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Engineering mathematics
Ganesh, A.
اطلاعات کتابشناختی
ریاضیات مهندسی: آنالیز توابع مختلط، نظریه معادلات دیفرانسیل با مشتقات جزئی
پدیدآور اصلی :
حاجیجمشیدی، فرزین
ناشر :
صفار،
سال انتشار :
1378
موضوع ها :
ریاضیات مهندسی. آنالیز ترکیبی. معادلات دیفرانسیل.
شماره راهنما :
TA 330 .H36 1378
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Cover
(1)
Preface
(6)
Acknowledgement
(7)
Contents
(12)
Unit-l.Differential Calculus—I
(18)
1.1 Introduction
(18)
1.2 Radius of Curvature
(18)
1.2.1 Radius of Curvature in Cartesian Form
(19)
1.2.2 Radius of Curvature in Parametric Form
(20)
Worked Out Examples
(21)
Exercise 1.1
(35)
1.2.3 Radius of Curvature in Pedal Form
(36)
1.2.4 Radius of Curvature in Polar Form
(36)
Worked Out Examples
(38)
Exercise 1.2
(43)
1.3 Some Fundamental Theorem
(44)
1.3.1 Rolle’s Theorem
(44)
1.3.2 Lagrange’s Mean Value Theorem
(44)
1.3.3 Cauchy’s Mean Value Theorem
(45)
1.3.4 Taylor’s Theorem
(46)
Worked Out Examples
(47)
Exercise 1.3
(67)
Additional Problems (From Previous Years VTU Exams.)
(69)
Objective Questions
(74)
Unit-ll Differential Calculus–II
(78)
2.1 Indeterminate Forms
(78)
2.1.1 Indeterminate Form 0/0
(78)
Wroked Out Examples
(79)
Exercise 2.1
(85)
2.1.2 Indeterminate Forms ∞ – ∞ and 0 × ∞
(86)
Worked Out Examples
(86)
Exercises 2.2
(91)
2.1.3 Indeterminate Forms 00, 1∞, ∞0, 0∞
(91)
Worked Out Examples
(91)
Exercise 2.3
(94)
2.2 Taylor’s Theorem for Functions of two Variables
(95)
Worked Out Examples
(95)
Exercise 2.4
(99)
2.3 Maxima and Minima of Functions of two Variables
(100)
2.3.1 Necessary and Sufficient Conditions for Maxima and Minima
(100)
Worked Out Examples
(101)
Exercise 2.5
(106)
2.4 Lagrange’s Method of Undetermined Multipliers
(106)
Working Rules
(107)
Worked Out Examples
(108)
Exercise 2.6
(111)
Additional Problems (From Previous Years VTU Exams.)
(111)
Objective Questions
(118)
Unit-lll Integral Calculus
(122)
3.1 Introduction
(122)
3.2 Multiple Integrals
(122)
3.3 Double Integrals
(122)
Worked Out Examples
(123)
Exercise 3.1
(129)
3.3.1 Evaluation of a Double Integral by Changing the Order of Integration
(130)
3.3.2 Evaluation of a Double Integral by Change of Variables
(130)
3.3.3 Applications to Area and Volume
(130)
Worked Out Examples
(131)
Type 1. Evaluation over a given region
(131)
Type 2. Evaluation of a double integral by changing the order of integration
(136)
Type 3. Evaluation by changing into polars
(139)
Type 4. Applications of double and triple integrals
(141)
Exercise 3.2
(145)
3.4 Beta and Gama Functions
(146)
3.4.1 Definitions
(146)
3.4.2 Properties of Beta and Gamma Functions
(146)
3.4.3 Relationship between Beta and Gamma functions
(150)
Worked Out Examples
(152)
Exercise 3.3
(173)
Additional Problems (From Previous Years VTU Exams)
(176)
Objective Questions
(179)
Unit-lV Vector Integration and Orthogonal Curvilinear Coordinates
(183)
4.1 Introduction
(183)
4.2 Vector Integration
(183)
4.2.1 Vector Line Integral
(183)
Worked Out Examples
(183)
Exercise 4.1
(189)
4.3 Integral Theorem
(190)
4.3.1 Green’s Theorem in a Plane
(190)
4.3.2 Surface integral and Volume integral
(190)
4.3.3 Stoke’s Theorem
(191)
4.3.4 Gauss Divergence Theorem
(191)
Worked Out Examples
(191)
Exercise 4.2
(205)
4.4 Orthogonal Curvilinear Coordinates
(206)
4.4.1 Definition
(206)
4.4.2 Unit Tangent and Unit Normal Vectors
(206)
4.4.3 The Differential Operators
(208)
Worked Out Examples
(209)
Exercise 4.3
(211)
4.4.4. Divergence of a Vector
(211)
Worked Out Examples
(212)
Exercise 4.4
(213)
4.4.5 Curl of a Vector
(213)
Worked Out Examples
(214)
Exercise 4.5
(215)
4.4.6. Expression for Laplacian ∇2 ψ
(216)
4.4.7. Particular Coordinate System
(216)
Worked Out Examples
(220)
Exercise 4.6
(225)
Additional Problems
(225)
Objective Questions
(227)
Unit-V Differential Equations-I
(231)
5.1 Introduction
(231)
5.2 Linear Differential Equations of Second and Higher Order with Constant Coefficients
(231)
5.3 Solution of a Homogeneous Second Order Linear Differential Equation
(232)
Worked Out Examples
(232)
Exercise 5.1
(236)
5.4 Inverse Differential Operator And Particular Integral
(237)
5.5 Special Forms of X
(238)
Worked Out Examples
(241)
Exercise 5.2
(253)
Exercise 5.3
(258)
Exercise 5.4
(268)
5.6 Method of Undetermined Coefficients
(268)
Worked Out Examples
(269)
Exercise 5.5
(279)
5.7 Solution of Simultaneous Differential Equations
(281)
Worked Out Examples
(282)
Exercise 5.6
(284)
Additional Problems (From Previous Years VTU Exams.)
(285)
Objective Questions
(294)
Unit-Vl Differential Equations-II
(297)
6.1 Methods of Variation of Parameters
(297)
Worked Out Examples
(298)
Exercise 6.1
(308)
6.2 Solution of Cauchy’s Homogeneous Linear Equation And Lengendre’s Linear Equation
(309)
Worked Out Examples
(311)
Exercise 6.2
(323)
6.3 Solution of Initial and Boundary Value Problems
(325)
Worked Out Examples
(325)
Exercise 6.3
(327)
Additional Problems (From Previous Years VTU Exams.)
(327)
Objective Questions
(335)
Unit Vll Laplace Transforms
(338)
7.1 Introduction
(338)
7.2 Definition
(338)
7.3 Properties of Laplace Transforms
(338)
7.3.1 Laplace Transforms of Some Standard Functions
(339)
Worked Out Examples
(342)
Exercise 7.1
(347)
7.3.2 Laplace Transforms of the form eat f (t)
(348)
Worked Out Examples
(349)
Exercise 7.2
(352)
7.3.3 Laplace Transforms of the form t n f (t) Where n is a Positive Integer
(353)
7.3.4 Laplace Transforms of f(t)/t
(354)
Worked Out Examples
(354)
Exercise 7.3
(362)
7.4 Laplace Transforms of Periodic Functions
(363)
Worked Out Examples
(364)
Exercise 7.3
(368)
7.5 Laplace Transforms of Unit Step Function and Unit impulse Function
(369)
Unit Step Function (Heaviside function)
(369)
7.5.1 Properties Associated with the Unit Step Function
(369)
7.5.2 Laplace Transform of the Unit Impulse Function
(371)
Exercise 7.4
(376)
Additional Problems (From Previous Years VTU Exams.)
(377)
Objective Questions
(382)
Unit Vlll Inverse Laplace Transforms
(386)
8.1 Introduction
(386)
8.2 Inverse Laplace Transforms of Some Standard Functions
(386)
Worked Out Examples
(389)
8.3 Inverse Laplace Transforms Using Partial Fractions
(393)
Exercise 8.1
(399)
8.4 Inverse Laplace Transforms of the Functions of the form F(s)/s
(401)
Worked Out Example
(401)
Exercise 8.2
(404)
8.5 Convolution Theorem
(405)
Worked out Examples
(406)
Exercise 8.3
(413)
8.6 Laplace Transforms of the Derivatives
(414)
8.7 Solution of Linear Differential Equations
(415)
Worked Out Examples
(415)
Solution of Simultaneous Differential Equations
(423)
Exercise 8.4
(427)
8.8 Applications of Laplace Transforms
(428)
Worked Out Examples
(429)
Exercise 8.5
(433)
Additional Problems (From Previous Years VTU Exams.)
(434)
Objective Questions
(439)
Model Question Paper–I
(444)
Model Question Paper–Il
(458)
