Chapter 1 Functions, Limits, and Continuity 1.1 Functions 1.1.1 Linear and Quadratic Functions 1.1.2 Concept of Function 1.1.3 Polynomial and Rational Functions 1.1.4 Exponential and Logarithmic Functions 1.1.5 Trigonometric Functions and Functional Properties 1.2 Limits of Function 1.2.1 The Concept of Limit 1.2.2 Computation of Limits 1.3 Continuity of Function 1.3.1 The Continuity of Function 1.3.2* Continuous Compounding Chapter Summary Review Exercises Chapter 2 Differentiation of One Variable 2.1 The Concept of Derivative 2.1.1 Instantaneous Velocity and Derivative 2.1.2 Slope of Tangent Line on Geometric Interpretation of Derivative 2.1.3 Definition of Derivative and Rates of Change 2.2 Computations of Derivatives 2.2.1 Techniques of the Differentiation 2.2.2 Calculation Rules of Derivative 2.3 Compound Function and Its Chain Rule 2.3.1 Compound Function and Its Chain Rule 2.3.2 Implicit Differentiation 2.4 Second-Order Derivative and Differential 2.4.1 Second-Order Derivative 2.4.2 The Concept and Computation of Differential 2.5 Application of the Derivative 2.5.1 Increasing and Decreasing Functions in the Derivative 2.5.2 Concavity and Points of Inflection of Functions 2.5.3 Relative Maximum and Relative Minimum of Functions Chapter Summary Review Exercises Chapter 3 Integration of One Variable 3.1 Indefinite Integration 3.1.1 The Concept of Indefinite Integration 3.1.2 The Computing Rules and Formulas of Indefinite Integration 3.1.3 Integration by Substitution 3.1.4 Integration by Parts 3.2 Definite Integration 3.2.1 Definite Integral and the Fundamental Theorem of Calculus 3.2.2 The Computation of Definite Integral 3.2.3 Applications of Integration 3.2.4 Improper Integrals Chapter Summary Review Exercises Chapter 4 Calculus of Several Variables 4.1 Functions of Several Variables 4.1.1 Functions of Two or More Variables 4.1.2 Graphs of Functions of Two Variables 4.2 Partial Derivatives 4.2.1 Compute and Interpret Partial Derivatives 4.2.2 Geometric Interpretation of Partial Derivatives 4.2.3 Second-order Partial Derivatives 4.2.4 The Chain Rule for Partial Derivatives 4.3 Optimizing Functions of Two Variables 4.3.1 The Extreme Value Property for a Function of Two Variables 4.3.2 Apply the Extreme Value Property to the Functions of Two Variables 4.3.3* The Method of Least-Squares 4.3.4* The Least-Squares Line 4.4 Double Integrals 4.4.1 The Double Integral over a Rectangular Region 4.4.2 Double Integrals over Nonrectangular Regions 4.4.3 The Applications of Double Integrals Chapter Summary Review Exercises APPENDIXES APPENDIX A APPENDIX B APPENDIX C English-Chinese Vocabulary

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