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《微積分(1)》是英文版大學數學微積分教材，分為上、下兩冊。上冊為單變量微積分學，包括函數、極限和連續、導數、中值定理及導數的應用以及一元函數積分學等內容；下冊為多變量微積分學，包括空間解析幾何及嚮量代數、多元函數微分學、重積分、綫積分與麵積分、級數及微分方程初步等內容。

《微積分(1)》由兩位國內作者和一位外籍教授共同完成，在內容體係安排上與國內主要微積分教材一緻，同時也充分參考和藉鑒瞭國外尤其是北美一些大學微積分教材的諸多特點，內容深入淺齣，語言簡潔通俗。

《微積分(1)》適閤作為大學本科生一學年微積分教學的教材，也可作為非英語教學的參考書。

CHAPTER 1 Functions, Limits and Continuity 1.1 Mathematical Sign Language 1.1.1 Sets 1.1.2 Number 1.1.3 Intervals 1.1.4 Implication and Equivalence 1.1.5 Inequalities and Numbers 1.1.6 Absolute Value of a Number 1.1.7 Summation Notation 1.1.8 Factorial Notation 1.1.9 Binomial Coefficients 1.2 Functions 1.2.1 Definition of a Function 1.2.2 Properties of Functions 1.2.3 Inverse and Composite Functions 1.2.4 Combining Functions 1.2.5 Elementary Functions 1.3 Limits 1.3.1 The Limit of a Sequence 1.3.2 The Limits of a Function 1.3.3 One-sided Limits 1.3.4 Limits Involving the Infinity Symbol 1.3.5 Properties of Limits of Functions 1.3.6 Calculating Limits Using Limit Laws 1.3.7 Two Important Limit Results 1.3.8 Asymptotic Functions and Small o Notation 1.4 Continuous and Discontinuous Functions 1.4.1 Definitions 1.4.2 Building Continuous Functions 1.4.3 Theorems on Continuous Functions 1.5 Further Results on Limits 1.5.1 The Precise Definition of a Limit 1.5.2 Limits at Infinity and Infinite Limits 1.5.3 Real Numbers and Limits 1.5.4 Asymptotes 1.5.5 Uniform Continuity 1.6 Additional Material 1.6.1 Cauchy 1.6.2 Heine 1.6.3 Weierstrass 1.7 Exercises 1.7.1 Evaluating Limits 1.7.2 Continuous Functions 1.7.3 Questions to Guide Your RevisionCHAPTER 2 Differential Calculus 2.1 The Derivative 2.1.1 The Tangent to a Curve 2.1.2 Instantaneous Velocity 2.1.3 The Definition of a Derivative 2.1.4 Notations for the Derivative 2.1.5 The Derivative as a Function 2.1.6 One-sided,Derivatives 2.1.7 Continuity of Differentiable Functions 2.1.8 Functions with no Derivative 2.2 Finding the Derivatives 2.2.1 Derivative Laws 2.2.2 Derivative of an Inverse Function 2.2.3 Differentiating a Composite Funetion--The Chain Rule 2.3 Derivatives of Higher Orders 2.4 Implicit Differentiation 2.4.1 Implicitly Defined Functions 2.4.2 Finding the Derivative of an Implicitly Defined Function 2.4.3 Logarithmic Differentiation 2.4.4 Functions Defined by Parametric Equations 2.5 Related Rates of Change 2.6 The Tangent Line Approximation and the Differential 2.7 Additional Material 2.7.1 Preliminary result needed to prove the Chain Rule 2.7.2 Proof of the Chain Rule 2.7.3 Leibnitz 2.7.4 Newton 2.8 Exercises 2.8.1 Finding Derivatives 2.8.2 Differentials 2.8.3 Questions to Guide Your Revision 3 The Mean Value Theorem and Applications of theCHAPTER 3 The Mean Value Theorem and Applications of the Derivative 3.1 The Mean Value Theorem 3.2 L'Hospital's Rule and Indeterminate Forms 3.3 Taylor Series 3.4 Monotonic and Concave Functions and Graphs 3.4.1 Monotonic Functions 3.4.2 Concave Functions 3.5 Maximum and Minimum Values of Functions 3.5.1 Global Maximum and Global Minimum 3.5.2 Curve Sketching 3.6 Solving Equations Numerically 3.6.I Decimal Search 3.6.2 Newton's Method 3.7 Additional Materia 3.7.1 Fermat 3.7.2 L'Elospital 3.8 Exercises 3.8.l The Mean Value Theorem 3.8.2 L'Hospital's Rules 3.8.3 Taylor's Theorem 3.8.4 Applications of the Derivative 3.8.5 Questions to Guide Your RevisionCHAPTER 4 Integral Calculus 4.1 The Indefinite Integral 4.1.1 Definitions and Properties of Indefinite Integrals 4.1.2 Basic Antiderivatives 4.1.3 Properties of Indefinite Integrals 4.1.4 Integration By Substitution 4.1.5 Further Results Using Integration by Substitution 4.1.6 Integration by Parts 4.1.7 Partial Fractions in Integration 4.1.8 Rationalizing Substitutions 4.2 Definite Integrals and, the Fundamental Theorem of Calculus 4.2.1 Introduction 4.2.2 The Definite Integral 4.2.3 Interpreting ∫f(x) dx as an Area 4.2.4 Interpreting ∫f(t) dt as a Distance 4.2.5 Properties of the'Definite Integral 4.2.6 The Fundamental Theorem of Calculus 4.2.7 Integration by Substitution 4.2.8 Integration by Parts 4.2.9 Numerical Integration 4.2.10 Improper Integrals 4.3 Applications of the Definite Integral 4.3.1 The Area of the Region Between Two Curves 4.3.2 Volumes of Solids of Revolution 4.3.3 Arc Length 4.4 Additional Material 4.4.1 Riemann 4.4.2 Lagrange 4.5 Exercises 4.5.1 Indefinite Integrals 4.5.2 Definite Integrals 4.5.3 Questions to Guide Your RevisionAnswersReference Books
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