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醉染图书微积分9787568028394
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Chapter 1 Functions(1)
1.1 Preliminary knowledge(1)
1.1.1 Inequalities and their properties(1)
1.1.2 Absolute value and its properties(5)
1.1.3 The range of variable(8)
1.2 Functions(10)
1.2.1 Concept of functions(10)
1.2.2 Features of a function(12)
1.. Inverse functions(16)
1.2.4 Coite functions(19)
1.2.5 Elementary functions(20)
1.2.6 Non-elementary functions(30)
1.2.7 Implicit functions(33)
Exercise 1(33)
Chapter 2 Limit and Continuity(36)
2.1 Limit(36)
2.1.1 Definition of a sequence(36)
2.1.2 Descriptive definition of limit of a sequence(36)
2.1.3 ntitative definition of limit of a sequence(38)
2.2 Limits of functions(39)
2.2.1 Definition of finite limits of functions as x→x0(39)
2.2.2 Definition of infinite limits of functions as x→x0(42)
2.. Limits of functions as independent variable tending to infinity(44)
2.2.4 Left limit and right limit(47)
2.2.5 The properties of limits of functions(48)
2.2.6 Oraio rules of limits(50)
2.2.7 Criteria of existence of limits and two important limits (54)
2.2.8 Infinitesimal, infinity and their basic properties(58)
2.2.9 Simple application of limit in economics(62)
. Continuity of functions(64)
..1 Continuity(64)
..2 Discontinuous points of a function(68)
.. Oraios and properties of continuous functions(69)
..4 Continuity of elementary functions(72)
..5 Continuity of the inverse functions(73)
.. Properties of continuous functions on closed interval(73)
Exercise 2(76)
Chapter 3 Derivative and differential(80)
3.1 Concept of derivative(80)
3.1.1 Introduction of derivative(80)
3.1.2 Definition of derivative(82)
3.1.3 Left-hand derivative and right-hand derivative(84)
3.1.4 The relationship between differentiability and continuity of functions(85)
3.1.5 Applying the definition of derivative to find derivatives(87)
3.1.6 Geometric interpretation of derivative(91)
3.2 Rules of finding derivatives(91)
3.2.1 Four arithmetic oraio rules of derivatives(91)
3.2.2 Derivative rules of coite functions(93)
3.. Derivative rules of inverse functions(95)
3.2.4 Derivative rules of implicit functions(96)
3.2.5 Derivative rules of function with parametric forms(97)
3.2.6 Some spe derivative rules(98)
3.2.7 Basic differentiation formulas(100)
3.2.8 Derivatives of higher order(102)
3.3 Differentials of functions(104)
3.3.1 Definition of differentials(104)
3.3.2 The equations of a tangent and a normal(107)
3.3.3 Formulas and oraio rule of differentials(109)
3.3.4 Application of differentials in approximating values(111)
Exercise 3(112)
Chapter 4 The mean value theorems and application of derivatives(116)
4.1 The mean value theorems(116)
4.1.1 Rolle’s theorem(116)
4.1.2 Lagrange’s theorem(118)
4.1.3 Cauchy’s theorem(121)
4.2 L’Hospital’s rule(1)
4.2.1 Evaluating limits of indeterminate forms of the type 00(124)
4.2.2 Evaluating the limits of indeterminate forms of the type ∞∞(126)
4.. Evaluating the limits of other indeterminate forms(127)
4.3 Taylor formula(129)
4.4 Discuss properties of functions by derivatives(136)
4.4.1 Monotonicity of functions(136)
4.4.2 Concavity and Convexity(140)
4.5 Extreme values(143)
4.6 Absolute maxima (minima) and its application(148)
4.6.1 Absolute maxima (minima)(148)
4.6.2 Applied problems of absolute maxima (minima)(150)
4.7 Graphing(152)
4.7.1 Asytte lines of curves(152)
4.7.2 Sophisticated graphing(154)
4.8 Application of derivatives in economics(158)
4.8.1 Marginal analysis(158)
4.8.2 Elasticity of function(164)
Exercise 4(169)
Chapter 5 Indefinite integrals(173)
5.1 Anti-derivative and indefinite integral(173)
5.1.1 Concept of anti-derivatives(173)
5.1.2 Concept of indefinite integrals(175)
5.2 Fundamental integral formulas(177)
5.3 Integral methods of substitution(180)
5.3.1 The first kind of substitution(180)
5.3.2 The second kind of substitution(185)
5.4 Integration by parts(189)
5.5 Evaluate indefinite integrals of some spe type(194)
5.5.1 Integrals of rational functions(194)
5.5.2 Integrals of irrational functions(198)
5.5.3 Integrals of trigonometric functions(199)
5.5.4 Integral of piecewise defined function(201)
Exercise 5(202)
Chapter 6 Definite integrals(205)
6.1 Definition of definite integrals(205)
6.1.1 Two examples for definite integrals(205)
6.1.2 Definition of definite integrals(207)
6.1.3 Geometric meaning of definite integrals(211)
6.2 Basic properties of definite integrals(212)
6.3 Fundamental theorem of calculus(219)
6.3.1 A function of upper limit of integral(219)
6.3.2 Newton-Leibniz formula(222)
6.4 Integration by substitution and by parts for definite integrals(224)
6.4.1 Integration by substitution for definite integrals(225)
6.4.2 Integration by parts for definite integrals(229)
6.5 Improper integrals(1)
6.5.1 Improper integrals on infinite intervals(1)
6.5.2 Improper integrals of unbounded functions()
6.6 Application of integrals(241)
6.6.1 Computing areas of plan figures(241)
6.6.2 Volume of a solid of revolution(245)
6.6.3 Some economic applications of integrals(247)
Exercise 6(249)
Answers to exercises(256)
Answers to exercise1(256)
Answers to exercise2(257)
Answers to exercise3(257)
Answers to exercise4(259)
Answers to exercise5(261)
Answers to exercise6(262)
毛纲源,武汉理工大资教授,于武汉大学,留校任教,后调入武汉工业大学(现合并为武汉理工大学)担任数学物理系系主任,在高校从事数学教学与科研工作40余年,除了出版多部专著(早在1998年,世界科技出版公司World Scientific Publishing Company就出版过他主编的线代数Linear Algebra的英文教材)和发表数十篇专业外,还发表10余篇考研数学。主讲微积分、线代数、概率论与数理统计等课程。理论功底深厚,教学经验丰富,思维独特。曾多次受邀在各地主讲考研数学,得到学员的广泛认可和一致:“知识渊博,讲解深入浅出,易于接受”“解题方法灵活,技巧独特,辅导针对极强”“对考研数学的出题形式、重点难点了如指掌,上他的辅导班受益匪浅”。
周海婴,北京师范大学珠海分校副教授,于南开大学,香港浸会大学数学博士,主讲微积分、概率论与数理统计、统计学、抽样技术等课程。在靠前外期刊发表中英文10余篇。
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