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Chapter 1 Limit and Continuity 1.1 Functions 1.1.1 Mopping 1.1.2 Function of Single Vorioble 1.1.3 Elementory Functions ond Hyperbolic Functions Exercise 1.1 1.2 The Concept of Limits and its Properties 1.2.1 Limits of Sequence 1.2.2 Limits of Functions 1.2.3 Properties of Limits Exercise 1.2 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 1.3 1.4 Infinitesimal and Infinite 1.4.1 Infinitesimal 1.4.2 Infinite 1.4.3 Comparison between Infinitesimal Exercise 1.4 1.5 Continuous Function 1.5.1 Continuity 1.5.2 Continuity of Elementary Functions 1.5.3 Discontinuity 1.5.4 Theorems about Continuous Functions on a Closed Interval Exercise 1.5 Chapter Review Exercise Chapter 2 Differentiation 2.1 The Derivative 2.1.1 Two Problems with one Theme 2.1.2 Definition of the Derivative 2.1.3 Geometric Interpretation of the Derivative 2.1.4 The Relationship between Differentiability and Continuity Exercise 2.1 2.2 Finding Rules for Derivative 2.2.1 Derivative of Basic Elementary Functions 2.2.2 Derivative of Arithmetic Combination 2.2.3 The Derivative Rule for Inverses 2.2.4 Derivative of Composition 2.2.5 Implicit Differentiation 2.2.6 Parametric Differentiation 2.2.7 Related Rates of Change Exercise 2.2 2.3 Higher-Order Derivatives Exercise 2.3 2.4 Differentials 2.4.1 Definition of Differentials 2.4.2 Differential Rules 2.4.3 Application of Differentials in Approximation