000			08506nam a2200361 i 4500
008			100903s2011 flua b 001 0 eng
010			_a2010034920
020			_a9781439816240 _q(hardback)
020			_a1439816247 _q(hardback)
035			_a(OCoLC)642287707
040			_aDLC _cDLC _dYDX _dBTCTA _dYDXCP _dUKM _dCDX
049			_aBAUN_MERKEZ
050	0	4	_aTA345 _b.D84 2011
082	0	0	_222
100	1		_aDuffy, Dean G
245	1	0	_aAdvanced engineering mathematics with MATLAB / _cDean G. Duffy
250			_a3rd ed
264		1	_aBoca Raton, FL : _bCRC Press, _c[2011]
264		4	_c©2011
300			_a1079 pages : _billustrations ; _c25 cm
336			_atext _btxt _2rdacontent
337			_aunmediated _bn _2rdamedia
338			_avolume _bnc _2rdacarrier
505	0	0	_tContents _t Dedication _t Contents _t Acknowledgments _t Author _t Introduction _t List of Definitions _tchapter 1 Complex Variables 1 _t1.1. Complex Numbers 1 _t1.2. Finding Roots 6 _t1.3. The Derivative in the Complex Plane: The Cauchy-Riemann Equations 9 _t1.4. Line Integrals 19 _t1.5. The Cauchy-Goursat Theorem 25 _t1.6. Cauchy's Integral Formula 28 _t1.7. Taylor and Laurent Expansions and Singularities 32 _t1.8. Theory of Residues 40 _t1.9. Evaluation of Real Definite Integrals 45 _t1.10. Cauchy's Principal Value Integral 54 _tchapter 2 First-Order Ordinary Differential Equations 63 _t2.1. Classification of Differential Equations 63 _t2.2. Separation of Variables 67 _t2.3. Homogeneous Equations 81 _t2.4. Exact Equations 82 _t2.5. Linear Equations 85 _t2.6. Graphical Solutions 98 _t2.7. Numerical Methods 101 _tchapter 3 Higher-Order Ordinary Differential Equations 115 _t3.1. Homogeneous Linear Equations with Constant Coefficients 120 _t3.2. Simple Harmonic Motion 129 _t3.3. Damped Harmonic Motion 134 _t3.4. Method of Undetermined Coefficients 139 _t3.5. Forced Harmonic Motion 145 _t3.6. Variation of Parameters 154 _t3.7. Euler-Cauchy Equation 160 _t3.8. Phase Diagrams 164 _t3.9. Numerical Methods 170 _tchapter 4 Fourier Series 177 _t4.1. Fourier Series 177 _t4.2. Properties of Fourier Series 191 _t4.3. Half-Range Expansions 199 _t4.4. Fourier Series with Phase Angles 206 _t4.5. Complex Fourier Series 208 _t4.6. The Use of Fourier Series in the Solution of Ordinary Differential Equations 213 _t4.7. Finite Fourier Series 222 _tchapter 5 The Fourier Transforms 239 _t5.1. Fourier Transforms 239 _t5.2. Fourier Transforms Containing the Delta Function 250 _t5.3. Properties of Fourier Transforms 253 _t5.4. Inversion of Fourier Transforms 267 _t5.5. Convolution 282 _t5.6. Solution of Ordinary Differential Equations by Fourier Transforms 285 _tchapter 6 The Laplace Transform 289 _t6.1. Definition and Elementary Properties 289 _t6.2. The Heaviside Step and Dirac Delta Functions 297 _t6.3. Some Useful Theorems 303 _t6.4. The Laplace Transform of a Periodic Function 312 _t6.5. Inversion by Partial Fractions: Heaviside's Expansion Theorem 315 _t6.6. Convolution 323 _t6.7. Integral Equations 328 _t6.8. Solution of Linear Differential Equations with Constant Coefficients 334 _t6.9. Inversion by Contour Integration 353 _tchapter 7 The Z-Transform 363 _t7.1. The Relationship of the Z-Transform to the Laplace Transform 364 _t7.2. Some Useful Properties 371 _t7.3. Inverse Z-Transforms 379 _t7.4. Solution of Difference Equations 389 _t7.5. Stability of Discrete-Time Systems 398 _tchapter 8 The Hilbert Transform 405 _t8.1. Definition 405 _t8.2. Some Useful Properties 416 _t8.3. Analytic Signals 423 _t8.4. Causality: The Kramers-Kronig Relationship 426 _tchapter 9 The Sturm-Liouville Problem 431 _t9.1. Eigenvalues and Eigenfunctions 431 _t9.2. Orthogonality of Eigenfunctions 442 _t9.3. Expansion in Series of Eigenfunctions 446 _t9.4. A Singular Sturm-Liouville Problem: Legendre's Equation 451 _t9.5. Another Singular Sturm-Liouville Problem: Bessel's Equation 468 _t9.6. Finite Element Method 490 _tchapter 10 The Wave Equation 499 _t10.1. The Vibrating String 500 _t10.2. Initial Conditions: Cauchy Problem 502 _t10.3. Separation of Variables 503 _t10.4. D'Alembert's Formula 524 _t10.5. The Laplace Transform Method 532 _t10.6. Numerical Solution of the Wave Equation 553 _tchapter 11 The Heat Equation 565 _t11.1. Derivation of the Heat Equation 566 _t11.2. Initial and Boundary Conditions 567 _t11.3. Separation of Variables 568 _t11.4. The Laplace Transform Method 612 _t11.5. The Fourier Transform Method 629 _t11.6. The Superposition Integral 636 _t11.7. Numerical Solution of the Heat Equation 649 _tchapter 12 Laplace's Equation 659 _t12.1. Derivation of Laplace's Equation 660 _t12.2. Boundary Conditions 662 _t12.3. Separation of Variables 663 _t12.4. The Solution of Laplace's Equation on the Upper Half-Plane 707 _t12.5. Poisson's Equation on a Rectangle 709 _t12.6. The Laplace Transform Method 713 _t12.7. Numerical Solution of Laplace's Equation 716 _t12.8. Finite Element Solution of Laplace's Equation 722 _tchapter 13 Green's Functions 731 _t13.1. What Is a Green's Function? 731 _t13.2. Ordinary Differential Equations 738 _t13.3. Joint Transform Method 762 _t13.4. Wave Equation 766 _t13.5. Heat Equation 777 _t13.6. Helmholtz's Equation 789 _tchapter 14 Vector Calculus 813 _t14.1. Review 813 _t14.2. Divergence and Curl 822 _t14.3. Line Integrals 827 _t14.4. The Potential Function 832 _t14.5. Surface Integrals 834 _t14.6. Green's Lemma 842 _t14.7. Stokes' Theorem 846 _t14.8. Divergence Theorem 853 _tchapter 15 Linear Algebra 863 _t15.1. Fundamentals of Linear Algebra 863 _t15.2. Determinants 871 _t15.3. Cramer's Rule 876 _t15.4. Row Echelon Form and Gaussian Elimination 879 _t15.5. Eigenvalues and Eigenvectors 890 _t15.6. Systems of Linear Differential Equations 899 _t15.7. Matrix Exponential 905 _tchapter 16 Probability 913 _t16.1. Review of Set Theory 914 _t16.2. Classic Probability 916 _t16.3. Discrete Random Variables 928 _t16.4. Continuous Random Variables 934 _t16.5. Mean and Variance 942 _t16.6. Some Commonly Used Distributions 947 _t16.7. Joint Distributions 956 _tchapter 17 Random Processes 969 _t17.1. Fundamental Concepts 973 _t17.2. Power Spectrum 980 _t17.3. Differential Equations Forced by Random Forcing 984 _t17.4. Two-State Markov Chains 993 _t17.5. Birth and Death Processes 1003 _t17.6. Poisson Processes 1017 _t17.7. Random Walk 1024 _t Answers to the Odd-Numbered Problems 1037 _t Index 1067
520			_a"Resoundingly popular in its first edition, Dean Duffy's Advanced Engineering Mathematics has been updated, expanded, and now more than ever provides the solid mathematics background required throughout the engineering disciplines. Melding the author's expertise as a practitioner and his years of teaching engineering mathematics, this text stands clearly apart from the many others available. <BR><BR>Relevant, insightful examples follow nearly every concept introduced and demonstrate its practical application. This edition includes two new chapters on differential equations, another on Hilbert transforms, and many new examples, problems, and projects that help build problem-solving skills. Most importantly, the book now incorporates the use of MATLAB throughout the presentation to reinforce the concepts presented. MATLAB code is included so readers can take an analytic result, fully explore it graphically, and gain valuable experience with this industry-standard software"--Provided by publisher
520			_a"Resoundingly popular in its first edition, Dean Duffy's Advanced Engineering Mathematics has been updated, expanded, and now more than ever provides the solid mathematics background required throughout the engineering disciplines. Melding the author's expertise as a practitioner and his years of teaching engineering mathematics, this text stands clearly apart from the many others available. Relevant, insightful examples follow nearly every concept introduced and demonstrate its practical application. This edition includes two new chapters on differential equations, another on Hilbert transforms, and many new examples, problems, and projects that help build problem-solving skills. Most importantly, the book now incorporates the use of MATLAB throughout the presentation to reinforce the concepts presented. MATLAB code is included so readers can take an analytic result, fully explore it graphically, and gain valuable experience with this industry-standard software"--Provided by publisher
504			_aIncludes bibliographical references and index
650		0	_aEngineering mathematics _xData processing
630	0	0	_aMATLAB
900			_a34752
900			_bsatın
942			_2lcc _cKT
999			_c32020 _d32020