目录 Chapter 1 Function and limit 1.1 Function 1.1.1 Set 1.1.2 Function 1.1.3 Elementary functions Exercises 1-1 1.2 Limit 1.2.1 Limit of sequence 1.2.2 Limit of function Exercises 1-2 1.3 Rules of limit operations 1.3.1 Rational operation rules 1.3.2 Operation rule for composite function Exercises 1-3 1.4 Principle of limit existence and two important limits 1.4.1 Principle of limit existence 1.4.2 Two important limits Exercises 1-4 1.5 Infinitesimal and infinity 1.5.1 Infinitesimal 1.5.2 Infinity 1.5.3 Comparison of infinitesimal order Exercises 1-5 1.6 Continuity of function and the properties 1.6.1 Continuity of function and discontinuity 1.6.2 Operations on continuous functions and the continuity of elementary functions 1.6.3 Properties of continuous functions on a closed interval Exercises 1-6 Summary Quiz Exercises Chapter 2 Derivative and differential 2.1 Definition of derivatives 2.1.1 Cited examples 2.1.2 Definition of derivatives 2.1.3 Geometric interpretation of derivative 2.1.4 Use the unit to explain derivative 2.1.5 Relationship between derivability and continuity 2.1.6 The application of derivative in natural science Exercises 2-1 2.2 Rules of finding derivatives 2.2.1 Derivative formulas for several fundamental elementary functions 2.2.2 Derivation rules of rational operations 2.2.3 Derivative of inverse functions 2.2.4 Derivation rules of composite functions Exercises 2-2 2.3 Higher-order derivatives 2.3.1 The concept of higher order derivative 2.3.2 The linear property and Leibniz formula Exercises 2-3 2.4 Derivation of implicit functions and parametric equations 2.4.1 Derivation of implicit functions 2.4.2 Logarithmic derivation method 2.4.3 Derivation of parametric equations 2.4.4 Derivative of the function expressed by the polar equation Exercises 2-4 2.5 Differential of the function 2.5.1 Concept of the differential 2.5.2 The necessary and sufficient condition for differential 2.5.3 Geometric meaning of differential 2.5.4 Differential rules of elementary functions 2.5.5 Application of the differential Exercises 2-5 2.6 The application of derivative in economic analysis 2.6.1 Marginal analysis 2.6.2 Elasticity analysis Exercises 2-6 Summary Quiz Exercises Chapter 3 The mean value theorem 3.1 Mean value theorems the differential calculus 3.1.1 Format Lemma 3.1.2 Rolle's Theorem 3.1.3 Lagrange's Theorem 3.1.4 Cauehy's Theorem Exercises 3-1 3.2 Taylor's Theorem Exercises 3-2 Summary Quiz Exercises Chapter 4 Applications of derivatives 4.1 Indeterminate form limit 4.1.1 The indeterminate form of type 00 4.1.2 The indeterminate form of type ∞∞ 4.1.3 Other indeterminate forms Exercises 4-1 4.2 Monotonicity and local extreme value 4.2.1 Monotonieity of functions 4.2.2 The extreme value of function 4.2.3 Maximum value and minimum value of function Exercises 4-2 4.3 The convexity, concavity and inflection point of function Exercises4-3 4.4 Description of the function graph 4.4.1 Asymptote of curve 4.4.2 Description of the function graph Exercises 4-4 4.5 Curvature 4.5.1 Differentiation of an arc 4.5.2 Calculation formula of curvature 4.5.3 Curvature circle Exercises 4-5 4.6 Approximation of equation 4.6.1 Bisection method 4.6.2 Tangent method Exercises 4-6 4.7 The application of extreme value of function in economic management 4.7.1 Demand analysis 4.7.2 Problems of minimum average cost 4.7.3 Problems of minimizing inventory cost 4.7.4 Problems of maximal profit 4.7.5 Problems of maxima
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