高等数学(上)(英文版)

Chapter 1 Limits 1．1 The Concept of Limits and its Properties 1．1．1 Limits of Sequence 1．1．2 Limits of Functions 1．1．3 Properties of Limits Exercise 1．1 1．2 Limits Theorem 1．2．1Rules for Finding Limits 1．2．2 The Sandwich Theorem 1．2．3 Monotonic Sequence Theorem 1．2．4 The Cauchy Criterion Exercise 1．2 1．3 Two Important Special limits Exercise 1．3 1．4 Infinitesimal and Infinite 1．4．1 Infinitesimal 1．4．2 Infinite Exercise 1．4 1．5 Continuous Function 1．5．1 Continuity 1．5．2 Discontinuity Exercise 1．5 1．6 Theorems about Continuous Function on a Closed Interval Exercise 1．6 Review and Exercise Chapter 2 Differentiation 2．1 The Derivative Exercise 2．1 2．2 Rules far Finding the Derivative 2．2．1 Derivative of Arithmetic Combination 2．2．2 The Derivative Rule for Inverses 2．2．3 Derivative of Composition 2．2．4 Implicit Differentiation 2．2．5 Parametric Differentiation 2．2．6 Related Rates of Change Exercise 2．2 2．3 Higher-Order Derivatives Exercise 2．3 2．4 Differentials Exercise 2．4 2．5 The Mean Value Theorem Exercise 2．5 2．6 L'Hopital's Rule Exercise 2．6 2．7 Taylor's Theorem Exercise 2．7 2．8 Applications of Derivatives 2．8．1 Monotonicity 2．8．2 Local Extreme Values 2．8．3 Extreme Values 2．8．4 Concavity 2．8．5 Graphing Functions Exercise 2．8 Review and Exercise …… Chapter 3 The Integration Chapter 4 Differential Equations Solutions to Selected Problem