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醉染图书微积分9787568028400
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Chapter 7 Infinite Series(1)
7.1 Series(1)
Exercises 7.1(5)
7.2 Series with Positive Terms(7)
7.2.1 The Comparison Tests(7)
7.2.2 The Root and Ratio Tests(11)
Exercises 7.2(14)
7.3 Alternating Series and Absolute Convergence(15)
7.3.1 Alternating Series (15)
7.3.2 Absolute Convergence(18)
Exercises 7.3(19)
7.4 Power Series(20)
Exercises 7.4(26)
7.5 Differentiation and Integration of Power Series(27)
Exercises 7.5(30)
7.6 Taylor Series(31)
7.6.1 The Taylor Polynomials at x=0 (or Maclaurin Polynomials)(31)
7.6.2 The Taylor’s series(or Maclaurin series) for function f at 0 (32)
7.6.3 The Taylor’s series for function f at a (an arbitrary real number)(33)
Exercises 7.6(38)
Chapter 8 Partial Derivatives and Double Integrals(39)
8.1 Functions of Two Variables(39)
Exercises 8.1(45)
8.2 LimisndCntinuity(45)
8.2.1 Limits(45)
8.2.2 Continuity(48)
Exercises 8.2(50)
8.3 Partial Derivatives(51)
8.3.1 Definition(51)
8.3.2 Economical Interpretations of Partial Derivatives(55)
8.3.3 Geometric Interpretations of Partial Derivatives(56)
Exercises 8.3(57)
8.4 Strategy for Finding Partial Derivatives(58)
8.4.1 The Chain Rule(58)
8.4.2 Implicit Differentiation(62)
8.4.3 Higher Derivatives(64)
Exercises 8.4(66)
8.5 Total Differentials(68)
8.5.1 Definition(68)
8.5.2 Relations between Continuity, Partial Derivatives, and Differentiability(69)
8.5.3 Rules for Finding Total Differentials(70)
8.5.4 The Invariance of First Order Total Differential Form(71)
Exercises 8.5(73)
8.6 Extremum of Functions of Two Variables(74)
8.6.1 Locating Maxima and Minima(74)
8.6.2 Methods of Finding Absolute Maxima and Minima(78)
8.6.3 Methods of Finding Conditional Extremum(79)
Exercises 8.6(82)
8.7 Directional Derivatives and The Gradient Vector(83)
8.7.1 Vectors and Vector Oraios(83)
8.7.2 Directional Derivatives and The Gradient Vector(85)
8.7.3 The Relation between Directional Derivatives and The Gradient Vector(88)
Exercises 8.7(90)
8.8 Double Integrals(91)
8.8.1 Definition and Properties(91)
8.8.2 Double Integrals in Rectangular Coordinates(94)
8.8.3 Polar Coordinates(102)
8.8.4 Double Integrals in Polar Coordinates(106)
8.8.5 Application of Double Integrals(108)
Exercises 8.8(109)
Chapter 9 Differential Equations(112)
9.1 Introduction(112)
Exercises 9.1(114)
9.2 First-Order Linear Differential Equations(114)
9.2.1 Separable Equations(115)
9.2.2 Homogeneous Differential Equations(117)
9.. First-Order Linear Differential Equations(118)
9.2.4 Total (or Exact) Differential Equations(121)
9.2.5 Bernoulli Equations(Equations reducible to a linear one)(1)
9.2.6 Euler Equations(124)
Exercises 9.2(126)
9.3 Second-order Differential Equations(127)
9.3.1 Reducible Second-Order Differential Equations(127)
9.3.2 Complex Numbers (129)
9.3.3 Homogeneous Linear Equations(133)
9.3.4 Nonhomogeneous Linear Equations(137)
Exercises 9.3(142)
Chapter 10 Difference Equations(143)
10.1 Introduction (143)
10.1.1 Definition(143)
10.1.2 Properties(144)
Exercises 10.1(147)
10.2 Linear Difference Equations(147)
10.2.1 nth-Order Difference Equations(147)
10.2.2 First-Order Difference Equations(149)
10.. Second-Order Difference Equations(156)
Exercises 10.2(161)
毛纲源,武汉理工大学资深教授,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”。
梁敏,北京师范大学珠海分校副教授,于天津大学,美国托莱多大学数学硕士,美国罗格斯大学统计学硕士。主讲微积分、线代数、概率论与数理统计、商务统计、运筹学等课程。在靠前外不错期刊发表中英文10余篇。
马迎秋,北京师范大学珠海分校副教授,于渤海大学,爱尔兰都柏林大学数学硕士。主讲微积分、线代数、数学教学论、数学教学设计、数学史与数学文化等课程。在靠前外不错期刊发表中英文10余篇。
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