كتاب Advanced Engineering Mathematics 2nd Ed
 منتدى هندسة الإنتاج والتصميم الميكانيكى بسم الله الرحمن الرحيم أهلا وسهلاً بك زائرنا الكريم نتمنى أن تقضوا معنا أفضل الأوقات وتسعدونا بالأراء والمساهمات إذا كنت أحد أعضائنا يرجى تسجيل الدخول أو وإذا كانت هذة زيارتك الأولى للمنتدى فنتشرف بإنضمامك لأسرتنا وهذا شرح لطريقة التسجيل فى المنتدى بالفيديو : http://www.eng2010.yoo7.com/t5785-topic وشرح لطريقة التنزيل من المنتدى بالفيديو: http://www.eng2010.yoo7.com/t2065-topic إذا واجهتك مشاكل فى التسجيل أو تفعيل حسابك وإذا نسيت بيانات الدخول للمنتدى يرجى مراسلتنا على البريد الإلكترونى التالى : Deabs2010@yahoo.com          منتدى هندسة الإنتاج والتصميم الميكانيكى :: المنتديات الهندسية :: منتدى الكتب والمحاضرات الهندسية :: منتدى كتب ومحاضرات الأقسام الهندسية المختلفة Tweetشاطر

كتاب Advanced Engineering Mathematics 2nd Ed كاتب الموضوعرسالة
مدير المنتدى  عدد المساهمات : 15493
التقييم : 26005
تاريخ التسجيل : 01/07/2009
العمر : 31
الدولة : مصر
العمل : مدير منتدى هندسة الإنتاج والتصميم الميكانيكى
الجامعة : المنوفية  موضوع: كتاب Advanced Engineering Mathematics 2nd Ed الإثنين 18 سبتمبر 2017, 3:25 am أخوانى فى اللهأحضرت لكم كتابAdvanced Engineering Mathematics 2nd Ed Michael D. Greenberg ويتناول الموضوعات الأتية : Contents Part I: Ordinary Differential Equations1 INTRODUCTION TO DIFFERENTIAL EQUATIONS IIntroduction 1Definitions 2Introduction to Modeling 2 EQUATIONS OF FIRST ORDER 2.1 Introduction 18The Linear Equation Homogeneous case 19Integrating factor method 22Existence and uniqueness for the linear equation 25Variation-of-parameter method 27Applications of the Linear Equation 342.3. 1 Electrical circuits 342.3.2 Radioactive decay; carbon dating 392.3.3 Population dynamics 412.3.4 Mixing problems 2.4 Separable Equations 462.4.1 Separable equations 46Existence and uniqueness (optional) 48Applications 53Nondimensionalization (optional) Exact Equations and Integrating Factors 622.5. 1 Exact differential equations 622.5.2 Integrating factors 66Chapter 2 Review 3 LINEAR DIFFERENTIAL EQUATIONS OF SECOND ORDER AND HIGHER 733.1 Introduction 733.2 Linear Dependence and Linear Independence 76vvi ContentsHomogeneous Equation: General Solution 833.3.1 General solution 833.3.2 Boundary-value problems Solution of Homogeneous Equation: Constant Coefficients Euler’s formula and review of the circular and hyperbolic functions 91Exponential solutions 953.4.3 Higher-order equations (« > 2) 99Repeated roots 102Stability Application to Harmonic Oscillator: Free Oscillation 110Solution of Homogeneous Equation: Nonconstant Coefficients Cauchy-Euler equation 118Reduction of order (optional) 123Factoring the operator (optional) Solution of Nonhomogeneous Equation 1333.7.1 General solution 3.7.2 Undetermined coefficients Application to Harmonic Oscillator: Forced Oscillation 1493.8. 1 Undamped case 1493.8.2 Damped case 152Systems of Linear Differential Equations 1563.9.1 Examples 1573.9.2 Existence and uniqueness 1603.9.3 Solution by elimination 162Chapter 3 Review 171Variation of parameters 141Variation of parameters for higher-order equations (optional) 4 POWER SERIES SOLUTIONS Introduction 173Power Series Solutions 1764.2.1 Review of power series 1764.2.2 Power series solution of differential equations 182The Method of Frobenius Singular points 193 iMethod of Frobenius 195Legendre Functions Singular Integrals; Gamma Function 2184.5.1 Singular integrals 2184.5.2 Gamma function 2234.5.3 Order of magnitude 225Bessel Functions 2304.6. 1 v ^ integer Legendre polynomials 212Orthogonality of the Pn ’s 214Generating functions and properties 4.6.2 v = integer 233General solution of Bessel equation 235Hankel functions (optional) 236Modified Bessel equation 236Equations reducible to Bessel equations 238 Chapter 4 Review  5 LAPLACE TRANSFORM 5.1 Introduction 247Calculation of the Transform 248Properties of the Transform 254Application to the Solution of Differential Equations 261Discontinuous Forcing Functions; Heaviside Step Function 269Impulsive Forcing Functions; Dirac Impulse Function (Optional) 275Additional Properties 281Chapter 5 Review 6 QUANTITATIVE METHODS: NUMERICAL SOLUTIONOF DIFFERENTIAL EQUATIONS 292/ ) 6.1 Introduction 292Euler’s Method 293Improvements: Midpoint Rule and Runge-Kutta Application to Systems and Boundary-Value Problems 3136.4.1 Systems and higher-order equations 3136.4.2 Linear boundary-value problems 317Stability and Difference Equations 3236.5.1 Introduction 3236.5.2 Stability 3246.5.3 Difference equations (optional) 328Chapter 6 Review Midpoint rule 299Second-order Runge-Kutta 302Fourth-order Runge-Kutta 304Empirical estimate of the order (optional) 307Multi-step and predictor-corrector methods (optional) 7 QUALITATIVE METHODS: PHASE PLANE AND NONLINEARDIFFERENTIAL EQUATIONS 337Introduction 337The Phase Plane 338Singular Points and Stability Applications Existence and uniqueness 348Singular points 350The elementary singularities and their stability 352Nonelementary singularities Singularities of nonlinear systems 360Applications 363Bifurcations Limit Cycles, van der Pol Equation, and the Nerve Impulse Limit cycles and the van der Pol equation 372Application to the nerve impulse and visual perception 375The Duffing Equation: Jumps and Chaos 3807.6. 1 Duffing equation and the jump phenomenon 3807.6.2 Chaos 383Chapter 7 Review Part II: Linear Algebra8 SYSTEMS OF LINEAR ALGEBRAIC EQUATIONS; GAUSS ELIMINATION 391Introduction 391Preliminary Ideas and Geometrical Approach 392Solution by Gauss Elimination 3968.3.1 Motivation 3968.3.2 Gauss elimination 4018.3.3 Matrix notation 4028.3.4 Gauss-Jordan reduction 4048.3.5 Pivoting 405Chapter 8 Review 9 VECTOR SPACE 412Introduction 412Vectors; Geometrical Representation 412Introduction of Angle and Dot Product 416n-Space 418Dot Product, Norm, and Angle for /?-Space Dot product, norm , and angle 421Properties of the dot product 423Properties of the norm 425Orthogonality 426Normalization 4279.6 Generalized Vector Space Vector space 430Inclusion of inner product and/or norm 4339.7 Span and Subspace 439Linear Dependence 444Bases, Expansions, Dimension Bases and expansions 448Dimension 450Orthogonal bases 4539.10 Best Approximation 457Contents i xBest approximation and orthogonal projection 458Kronecker delta Chapter 9 Review 462( •) 10 MATRICES AND LINEAR EQUATIONS 465i \ Introduction 465Matrices and Matrix Algebra 465The Transpose Matrix 481Determinants 486Rank; Application to Linear Dependence and to Existenceand Uniqueness for Ax — c 49510.5. 1 Rank 49510.5.2 Application of rank to the system Ax = c 500Inverse Matrix, Cramer’s Rule, Factorization 50810.6. 1 Inverse matrix 50810.6.2 Application to a mass-spring system 51410.6.3 Cramer’s rule 51710.6.4 Evaluation of A ” 1 by elementary row operations 51810.6.5 LU-factorization 520Change of Basis (Optional) 526Vector Transformation (Optional ) 530Chapter 10 Review 11 THE EIGENVALUE PROBLEM 5411 1 . 1 Introduction 54111.2 Solution Procedure and Applications 54211.2. 1 Solution and applications 54211.2.2 Application to elementary singularities in the phase plane 54911.3 Symmetric Matrices 554Eigenvalue problem Ax = Xx 554Nonhomogeneous problem Ax = Ax + c (optional) 11.4 Diagonalization 56911.5 Application to First-Order Systems with Constant Coefficients (optional) 58311.6 Quadratic Forms (Optional) 589Chapter ! I Review 12 EXTENSION TO COMPLEX CASE (OPTIONAL) 59912.1 Introduction 59912.2 Complex n-Space 59912.3 Complex Matrices 603Chapter 12 Review 61 lPart III: Scalar and Vector Field Theory13 DIFFERENTIAL CALCULUS OF FUNCTIONS OF SEVERAL VARIABLES 613x Contents13.1 Introduction 61313.2 Preliminaries 61413.2.1 Functions 61413.2.2 Point set theory definitions 61413.3 Partial Derivatives 62013.4 Composite Functions and Chain Differentiation 62513.5 Taylor’s Formula and Mean Value Theorem 62913.5.1 Taylor’s formula and Taylor series for f i x ) 63013.5.2 Extension to functions of more than one variable 63613.6 Implicit Functions and Jacobians 64213.6. 1 Implicit function theorem 64213.6.2 Extension to multivariable case 64513.6.3 Jacobians 64913.6.4 Applications to change of variables 65213.7 Maxima and Minima 65613.7.1 Single variable case 65613.7.2 Multivariable case 65813.7.3 Constrained extrema and Lagrange multipliers 66513.8 Leibniz Rule 675Chapter 13 Review 14 VECTORS IN 3-SPACE 68314.1 Introduction 68314.2 Dot and Cross Product 68314.3 Cartesian Coordinates 68714.4 Multiple Products 69214.4. 1 Scalar triple product 69214.4.2 Vector triple product 69314.5 Differentiation of a Vector Function of a Single Variable 69514.6 Non-Cartesian Coordinates (Optional ) 69914.6.1 Plane polar coordinates 70014.6.2 Cylindrical coordinates 70414.6.3 Spherical coordinates 70514.6.4 Omega method 707Chapter 14 Review 71215 CURVES, SURFACES, AND VOLUMES 71415.1 Introduction 71415.2 Curves and Line Integrals 71415.2.1 Curves 71415.2.2 Arc length 71615.2.3 Line integrals 71815.3 Double and Triple Integrals 72315.3. 1 Double integrals 72315.3.2 Triple integrals 72715.4 Surfaces 733/Contents xi15.4. 1 Parametric representation of surfaces 73315.4.2 Tangent plane and normal 734Surface Integrals 73915.5. 1 Area element dA 73915.5.2 Surface integrals 743Volumes and Volume Integrals 74815.6.1 Volume element clV 74915.6.2 Volume integrals 752Chapter 15 Review 16 SCALAR AND VECTOR FIELD THEORY 75716.1 Introduction 75716.2 Preliminaries 75816.2.1 Topological considerations 75816.2.2 Scalar and vector fields 75816.3 Divergence 76116.4 Gradient 76616.5 Curl 77416.6 Combinations; Lapiacian 77816.7 Non-Cartesian Systems; Div, Grad, Curl, and Lapiacian (Optional) 78216.7.1 Cylindrical coordinates 78316.7.2 Spherical coordinates 78616.8 Divergence Theorem 79216.8. 1 Divergence theorem 79216.8.2 Two-dimensional case 80216.8.3 Non-Cartesian coordinates (optional) 80316.9 Stokes’s Theorem 81016.9. 1 Line integrals 81416.9.2 Stokes’s theorem 81416.9.3 Green’s theorem 81816.9.4 Non-Cartesian coordinates (optional) 82016.10 Irrotational Fields 82616.10.1 Irrotational fields 82616.10.2 Non-Cartesian coordinates 835Chapter 16 Review Part IV: Fourier Methods and Partial Differential Equations17 FOURIER SERIES, FOURIER INTEGRAL, FOURIER TRANSFORM 84417.1 Introduction 84417.2 Even, Odd, and Periodic Functions 84617.3 Fourier Series of a Periodic Function 85017.3. 1 Fourier series 85017.3.2 Euler’s formulas 85717.3.3 Applications 859xii Contents17.3.4 Complex exponential form for Fourier series 864Half- and Quarter-Range Expansions 869Manipulation of Fourier Series (Optional) 87317.6 Vector Space Approach 88117.7 The Sturm-Liouvilie Theory 887Sturm-Liouville problem 887Lagrange identity and proofs (optional) 17.8 Periodic and Singular Sturm-Liouville Problems 90517.9 Fourier Integral 91317.10 Fourier Transform 91917.10.1 Transition from Fourier integral to Fourier transform 92017.10.2 Properties and applications 92217.11 Fourier Cosine and Sine Transforms, and Passagefrom Fourier Integral to Laplace Transform (Optional ) 93417.11. 1 Cosine and sine transforms 93417.11.2 Passage from Fourier integral to Laplace transform 937Chapter 17 Review 18 DIFFUSION EQUATION 94318.1 Introduction 943Preliminary Concepts 94418.2.1 Definitions 94418.2.2 Second-order linear equations and their classification 94618.2.3 Diffusion equation and modeling 948Separation of Variables 95418.3.1 The method of separation of variables 95418.3.2 Verification of solution (optional) 96418.3.3 Use of Sturm-Liouville theory (optional ) 965Fourier and Laplace Transforms (Optional ) 981The Method of Images (Optional ) 99218.5. 1 Illustration of the method 99218.5.2 Mathematical basis for the method 994Numerical Solution 99818.6. 1 The finite-difference method 99818.6.2 Implicit methods: Crank-Nicolson, with iterative solution (optional) 1005Chapter 18 Review 19 WAVE EQUATION 1017 {19.1 Introduction 101719.2 Separation of Variables; Vibrating String 102319.2.1 Solution by separation of variables19.2.2 Traveling wave interpretation 102719.2.3 Using Sturm-Liouville theory (optional) 102919.3 Separation of Variables; Vibrating Membrane 103519.4 Vibrating String; d’Alembert’s Solution 104319.4. 1 d’Alembert’s solution Contents xiii19.4.2 Use of images 104919.4.3 Solution by integral transforms (optional) 1051Chapter 19 Review 105520 LAPLACE EQUATION 105820.1 Introduction 105820.2 Separation of Variables; Cartesian Coordinates 105920.3 Separation of Variables; Non-Cartesian Coordinates 107020.3. 1 Plane polar coordinates 107020.3.2 Cylindrical coordinates (optional) 107720.3.3 Spherical coordinates (optional) 108120.4 Fourier Transform (Optional) 108820.5 Numerical Solution 109220.5. 1 Rectangular domains 109220.5.2 Nonrectangular domains 109720.5.3 Iterative algorithms (optional) 1100Chapter 20 Review 1106Part V: Complex Variable Theory21 FUNCTIONS OF A COMPLEX VARIABLE 110821.1 Introduction 1108Complex Numbers and the Complex Plane 1109Elementary Functions 111421.3. 1 Preliminary ideas 111421.3.2 Exponential function 111621.3.3 Trigonometric and hyperbolic functions 111821.3.4 Application of complex numbers to integration and thesolution of differential equations 1120Polar Form, Additional Elementary Functions, and Multi-valuedness21.4. 1 Polar form 112521.4.2 Integral powers of z and de Moivre's formula 112721.4.3 Fractional powers 112821.4.4 The logarithm of z 112921.4.5 General powers of z 113021.4.6 Obtaining single-valued functions by branch cuts 113121.4.7 More about branch cuts (optional ) 1132The Differential Calculus and Analyticity 1136Chapter 21 Review 22 CONFORMAL MAPPING 115022.1 Introduction 115022.2 The Idea Behind Conformal Mapping22.3 The Bilinear Transformation 11581 150xiv Contents22.4 Additional Mappings and Applications 116622.5 More General Boundary Conditions 117022.6 Applications to Fluid Mechanics 1174Chapter 22 Review 118023 THE COMPLEX INTEGRAL CALCULUS 118223.1 Introduction 118223.2 Complex Integration  Cauchy’s Theorem 118923.4 Fundamental Theorem of the Complex Integral Calculus 119523.5 Cauchy Integral Formula 1199Chapter 23 Review 1207Definition and properties 1182Bounds 24 TAYLOR SERIES, LAURENT SERIES, AND THE RESIDUE THEOREM 1209Introduction 1209Complex Series and Taylor Series 120924.2.1 Complex series 120924.2.2 Taylor series 1214Laurent Series 1225Classification of Singularities 1234Residue Theorem 124024.5.1 Residue theorem 124024.5.2 Calculating residues 124224.5.3 Applications of the residue theorem 1243Chapter 24 Review REFERENCES 1260APPENDICESA Review of Partial Fraction Expansions 1263B Existence and Uniqueness of Solutions of Systems ofLinear Algebraic Equations 1267C Table of Laplace Transforms 1271D Table of Fourier Transforms 1274E Table of Fourier Cosine and Sine Transforms 1276F Table of Conformal Maps 1278ANSWERS TO SELECTED EXERCISES 1282INDEX 1315  كلمة سر فك الضغط : books-world.netThe Unzip Password : books-world.netأتمنى أن تستفيدوا منه وأن ينال إعجابكم رابط تنزيل كتاب Advanced Engineering Mathematics 2nd Ed كيفية التسجيل فى منتدى هندسة الإنتاج والتصميم الميكانيكىطريقة التنزيل من المنتدى خطوة بخطوة الهارد الشامل والمتكامل لقسم ميكانيكا*****************************************************************************************   كتاب Advanced Engineering Mathematics 2nd Ed صفحة 2 من اصل 1

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