MARC details
| 000 -LEADER |
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| fixed length control field |
12175nam a22002537a 4500 |
| 003 - CONTROL NUMBER IDENTIFIER |
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| control field |
MU |
| 005 - DATE AND TIME OF LATEST TRANSACTION |
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| control field |
20220803043306.0 |
| 008 - FIXED-LENGTH DATA ELEMENTS--GENERAL INFORMATION |
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| fixed length control field |
220803b |||||||| |||| 00| 0 eng d |
| 020 ## - INTERNATIONAL STANDARD BOOK NUMBER |
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| International Standard Book Number |
9780470646137 |
| Terms of availability |
Tzs 150,000/= |
| 040 ## - CATALOGING SOURCE |
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| Original cataloging agency |
MU Library |
| Language of cataloging |
MU Library |
| Transcribing agency |
MU Library |
| Modifying agency |
MU Library |
| Description conventions |
AACR |
| 050 ## - LIBRARY OF CONGRESS CALL NUMBER |
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| Classification number |
QA401 |
| Item number |
1 |
| 082 ## - DEWEY DECIMAL CLASSIFICATION NUMBER |
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| Edition number |
22 |
| Classification number |
510.2462 KRE |
| Item number |
1 |
| 100 ## - MAIN ENTRY--PERSONAL NAME |
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| Personal name |
Kreyszig, Erwin |
| 245 ## - TITLE STATEMENT |
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| Title |
Advanced engineering mathematics |
| Statement of responsibility, etc. |
/ Erwin, Kreyszig; E. J.; Norminton, and Herbert Kreyszig, |
| 250 ## - EDITION STATEMENT |
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| Edition statement |
10th ed. |
| Remainder of edition statement |
International students edition |
| 260 ## - PUBLICATION, DISTRIBUTION, ETC. |
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| Place of publication, distribution, etc. |
Hoboken, N.J. : Wiley, |
| Name of publisher, distributor, etc. |
: Chichester : John Wiley [distributor] |
| Date of publication, distribution, etc. |
2011. |
| 300 ## - PHYSICAL DESCRIPTION |
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| Extent |
xv,1001p.: |
| Other physical details |
ill.;( chiefly colour) ; |
| Dimensions |
28cm. |
| 501 ## - WITH NOTE |
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| With note |
FEATURES<br/>Simplicity of Examples: To make the book teachable, why choose complicated examples when well-written simple ones are as instructive or even better?<br/>Independence of Chapters: To provide flexibility in tailoring courses to special needs.<br/>Self-Contained Presentation: Except for a few clearly marked places where a proof would exceed the level of the book and a reference is given instead.<br/>Modern Standard Notation: To help students with other courses, modern books, and mathematical and engineering journals. |
| 504 ## - BIBLIOGRAPHY, ETC. NOTE |
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| Bibliography, etc. note |
Includes references and index. |
| 505 ## - FORMATTED CONTENTS NOTE |
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| Formatted contents note |
PART A Ordinary Differential Equations (ODEs) 1<br/><br/>CHAPTER 1 First-Order ODEs 2<br/><br/>1.1 Basic Concepts. Modeling 2<br/><br/>1.2 Geometric Meaning of y ƒ(x, y). Direction Fields, Euler’s Method 9<br/><br/>1.3 Separable ODEs. Modeling 12<br/><br/>1.4 Exact ODEs. Integrating Factors 20<br/><br/>1.5 Linear ODEs. Bernoulli Equation. Population Dynamics 27<br/><br/>1.6 Orthogonal Trajectories. Optional 36<br/><br/>1.7 Existence and Uniqueness of Solutions for Initial Value Problems 38<br/><br/>CHAPTER 2 Second-Order Linear ODEs 46<br/><br/>2.1 Homogeneous Linear ODEs of Second Order 46<br/><br/>2.2 Homogeneous Linear ODEs with Constant Coefficients 53<br/><br/>2.3 Differential Operators. Optional 60<br/><br/>2.4 Modeling of Free Oscillations of a Mass–Spring System 62<br/><br/>2.5 Euler–Cauchy Equations 71<br/><br/>2.6 Existence and Uniqueness of Solutions. Wronskian 74<br/><br/>2.7 Nonhomogeneous ODEs 79<br/><br/>2.8 Modeling: Forced Oscillations. Resonance 85<br/><br/>2.9 Modeling: Electric Circuits 93<br/><br/>2.10 Solution by Variation of Parameters 99<br/><br/>CHAPTER 3 Higher Order Linear ODEs 105<br/><br/>3.1 Homogeneous Linear ODEs 105<br/><br/>3.2 Homogeneous Linear ODEs with Constant Coefficients 111<br/><br/>3.3 Nonhomogeneous Linear ODEs 116<br/><br/>CHAPTER 4 Systems of ODEs. Phase Plane. Qualitative Methods 124<br/><br/>4.0 For Reference: Basics of Matrices and Vectors 124<br/><br/>4.1 Systems of ODEs as Models in Engineering Applications 130<br/><br/>4.2 Basic Theory of Systems of ODEs. Wronskian 137<br/><br/>4.3 Constant-Coefficient Systems. Phase Plane Method 140<br/><br/>4.4 Criteria for Critical Points. Stability 148<br/><br/>4.5 Qualitative Methods for Nonlinear Systems 152<br/><br/>4.6 Nonhomogeneous Linear Systems of ODEs 160<br/><br/>CHAPTER 5 Series Solutions of ODEs. Special Functions 167<br/><br/>5.1 Power Series Method 167<br/><br/>5.2 Legendre's Equation. Legendre Polynomials Pn(x) 175<br/><br/>5.3 Extended Power Series Method: Frobenius Method 180<br/><br/>5.4 Bessel’s Equation. Bessel Functions (x) 187<br/><br/>5.5 Bessel Functions of the Y (x). General Solution 196<br/><br/>CHAPTER 6 Laplace Transforms 203<br/><br/>6.1 Laplace Transform. Linearity. First Shifting Theorem (s-Shifting) 204<br/><br/>6.2 Transforms of Derivatives and Integrals. ODEs 211<br/><br/>6.3 Unit Step Function (Heaviside Function). Second Shifting Theorem (t-Shifting) 217<br/><br/>6.4 Short Impulses. Dirac's Delta Function. Partial Fractions 225<br/><br/>6.5 Convolution. Integral Equations 232<br/><br/>6.6 Differentiation and Integration of Transforms. ODEs with Variable Coefficients 238<br/><br/>6.7 Systems of ODEs 242<br/><br/>6.8 Laplace Transform: General Formulas 248<br/><br/>6.9 Table of Laplace Transforms 249<br/><br/>PART B Linear Algebra. Vector Calculus 255<br/><br/>CHAPTER 7 Linear Algebra: Matrices, Vectors, Determinants. Linear Systems 256<br/><br/>7.1 Matrices, Vectors: Addition and Scalar Multiplication 257<br/><br/>7.2 Matrix Multiplication 263<br/><br/>7.3 Linear Systems of Equations. Gauss Elimination 272<br/><br/>7.4 Linear Independence. Rank of a Matrix. Vector Space 282<br/><br/>7.5 Solutions of Linear Systems: Existence, Uniqueness 288<br/><br/>7.6 For Reference: Second- and Third-Order Determinants 291<br/><br/>7.7 Determinants. Cramer’s Rule 293<br/><br/>7.8 Inverse of a Matrix. Gauss–Jordan Elimination 301<br/><br/>7.9 Vector Spaces, Inner Product Spaces. Linear Transformations. Optional 309<br/><br/>CHAPTER 8 Linear Algebra: Matrix Eigenvalue Problems 322<br/><br/>8.1 The Matrix Eigenvalue Problem. Determining Eigenvalues and Eigenvectors 323<br/><br/>8.2 Some Applications of Eigenvalue Problems 329<br/><br/>8.3 Symmetric, Skew-Symmetric, and Orthogonal Matrices 334<br/><br/>8.4 Eigenbases. Diagonalization. Quadratic Forms 339<br/><br/>8.5 Complex Matrices and Forms. Optional 346<br/><br/>CHAPTER 9 Vector Differential Calculus. Grad, Div, Curl 354<br/><br/>9.1 Vectors in 2-Space and 3-Space 354<br/><br/>9.2 Inner Product (Dot Product) 361<br/><br/>9.3 Vector Product (Cross Product) 368<br/><br/>9.4 Vector and Scalar Functions and Their Fields. Vector Calculus: Derivatives 375<br/><br/>9.5 Curves. Arc Length. Curvature. Torsion 381<br/><br/>9.6 Calculus Review: Functions of Several Variables. Optional 392<br/><br/>9.7 Gradient of a Scalar Field. Directional Derivative 395<br/><br/>9.8 Divergence of a Vector Field 403<br/><br/>9.9 Curl of a Vector Field 406<br/><br/>CHAPTER 10 Vector Integral Calculus. Integral Theorems 413<br/><br/>10.1 Line Integrals 413<br/><br/>10.2 Path Independence of Line Integrals 419<br/><br/>10.3 Calculus Review: Double Integrals. Optional 426<br/><br/>10.4 Green’s Theorem in the Plane 433<br/><br/>10.5 Surfaces for Surface Integrals 439<br/><br/>10.6 Surface Integrals 443<br/><br/>10.7 Triple Integrals. Divergence Theorem of Gauss 452<br/><br/>10.8 Further Applications of the Divergence Theorem 458<br/><br/>10.9 Stokes’s Theorem 463<br/><br/>PART C Fourier Analysis. Partial Differential Equations (PDEs) 473<br/><br/>CHAPTER 11 Fourier Analysis 474<br/><br/>11.1 Fourier Series 474<br/><br/>11.2 Arbitrary Period. Even and Odd Functions. Half-Range Expansions 483<br/><br/>11.3 Forced Oscillations 492<br/><br/>11.4 Approximation by Trigonometric Polynomials 495<br/><br/>11.5 Sturm–Liouville Problems. Orthogonal Functions 498<br/><br/>11.6 Orthogonal Series. Generalized Fourier Series 504<br/><br/>11.7 Fourier Integral 510<br/><br/>11.8 Fourier Cosine and Sine Transforms 518<br/><br/>11.9 Fourier Transform. Discrete and Fast Fourier Transforms 522<br/><br/>11.10 Tables of Transforms 534<br/><br/>CHAPTER 12 Partial Differential Equations (PDEs) 540<br/><br/>12.1 Basic Concepts of PDEs 540<br/><br/>12.2 Modeling: Vibrating String, Wave Equation 543<br/><br/>12.3 Solution by Separating Variables. Use of Fourier Series 545<br/><br/>12.4 D’Alembert’s Solution of the Wave Equation. Characteristics 553<br/><br/>12.5 Modeling: Heat Flow from a Body in Space. Heat Equation 557<br/><br/>12.6 Heat Equation: Solution by Fourier Series. Steady Two-Dimensional Heat Problems. Dirichlet Problem 558<br/><br/>12.7 Heat Equation: Modeling Very Long Bars. Solution by Fourier Integrals and Transforms 568<br/><br/>12.8 Modeling: Membrane, Two-Dimensional Wave Equation 575<br/><br/>12.9 Rectangular Membrane. Double Fourier Series 577<br/><br/>12.10 Laplacian in Polar Coordinates. Circular Membrane. Fourier–Bessel Series 585<br/><br/>12.11 Laplace’s Equation in Cylindrical and Spherical Coordinates. Potential 593<br/><br/>12.12 Solution of PDEs by Laplace Transforms 600<br/><br/>PART D Complex Analysis 607<br/><br/>CHAPTER 13 Complex Numbers and Functions. Complex Differentiation 608<br/><br/>13.1 Complex Numbers and Their Geometric Representation 608<br/><br/>13.2 Polar Form of Complex Numbers. Powers and Roots 613<br/><br/>13.3 Derivative. Analytic Function 619<br/><br/>13.4 Cauchy–Riemann Equations. Laplace’s Equation 625<br/><br/>13.5 Exponential Function 630<br/><br/>13.6 Trigonometric and Hyperbolic Functions. Euler's Formula 633<br/><br/>13.7 Logarithm. General Power. Principal Value 636<br/><br/>CHAPTER 14 Complex Integration 643<br/><br/>14.1 Line Integral in the Complex Plane 643<br/><br/>14.2 Cauchy's Integral Theorem 652<br/><br/>14.3 Cauchy's Integral Formula 660<br/><br/>14.4 Derivatives of Analytic Functions 664<br/><br/>CHAPTER 15 Power Series, Taylor Series 671<br/><br/>15.1 Sequences, Series, Convergence Tests 671<br/><br/>15.2 Power Series 680<br/><br/>15.3 Functions Given by Power Series 685<br/><br/>15.4 Taylor and Maclaurin Series 690<br/><br/>15.5 Uniform Convergence. Optional 698<br/><br/>CHAPTER 16 Laurent Series. Residue Integration 708<br/><br/>16.1 Laurent Series 708<br/><br/>16.2 Singularities and Zeros. Infinity 714<br/><br/>16.3 Residue Integration Method 719<br/><br/>16.4 Residue Integration of Real Integrals 725<br/><br/>CHAPTER 17 Conformal Mapping 735<br/><br/>17.1 Geometry of Analytic Functions: Conformal Mapping 736<br/><br/>17.2 Linear Fractional Transformations (Möbius Transformations) 741<br/><br/>17.3 Special Linear Fractional Transformations 745<br/><br/>17.4 Conformal Mapping by Other Functions 749<br/><br/>17.5 Riemann Surfaces. Optional 753<br/><br/>CHAPTER 18 Complex Analysis and Potential Theory 756<br/><br/>18.1 Electrostatic Fields 757<br/><br/>18.2 Use of Conformal Mapping. Modeling 761<br/><br/>18.3 Heat Problems 765<br/><br/>18.4 Fluid Flow 768<br/><br/>18.5 Poisson's Integral Formula for Potentials 774<br/><br/>18.6 General Properties of Harmonic Functions. Uniqueness Theorem for the Dirichlet Problem 778<br/><br/>PART E Numeric Analysis 785<br/><br/>Software 786<br/><br/>CHAPTER 19 Numerics in General 788<br/><br/>19.1 Introduction 788<br/><br/>19.2 Solution of Equations by Iteration 795<br/><br/>19.3 Interpolation 805<br/><br/>19.4 Spline Interpolation 817<br/><br/>19.5 Numeric Integration and Differentiation 824<br/><br/>CHAPTER 20 Numeric Linear Algebra 841<br/><br/>20.1 Linear Systems: Gauss Elimination 841<br/><br/>20.2 Linear Systems: LU-Factorization, Matrix Inversion 849<br/><br/>20.3 Linear Systems: Solution by Iteration 855<br/><br/>20.4 Linear Systems: Ill-Conditioning, Norms 861<br/><br/>20.5 Least Squares Method 869<br/><br/>20.6 Matrix Eigenvalue Problems: Introduction 873<br/><br/>20.7 Inclusion of Matrix Eigenvalues 876<br/><br/>20.8 Power Method for Eigenvalues 882<br/><br/>20.9 Tridiagonalization and QR-Factorization 885<br/><br/>CHAPTER 21 Numerics for ODEs and PDEs 897<br/><br/>21.1 Methods for First-Order ODEs 898<br/><br/>21.2 Multistep Methods 908<br/><br/>21.3 Methods for Systems and Higher Order ODEs 912<br/><br/>21.4 Methods for Elliptic PDEs 919<br/><br/>21.5 Neumann and Mixed Problems. Irregular Boundary 928<br/><br/>21.6 Methods for Parabolic PDEs 933<br/><br/>21.7 Method for Hyperbolic PDEs 939<br/><br/>PART F Optimization, Graphs 947<br/><br/>CHAPTER 22 Unconstrained Optimization. Linear Programming 948<br/><br/>22.1 Basic Concepts. Unconstrained Optimization: Method of Steepest Descent 949<br/><br/>22.2 Linear Programming 952<br/><br/>22.3 Simplex Method 956<br/><br/>22.4 Simplex Method: Difficulties 960<br/><br/>CHAPTER 23 Graphs. Combinatorial Optimization 967<br/><br/>23.1 Graphs and Digraphs 967<br/><br/>23.2 Shortest Path Problems. Complexity 972<br/><br/>23.3 Bellman's Principle. Dijkstra’s Algorithm 977<br/><br/>23.4 Shortest Spanning Trees: Greedy Algorithm 980<br/><br/>23.5 Shortest Spanning Trees: Prim’s Algorithm 984<br/><br/>23.6 Flows in Networks 987<br/><br/>23.7 Maximum Flow: Ford–Fulkerson Algorithm 993<br/><br/>23.8 Bipartite Graphs. Assignment Problems 996<br/><br/>APPENDIX 1 References A1<br/><br/>APPENDIX 2 Answers to Selected Problems A4<br/><br/>APPENDIX 3 Auxiliary Material A51<br/><br/>A3.1 Formulas for Special Functions A51<br/><br/>A3.2 Partial Derivatives A57<br/><br/>A3.3 Sequences and Series A60<br/><br/>A3.4 Grad, Div, Curl, 2 in Curvilinear Coordinates A62<br/><br/>APPENDIX 4 Additional Proofs A65<br/><br/>APPENDIX 5 Tables A85<br/><br/>INDEX I1<br/><br/>PHOTO CREDITS P1<br/><br/>NEW TO THIS EDITION<br/>Revised Problem Sets: This edition includes an extensive revision of the problem sets, making them even more effective, useful, and up-to-date.<br/>Chapter Introductions: These have also been rewritten to be more accessible and helpful to students.<br/>Rewrites: Some material has been rewritten specifically to better help students draw conclusions and tackle more advanced material.<br/>Chapter Revisions: Many of the chapters in this edition have been rewritten entirely. Some have had material added, including but not limited to:<br/>Introduction of Euler’s Method in section 1.2<br/>Partial Derivatives on a Surface in section 9.6<br/>Introduction to the Heat Equation in section 12.5 |
| 650 ## - SUBJECT ADDED ENTRY--TOPICAL TERM |
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| Topical term or geographic name entry element |
Engineering mathematics |
| General subdivision |
Mathematical physics |
| 856 ## - ELECTRONIC LOCATION AND ACCESS |
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| Uniform Resource Identifier |
<a href="https://www.wiley.com/en-ie/Advanced+Engineering+Mathematics,+10th+Edition+International+Student+Version-p-9780470646137">https://www.wiley.com/en-ie/Advanced+Engineering+Mathematics,+10th+Edition+International+Student+Version-p-9780470646137</a> |
| 942 ## - ADDED ENTRY ELEMENTS (KOHA) |
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| Source of classification or shelving scheme |
Dewey Decimal Classification |
| Koha item type |
Book |
| Suppress in OPAC |
No |
