.2 Definition of the Derivative
2.1.3 Geometric Interpretation of the De rivative
2.1.4 The Relationship between DifferentiabiIity and Continuity
Exercise
2.2 Finding Rules for Derivative
2,2.1 Derivative of Basic Elementa ry Functions
2.2.2 Derivative of Arithmetic CombinQtion
2.2.3 The Derivative Rule for Inverses
2.2.4 Derivative 04 Composition
2.2.5 Implicit DitferentiatIon
2.2.6 Parametric Dlfferentjalion
2.2.7 Related Rates Of Change
Exercise
2.3 Higher-Order Derivatives
Exercise
2.4 Differentials
2.4.1 Definition of Differentials
2.4.2 Differential Rules
2.4.3 Application of Diffe rentials in Approximation
Exercise
2.5 The Mean Value Theorem
2.5.1 Fermat’s Theorem
2.5.2 Rolle’s Theorem
2.5.3 Lagrange’s Theorem
2.5.4 Cauchy’s Theorem
Exercise
……

Chapter 3 The Integration
Chapter 4 Differential Equations
Solutions to Selected Problem
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