Advanced Engineering Mathematics 无水印原版pdf

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ADVANCED ENGINEERING MATHEMATICS art y ryn CRC) CRC Press Taylor Francis Group Boca raton London New York CRC Press is an imprint of the yor francis group, an informa MATLAB is a trademark of The MathWorks, Inc. and is used with permission. The math Works does not warrant the accuracy of the text or exercises in this book. This book's use or discussion of MATLAB software or rclated products does not constitute endorsement or sponsorship by The MathWorks of a particular pedagogical approach or particular use of the matlab software CRC Press Taylor Francis Group 6000 Broken Sound Parkway nw, Suite 300 Boca raton, fl 33487-2742 @2014 by Taylor Francis Group, LLC CRC Press is an imprint of Taylor Francis Group, an Informa business No claim to original U.S. Government works Version date: 20130801 International Standard Book Number-13: 978-1-4822-1939-5( Book- PDF This book contains information obtained from authentic and highly regarded sources. Reasonable efforts have been made to publish reliable data and information, but the author and publisher cannot assume responsibility for the valid ity of all materials or the consequences of their use. The authors and publishers have attempted to trace the copyright holders of all material reproduced in this publication and apologize to copyright holders if permission to publish in this orm has not been obtained. If any copyright material has not been acknowledged please write and let us know so we may rectify in any future reprint Except as permitted under U.S. Copyright Law, no part of this book may be reprinted, reproduced, transmitted, or uti- lized in any form by any electronic, mechanical, or other means, now known or hereafter invented, including photocopy- ing, microfilming, and recording, or in any information storage or retrieval system, without written permission from the ublishers Forpermissiontophotocopyorusematerialelectronicallyfromthisworkpleaseaccesswww.copyright.com(http:// www.copyright.com/)orcontacttheCopyrightClearanceCenter,Inc.(ccC),222RosewoodDrive,Danvers,Mao1923, 978-750-8400. CCC is a not-for-profit organization that provides licenses and registration for a variety of users. For organizations that have been granted a photocopy license by the CCC, a separate system of payment has been arranged Trademark Notice: Product or corporate names may be trademarks or registered trademarks, and are used only for identification and explanation without intent to in fringe Visit the Taylor francis Web site at http://www.taylorandfrancis.com and the crc Press Web site at http://www.crcpress.com Contents reface. 看鲁借 XIX Acknowledgments 1. Linear Algebraic Equations, Matrices, and Eigenvalues………………… 1 Solving Systems and Row Echelon Forms∴…………………… 1.1.1 Matri 1.1.2 Augmented matrices........ ····················.·······.··:· 1.1.3 Row Reduced Echelon Form(RREF) 6 1.1.4 Problems 13 1.2 Matrix Addition, multiplication, and transpose 1.2.1 Special Kinds of matrices………………………………………21 1.2.2 Powers of a matrix ···· 1.2.3 Transpose 24 1.2. 4 Elementary matrices............................. 24 1.2.5 Problems 1. 3 Homogeneous Systems, Spanning Set, and Basic Solutions.......... 26 1.3.1 Problems 32 1.4 Solutions of Nonhomogeneous systems 面面 33 1.4.1 Problems .·········· 香鲁看,普看 36 1.5 Inverse matrix ■面击 37 1.5.1 Row Reduction algorithm for Constructing the inverse ..............40 1.5.2 Inverse of a partitioned matrix 43 1.5.3 Problems ∴· 1.6 Determinant, Adjugate Matrix, and Cramer's rule 47 1.6.1 Adjugate matrix ·鲁番鲁看鲁帝普鲁香看鲁番 53 1.6.2 Cramer's rule 1.6.3 Problems 57 1.7 Linear Independence, Basis and dimension.………… 61 171 Linear Independence.………………………………62 17.2 Vector Spaces and Subspaces…………………………… 1.7.3 Problems∴ 69 Key terms ······ 71 MATLAB Commands Mathematica commands References 2. Matrix Theory b·····a··b· 2.1 Eigenvalues and Eigenvectors∴…………… 75 2.1.1 The Adjugate Matrix Method for Finding an eigenvector. ............79 2.1.2 Complex Numbers 看鲁 82 2.13 Complex Eigenvalues and Eigenvectors……… 2.1.4 Eigenvalues and eigenvectors of triangular and Diagonal Matrices 面面 85 Contents 2.1.5 MATLABe and MathematicaTM 86 2.1.6 Problems 87 2.2 Basis of eigenvectors and diagonalization 2.2.1 Diagonalizing a Matrix ···········.·······.· 2.2.2 Deficient Eigenvalues 2.2.3 Problems 2.3 Inner Product and Orthogonal sets of vectors ................. 101 2.3.1 Orthogonal Set of Vectors........................ 105 2.3.2 The gram-Schmidt Process 106 2.3.3 Orthogonal Projections ..109 2.3.4 Problems 酯普D香鲁帝 ..112 2. 4 Orthonormal Bases and Orthogonal matrices 114 24.1 Orthogonal Sets and Bases………………… 114 2.4.2 Orthogonal matrices 116 243 Appendix…… 118 2.4.4 Problems 119 2.5 Least squares Solutions..............,....... 121 2.5.1 The Normal equations ·..··.···· 123 2.5.1.1 Least Squares Solution and Orthogonal matrices ...... 127 2.5.2 Problems ..129 26 Symmetric Matrices, Definite matrices, and Applications…………131 2.6.1A pectral Theor 131 2.6.1.1 A Spectral Formula 135 2.6.1.2 Positive Definite and positive semi-Definite matrices.... 136 2613 Application to A2A-√A… ∴.137 261.4 Application to Least Squares Solutions……………138 2.6.2 Further Study of Positive Definite Matrices 普D 139 2.6.2.1 Vibrations and the generalized eigenvalue problem 140 2.6.2.2 Positive definiteness and determinants ..,.,.......,....141 2.6.3 Problems 146 2.7 Factorizations: QR and svd 148 2.7.1 QR Factorization 148 272 QR and Solving Systems…………………………150 273 QR and Least Squares Solutions…………………… 2.7.4SVD.151 2.7.5 SVD and L ss 158 2.7.6 Moore-Penrose Generalized Inverse.................... 159 2.7.7 Problems∴ 163 2.8 Factorizations: lu and Cholesky 165 2.8.1 LU Factorizations. ............................................................165 2.8.2 Cholesky Factorizations........................... 168 2.8.3 Problems 169 2.9 Rayleigh Quotient 鲁 ,··D·带曹 170 2.9.1 A Rayleigh Theorem 172 29.2 Problems 174 2.10 Short Take: Inner Product and Hilbert Spaces 垂D·鲁非 175 2.10.1 Linear Functionals and Operators 177 2.10.2 Norm and Bounded Linear operators 179 2.10.3 Convergence, Cauchy Completeness, and Hilbert Spaces 183 Conten its 2.10.4 Bounded linear functionals and operator adjoint 186 2.10.5 Application to Signal restoration……………………………………187 2.10.6 Projection and minimization......................... 188 2.10.7 Weak Convergence and Compactness 210.8 Problems 191 Key terms 192 MATLABI COmmands ..194 Mathematica commands .194 References ∴194 3. Scalar ODEs I: Homogeneous Problems 19 3.1 Linear first-Order Odes ····.·; ;··;·· 195 3.1.1 Scalar odes ···.;········ ∴..195 3.1.2 Linear first-Order ODes 章········ 196 3.1.3 Steady-State and transient solutions .··.·.;·.····.·:· 202 3.1.4 Problems 205 32 Separable and Exact ODEs∴…………………………………,209 321 Separable Odes… 209 3.2.2 Exact ODEs 211 3.2. 3 Existence of Solution(s) of an iVp 垂d 215 3.2.4 Problems 219 3.3 Second-Order linear homogeneous odes a.44 222 3.3.1 Spring-Mass-Damper Systems 垂曲面面面击d面面击函国面 222 3.3.2 Series RlC Circuit 番 ;········: 3. 3.3 The Underdamped Case 230 3.3.4 The Amplitude and phase Form ····························,.········· 232 3.3.5 Figures of Merit in Graphs of Underdamped Solutions. . ...... 235 3.3.6 The Critically Damped Case 237 3.3.7 The wronskian determinant. .,,,..,....................,.,......238 3. 3. 8 Problems ······· 23 34 Higher-Order Linear OdEs…… 244 3.4.1 The Zoo of solutions of lcchodes · 250 3.4.2 Differential Operator Notation 251 3.4.3 Shift Theorem 3.4.4 Problems ·.:.··4 254 3.5 Cauchy-Euler Odes 3.5.1 Problems ∴.,260 Key terms.,,,,…, ····· ·············· .261 Mathematica command ................................... 262 Reference ··.·.······· ········:·:·: ..262 4. Scalar odes ii: Nonhomogeneous Problems….…….263 4.1 Nonhomogeneous Odes 263 4.1.1 Special Case: RHS from the Zoo and Constant Coefficients on lhs 264 4.1.2 The method of coefficients to be determined 265 4.1.3 Justification for the Method 269 4.1.4 Using a Shift Theorem…………………………………… 270 4.1.5 Problems 番看普番 .271 Contents 4.2 Forced Oscillations ∴273 42. 1 The resonance case 274 4.2.2 Steady-State Solution, Frequency Response, and Practical resonance ∴....276 4.2.3 Maximum Frequency Response ..281 4.2.4 Beats Phenomenon, Fast and Slow Frequencies, and Frequency response 83 4.2.5 Problems∴ 只了 4.3 Variation of parameters 4.3.1 Method of variation of parameters ....,.....,...........................,294 4.3.2 Problems ····,· D鲁D鲁 298 4.4 Laplace transforms: Basic Techniques 4.4.1 Problems ..305 4.5 Laplace Transforms: Unit Step and Other Techniques............. 307 4.5.1 Writing a Function in Terms of Step Function(s)……………………308 4.5.2 Graph of a Solution of an ODE Involving a Step Function……….310 4.5. 3 Convolution 垂鲁帝·鲁D番鲁帝鲁·番鲁D鲁帝鲁D普 312 4.5.4 Convolution and particular solutions 314 4.5.5 Delta"Functions 318 4.5.6 Laplace Transform of a periodic Function................ 321 4.5.7 Remarks 321 4.5.8 Problems 321 4.6 Scalar Difference Equations................... 323 4.6.1 General Solution and the Casorati Determinant "···········. 30 4.6.2 Nonhomogeneous linear Difference equation ∴.334 4.6. 3 The method of Undetermined coefficients. ..............................334 4.6.4 Problems 338 4.7 Short Take: z-Transforms 340 4.7.1 Sinusoidal Signals 344 4.7.2 Steady-State Solution ,·····,···.····· 345 4.7.3 Convolution and z-Transforms ....348 4.7.4 Transfer Function 348 47.5 Problems 49 Key Terms.……………………… 349 R eferences∴∴…… ∴351 5. Linear Systems of Odes………353 5.1 Systems of ODEs ······..·····..· 353 5.1.1 Systems of Second-Order equations 357 5.1.2 Compartment models 358 5.1.3 Problems.................................... 360 5.2 Solving linear Homogenous Systems of OdEs………………………… 362 5.2.1 Fundamental Matrix and etA 5.2.2 Equivalence of Second-Order LCCHODE and LCCHS in]P< ·· 368 372 LA 5.2.3 Maclaurin series for e 375 5.2.4 Nonconstant Coefficients D鲁 376 5.2.5 Problems∴ 377 5.3 Complex or Deficient Eigenvalues 381 Conten its 5.3.1 Complex eigenvalues………………………………… 381 53.2 Solving Homogeneous Systems of Second- Order Equations………385 5.3. 3 Deficient eigenvalues .387 5.3.4 Laplace Transforms and e 390 53.5 Stability… 391 5.3.6 Problems 面击 392 unhomogeneous linear systems 395 5.4.1 Problems onant Nonhomogeneous Systems 403 56 Linear Control Theory: Complete Controllability.……,…… 5.5.1 dal force 408 5.5.2 Problems 411 鲁鲁垂看 ·.····· 412 5.6.1 Some other Control problems. .............................................419 5.6.2 Problems ··;.·;··;··;·;·······;··· 421 5.7 Linear Systems of Difference equations 422 57.1 Color blindness 5.7.2 General solution and the casorati determinant 425 5.7.3 Complex eigenvalues∴………………,27 5.7.4 Equivalence of Second-Order Scalar Difference Equation and a System in r ·日.‘· 428 5.7.5 Ladder Network Electrical Circuits.................... 429 5.7.6 Stability 434 5.7.7 Problems 436 5.8 Short Take: Periodic linear Differential equations 439 5.8.1 The Stroboscopic, or"Return, "Map ,441 5.8.2 Floquet Representation 442 5.8.3 Stability 44 5.8.4 Hills equation 5.8.5 Periodic Solution of a nonhomogeneous ODE System ..448 5.8.6 Problems 451 Key terms 454 MATLAB Commands 翻面 ∴455 References 455 6. Geometry, Calculus, and other tools……………….…………….457 6. 1 Dot Product, Cross Product, Lines and planes.........,........ 457 6.1.1 Dot Product and cross product 457 6.1.2 Lines∴459 6.1.3 Planes .········ 459 6.1.4 Problems ∴..461 6.2 Trigonometry, Polar, Cylindrical, and Spherical coordinates ·.·..··. 463 6.2.1 Cylindrical Coordinates 465 6.2.2 Spherical Coordinates 465 6.2. 3 Right-Handed Orthogonal Bases for IR 467 6.2. 4 Orthonormal Basis in Spherical co .468 62 Relationships to the standard c.n. Basis……… 6.2.6 Problems 471 Contents 6.3 Curves and surfaces .·············· 471 6.3.1 Curves and calculus 474 6.3.2 Zhukovskii airfoil 477 6.3.3 Surfaces ······.··.·········.···· 478 6.3.4 Problems ,,482 6.4 Partial Derivatives 485 64.1 Linear Approximation………… 垂垂D 486 6.4.2 Multivariable chain rules 489 6.4.3 Gradient Vector in R3 492 6.4.4 Scalar potential functions 493 64.5 Problems∴ 495 6.5 Tangent Plane and normal vector ∴498 6.5.1 Problems 番帝 504 6.6 Area, Volume, and Linear transformations .505 6.6.1 Linear transformations 511 6.6.2 Linear Transformations, Area, and volume 514 6.6.3 Change of variables, Area, and volume 516 6.6.4 Element of surface area 519 6.6.5 Problems 画面 520 67 Differential Operators and Curvilinear Coordinates……… 522 671 Properties of the Operators grad,div, and cur………………524 6.7.2 Curvilinear coordinates 525 673 Differential Operators in( urvilinear coordinates………………529 6.7. 4 Summary of Operators in Cylindrical Coordinates........... 533 675 Summary of Operators in Spherical Coordinates………… 533 67.6 Problems∴ D鲁圈D D鲁 534 6.8 Rotating Coordinate frames....................... 537 6.8.1 ODEs Describing Rotation 537 6.8.2 Velocity and Acceleration………………… 6.8.3 Velocity and Acceleration in a Rotating Frame Whose 540 Origin Is moving…… 曹口看·D曹带日D鲁曹D,曹DD看D·■ 543 6.8.4 Problems Key te 546 Mathematica command 548 Re eference 酯 548 7. Integral Theorems, Multiple Integrals, and Applications∴……………549 7.1 Integrals for a Function of a Single variable 49 鲁· 7.1.1 Improper Integrals………………………………………… 53 7.1.2 Problems ·.::..···.;;··············.··· ∴.554 7.2 Line Integral ∴555 7.2.1 Line Integrals of Vector-Valued Functions 560 7.2.2 Fundamental theorem of line integrals 7.2.3 Path direction 565 7.2.4 Other Notations 7.2.5 Problems 567 73 Double Integrals, Green' s Theorem, and Applications………… 570 7.3.1 Double Integral as volume 574 7.3.2 Polar Coordinates ∴,580

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坎离既济 很清晰,很有价值的参考书。
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