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15760cam a2200409 a 4500 |
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OSt |
| 005 - DATE AND TIME OF LATEST TRANSACTION |
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20260817085912.0 |
| 008 - FIXED-LENGTH DATA ELEMENTS--GENERAL INFORMATION |
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| fixed length control field |
110725s2011 njua b 001 0 eng |
| 020 ## - INTERNATIONAL STANDARD BOOK NUMBER |
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| International Standard Book Number |
9780470458365 |
| 040 ## - CATALOGING SOURCE |
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AKCL |
| 042 ## - AUTHENTICATION CODE |
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pcc |
| 082 ## - DEWEY DECIMAL CLASSIFICATION NUMBER |
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| Classification number |
510 |
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KRE-A11 |
| 100 1# - MAIN ENTRY--PERSONAL NAME |
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| Personal name |
Kreyszig, Erwin. |
| 245 10 - TITLE STATEMENT |
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| Title |
Advanced Engineering Mathematics / |
| Statement of responsibility, etc. |
Erwin Kreyszig |
| 250 ## - EDITION STATEMENT |
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| Edition statement |
11th ed. |
| 260 ## - PUBLICATION, DISTRIBUTION, ETC. |
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| Place of publication, distribution, etc. |
New Delhi: |
| Name of publisher, distributor, etc. |
Wiley India Pvt. Ltd., |
| Date of publication, distribution, etc. |
2025. |
| 300 ## - PHYSICAL DESCRIPTION |
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| Extent |
XXIII,1022p. |
| 520 ## - SUMMARY, ETC. |
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| Summary, etc. |
Advanced Engineering Mathematics, 11th Edition, is known for its comprehensive coverage, careful and correct mathematics, outstanding exercises, and self-contained subject matter parts for maximum flexibility. It opens with ordinary differential equations and ends with the topic of mathematical statistics. The analysis chapters address: Fourier analysis and partial differential equations, complex analysis, and numeric analysis. The book is written by a pioneer in the field of applied mathematics. This comprehensive volume is designed to equip students and professionals with the mathematical tools necessary to tackle complex engineering challenges and drive innovation.<br/><br/> <br/><br/>This edition of the text maintains those aspects of the previous editions that have led to the book being so successful. In addition to introducing a new appendix on emerging topics in applied mathematics, each chapter now features a dedicated section on how mathematical modeling and engineering can address environmental and societal challenges, promoting sustainability and ethical practices. This edition includes a revision of the problem sets, making them even more effective, useful, and up-to-date by adding the problems on open-source mathematical software. |
| 650 #0 - SUBJECT ADDED ENTRY--TOPICAL TERM |
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| Topical term or geographic name entry element |
Mathematics |
| 650 #0 - SUBJECT ADDED ENTRY--TOPICAL TERM |
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| Topical term or geographic name entry element |
Mathematical physics. |
| 650 #0 - SUBJECT ADDED ENTRY--TOPICAL TERM |
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| Topical term or geographic name entry element |
Engineering mathematics. |
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Books |
| 300 ## - PHYSICAL DESCRIPTION |
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27 cm. |
| 336 ## - CONTENT TYPE |
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text |
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txt |
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rdacontent |
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unmediated |
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n |
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rdamedia |
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volume |
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nc |
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rdacarrier |
| 504 ## - BIBLIOGRAPHY, ETC. NOTE |
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| Bibliography, etc. note |
Includes bibliographical references and index. |
| 505 ## - FORMATTED CONTENTS NOTE |
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| Formatted contents note |
PART A Ordinary Differential Equations (ODEs)<br/><br/> <br/><br/>CHAPTER 1 First-Order ODEs<br/><br/>1.1 Basic Concepts. Modeling<br/><br/>1.2 Geometric Meaning of y’ = ƒ(x, y). Direction Fields, Euler’s Method<br/><br/>1.3 Separable ODEs. Modeling<br/><br/>1.4 Exact ODEs. Integrating Factors<br/><br/>1.5 Linear ODEs. Bernoulli Equation. Population Dynamics<br/><br/>1.6 Orthogonal Trajectories. Optional<br/><br/>1.7 Existence and Uniqueness of Solutions for Initial Value Problems<br/><br/> Sustainability and Ethical Considerations<br/><br/> Chapter 1 Review Questions and Problems<br/><br/> Summary of Chapter 1<br/><br/> <br/><br/>CHAPTER 2 Second-Order Linear ODEs<br/><br/>2.1 Homogeneous Linear ODEs of Second Order<br/><br/>2.2 Homogeneous Linear ODEs with Constant Coefficients<br/><br/>2.3 Differential Operators. Optional<br/><br/>2.4 Modeling of Free Oscillations of a Mass–Spring System<br/><br/>2.5 Euler–Cauchy Equations<br/><br/>2.6 Existence and Uniqueness of Solutions. Wronskian<br/><br/>2.7 Nonhomogeneous ODEs<br/><br/>2.8 Modeling: Forced Oscillations. Resonance<br/><br/>2.9 Modeling: Electric Circuits<br/><br/>2.10 Solution by Variation of Parameters<br/><br/>Sustainability and Ethical Considerations<br/><br/>Chapter 2 Review Questions and Problems<br/><br/>Summary of Chapter 2<br/><br/> <br/><br/>CHAPTER 3 Higher Order Linear ODEs<br/><br/>3.1 Homogeneous Linear ODEs<br/><br/>3.2 Homogeneous Linear ODEs with Constant Coefficients<br/><br/>3.3 Nonhomogeneous Linear ODEs<br/><br/>Sustainability and Ethical Considerations<br/><br/>Chapter 3 Review Questions and Problems<br/><br/>Summary of Chapter 3<br/><br/> <br/><br/>CHAPTER 4 Systems of ODEs. Phase Plane. Qualitative Methods<br/><br/>4.0 For Reference: Basics of Matrices and Vectors<br/><br/>4.1 Systems of ODEs as Models in Engineering Applications<br/><br/>4.2 Basic Theory of Systems of ODEs. Wronskian<br/><br/>4.3 Constant-Coefficient Systems. Phase Plane Method<br/><br/>4.4 Criteria for Critical Points. Stability<br/><br/>4.5 Qualitative Methods for Nonlinear Systems<br/><br/>4.6 Nonhomogeneous Linear Systems of ODEs<br/><br/>Sustainability and Ethical Considerations<br/><br/>Chapter 4 Review Questions and Problems<br/><br/>Summary of Chapter 4<br/><br/> <br/><br/>CHAPTER 5 Series Solutions of ODEs. Special Functions<br/><br/>5.1 Power Series Method<br/><br/>5.2 Legendre’s Equation. Legendre Polynomials (x)<br/><br/>5.3 Extended Power Series Method: Frobenius Method<br/><br/>5.4 Bessel’s Equation. Bessel Functions (x)<br/><br/>5.5 Bessel Functions of the (x). General Solution<br/><br/>Sustainability and Ethical Considerations<br/><br/>Chapter 5 Review Questions and Problems<br/><br/>Summary of Chapter 5<br/><br/> <br/><br/>CHAPTER 6 Laplace Transforms<br/><br/>6.1 Laplace Transform. Linearity. First Shifting Theorem (s-Shifting)<br/><br/>6.2 Transforms of Derivatives and Integrals. ODEs<br/><br/>6.3 Unit Step Function (Heaviside Function). Second Shifting Theorem (t-Shifting)<br/><br/>6.4 Short Impulses. Dirac’s Delta Function. Partial Fractions<br/><br/>6.5 Convolution. Integral Equations<br/><br/>6.6 Differentiation and Integration of Transforms. ODEs with Variable Coefficients<br/><br/>6.7 Systems of ODEs<br/><br/>6.8 Laplace Transform: General Formulas<br/><br/>6.9 Table of Laplace Transforms<br/><br/>Sustainability and Ethical Considerations<br/><br/>Chapter 6 Review Questions and Problems<br/><br/>Summary of Chapter 6<br/><br/> <br/><br/>PART B Linear Algebra. Vector Calculus<br/><br/> <br/><br/>CHAPTER 7 Linear Algebra: Matrices, Vectors, Determinants. Linear Systems<br/><br/>7.1 Matrices, Vectors: Addition and Scalar Multiplication<br/><br/>7.2 Matrix Multiplication<br/><br/>7.3 Linear Systems of Equations. Gauss Elimination<br/><br/>7.4 Linear Independence. Rank of a Matrix. Vector Space<br/><br/>7.5 Solutions of Linear Systems: Existence, Uniqueness<br/><br/>7.6 For Reference: Second- and Third-Order Determinants<br/><br/>7.7 Determinants. Cramer’s Rule<br/><br/>7.8 Inverse of a Matrix. Gauss–Jordan Elimination<br/><br/>7.9 Vector Spaces, Inner Product Spaces. Linear Transformations. Optional<br/><br/>Sustainability and Ethical Considerations<br/><br/>Chapter 7 Review Questions and Problems<br/><br/>Summary of Chapter 7<br/><br/> <br/><br/>CHAPTER 8 Linear Algebra: Matrix Eigenvalue Problems<br/><br/>8.1 The Matrix Eigenvalue Problem. Determining Eigenvalues and Eigenvectors<br/><br/>8.2 Some Applications of Eigenvalue Problems<br/><br/>8.3 Symmetric, Skew-Symmetric, and Orthogonal Matrices<br/><br/>8.4 Eigenbases. Diagonalization. Quadratic Forms<br/><br/>8.5 Complex Matrices and Forms. Optional<br/><br/>Sustainability and Ethical Considerations<br/><br/>Chapter 8 Review Questions and Problems<br/><br/>Summary of Chapter 8<br/><br/> <br/><br/>CHAPTER 9 Vector Differential Calculus. Grad, Div, Curl<br/><br/>9.1 Vectors in 2-Space and 3-Space<br/><br/>9.2 Inner Product (Dot Product)<br/><br/>9.3 Vector Product (Cross Product)<br/><br/>9.4 Vector and Scalar Functions and Their Fields. Vector Calculus: Derivatives<br/><br/>9.5 Curves. Arc Length. Curvature. Torsion<br/><br/>9.6 Calculus Review: Functions of Several Variables. Optional<br/><br/>9.7 Gradient of a Scalar Field. Directional Derivative<br/><br/>9.8 Divergence of a Vector Field<br/><br/>9.9 Curl of a Vector Field<br/><br/>Sustainability and Ethical Considerations<br/><br/>Chapter 9 Review Questions and Problems<br/><br/>Summary of Chapter 9<br/><br/> <br/><br/>CHAPTER 10 Vector Integral Calculus. Integral Theorems<br/><br/>10.1 Line Integrals<br/><br/>10.2 Path Independence of Line Integrals<br/><br/>10.3 Calculus Review: Double Integrals. Optional<br/><br/>10.4 Green’s Theorem in the Plane<br/><br/>10.5 Surfaces for Surface Integrals<br/><br/>10.6 Surface Integrals<br/><br/>10.7 Triple Integrals. Divergence Theorem of Gauss<br/><br/>10.8 Further Applications of the Divergence Theorem<br/><br/>10.9 Stokes’s Theorem<br/><br/>Sustainability and Ethical Considerations<br/><br/>Chapter 10 Review Questions and Problems<br/><br/>Summary of Chapter 10<br/><br/> <br/><br/>PART C Fourier Analysis. Partial Differential Equations (PDEs)<br/><br/> <br/><br/>CHAPTER 11 Fourier Analysis<br/><br/>11.1 Fourier Series<br/><br/>11.2 Arbitrary Period. Even and Odd Functions. Half-Range Expansions<br/><br/>11.3 Forced Oscillations<br/><br/>11.4 Approximation by Trigonometric Polynomials<br/><br/>11.5 Sturm–Liouville Problems. Orthogonal Functions<br/><br/>11.6 Orthogonal Series. Generalized Fourier Series<br/><br/>11.7 Fourier Integral<br/><br/>11.8 Fourier Cosine and Sine Transforms<br/><br/>11.9 Fourier Transform. Discrete and Fast Fourier Transforms<br/><br/>11.10 Tables of Transforms<br/><br/>Sustainability and Ethical Considerations<br/><br/>Chapter 11 Review Questions and Problems<br/><br/>Summary of Chapter 11<br/><br/> <br/><br/>CHAPTER 12 Partial Differential Equations (PDEs)<br/><br/>12.1 Basic Concepts of PDEs<br/><br/>12.2 Modeling: Vibrating String, Wave Equation<br/><br/>12.3 Solution by Separating Variables. Use of Fourier Series<br/><br/>12.4 D’Alembert’s Solution of the Wave Equation. Characteristics<br/><br/>12.5 Modeling: Heat Flow from a Body in Space. Heat Equation<br/><br/>12.6 Heat Equation: Solution by Fourier Series. Steady Two-Dimensional Heat Problems. Dirichlet Problem<br/><br/>12.7 Heat Equation: Modeling Very Long Bars. Solution by Fourier Integrals and Transforms<br/><br/>12.8 Modeling: Membrane, Two-Dimensional Wave Equation<br/><br/>12.9 Rectangular Membrane. Double Fourier Series<br/><br/>12.10 Laplacian in Polar Coordinates. Circular Membrane. Fourier–Bessel Series<br/><br/>12.11 Laplace’s Equation in Cylindrical and Spherical Coordinates. Potential<br/><br/>12.12 Solution of PDEs by Laplace Transforms<br/><br/>Sustainability and Ethical Considerations<br/><br/>Chapter 12 Review Questions and Problems<br/><br/>Summary of Chapter 12<br/><br/> <br/><br/>PART D Complex Analysis<br/><br/> <br/><br/>CHAPTER 13 Complex Numbers and Functions. Complex Differentiation<br/><br/>13.1 Complex Numbers and Their Geometric Representation<br/><br/>13.2 Polar Form of Complex Numbers. Powers and Roots<br/><br/>13.3 Derivative. Analytic Function<br/><br/>13.4 Cauchy–Riemann Equations. Laplace’s Equation<br/><br/>13.5 Exponential Function<br/><br/>13.6 Trigonometric and Hyperbolic Functions. Euler’s Formula<br/><br/>13.7 Logarithm. General Power. Principal Value<br/><br/>Sustainability and Ethical Considerations<br/><br/>Chapter 13 Review Questions and Problems<br/><br/>Summary of Chapter 13<br/><br/> <br/><br/>CHAPTER 14 Complex Integration<br/><br/>14.1 Line Integral in the Complex Plane<br/><br/>14.2 Cauchy’s Integral Theorem<br/><br/>14.3 Cauchy’s Integral Formula<br/><br/>14.4 Derivatives of Analytic Functions<br/><br/>Sustainability and Ethical Considerations<br/><br/>Chapter 14 Review Questions and Problems<br/><br/>Summary of Chapter 14<br/><br/> <br/><br/>CHAPTER 15 Power Series, Taylor Series<br/><br/>15.1 Sequences, Series, Convergence Tests<br/><br/>15.2 Power Series<br/><br/>15.3 Functions Given by Power Series<br/><br/>15.4 Taylor and Maclaurin Series<br/><br/>15.5 Uniform Convergence. Optional<br/><br/>Sustainability and Ethical Considerations<br/><br/>Chapter 15 Review Questions and Problems<br/><br/>Summary of Chapter 15<br/><br/> <br/><br/>CHAPTER 16 Laurent Series. Residue Integration<br/><br/>16.1 Laurent Series<br/><br/>16.2 Singularities and Zeros. Infinity<br/><br/>16.3 Residue Integration Method<br/><br/>16.4 Residue Integration of Real Integrals<br/><br/>Sustainability and Ethical Considerations<br/><br/>Chapter 16 Review Questions and Problems<br/><br/>Summary of Chapter 16<br/><br/> <br/><br/>CHAPTER 17 Conformal Mapping<br/><br/>17.1 Geometry of Analytic Functions: Conformal Mapping<br/><br/>17.2 Linear Fractional Transformations (Möbius Transformations)<br/><br/>17.3 Special Linear Fractional Transformations<br/><br/>17.4 Conformal Mapping by Other Functions<br/><br/>17.5 Riemann Surfaces. Optional<br/><br/>Sustainability and Ethical Considerations<br/><br/>Chapter 17 Review Questions and Problems<br/><br/>Summary of Chapter 17<br/><br/> <br/><br/>CHAPTER 18 Complex Analysis and Potential Theory<br/><br/>18.1 Electrostatic Fields<br/><br/>18.2 Use of Conformal Mapping. Modeling<br/><br/>18.3 Heat Problems<br/><br/>18.4 Fluid Flow<br/><br/>18.5 Poisson’s Integral Formula for Potentials<br/><br/>18.6 General Properties of Harmonic Functions. Uniqueness Theorem for the Dirichlet Problem<br/><br/>Sustainability and Ethical Considerations<br/><br/>Chapter 18 Review Questions and Problems<br/><br/>Summary of Chapter 18<br/><br/> <br/><br/>PART E Numeric Analysis<br/><br/> Software<br/><br/> <br/><br/>CHAPTER 19 Numerics in General<br/><br/>19.1 Introduction<br/><br/>19.2 Solution of Equations by Iteration<br/><br/>19.3 Interpolation<br/><br/>19.4 Spline Interpolation<br/><br/>19.5 Numeric Integration and Differentiation<br/><br/>Sustainability and Ethical Considerations<br/><br/>Chapter 19 Review Questions and Problems<br/><br/>Summary of Chapter 19<br/><br/> <br/><br/>CHAPTER 20 Numeric Linear Algebra<br/><br/>20.1 Linear Systems: Gauss Elimination<br/><br/>20.2 Linear Systems: LU-Factorization, Matrix Inversion<br/><br/>20.3 Linear Systems: Solution by Iteration<br/><br/>20.4 Linear Systems: Ill-Conditioning, Norms<br/><br/>20.5 Least Squares Method<br/><br/>20.6 Matrix Eigenvalue Problems: Introduction<br/><br/>20.7 Inclusion of Matrix Eigenvalues<br/><br/>20.8 Power Method for Eigenvalues<br/><br/>20.9 Tridiagonalization and QR-Factorization<br/><br/>Sustainability and Ethical Considerations<br/><br/>Chapter 20 Review Questions and Problems<br/><br/>Summary of Chapter 20<br/><br/> <br/><br/>CHAPTER 21 Numerics for ODEs and PDEs<br/><br/>21.1 Methods for First-Order ODEs<br/><br/>21.2 Multistep Methods<br/><br/>21.3 Methods for Systems and Higher Order ODEs<br/><br/>21.4 Methods for Elliptic PDEs<br/><br/>21.5 Neumann and Mixed Problems. Irregular Boundary<br/><br/>21.6 Methods for Parabolic PDEs<br/><br/>21.7 Method for Hyperbolic PDEs<br/><br/>Sustainability and Ethical Considerations<br/><br/>Chapter 21 Review Questions and Problems<br/><br/>Summary of Chapter 21<br/><br/> <br/><br/>PART F Optimization, Graphs<br/><br/> <br/><br/>CHAPTER 22 Unconstrained Optimization. Linear Programming<br/><br/>22.1 Basic Concepts. Unconstrained Optimization: Method of Steepest Descent<br/><br/>22.2 Linear Programming<br/><br/>22.3 Simplex Method<br/><br/>22.4 Simplex Method: Difficulties<br/><br/>Sustainability and Ethical Considerations<br/><br/>Chapter 22 Review Questions and Problems<br/><br/>Summary of Chapter 22<br/><br/> <br/><br/>CHAPTER 23 Graphs. Combinatorial Optimization<br/><br/>23.1 Graphs and Digraphs<br/><br/>23.2 Shortest Path Problems. Complexity<br/><br/>23.3 Bellman’s Principle. Dijkstra’s Algorithm<br/><br/>23.4 Shortest Spanning Trees: Greedy Algorithm<br/><br/>23.5 Shortest Spanning Trees: Prim’s Algorithm<br/><br/>23.6 Flows in Networks<br/><br/>23.7 Maximum Flow: Ford–Fulkerson Algorithm<br/><br/>23.8 Bipartite Graphs. Assignment Problems<br/><br/>Sustainability and Ethical Considerations<br/><br/>Chapter 23 Review Questions and Problems<br/><br/>Summary of Chapter 23<br/><br/> <br/><br/>PART G Probability, Statistics (available online)<br/><br/> Software<br/><br/> <br/><br/>CHAPTER 24 Data Analysis. Probability Theory<br/><br/>24.1 Data Representation. Average. Spread<br/><br/>24.2 Experiments, Outcomes, Events<br/><br/>24.3 Probability<br/><br/>24.4 Permutations and Combinations<br/><br/>24.5 Random Variables. Probability Distributions<br/><br/>24.6 Mean and Variance of a Distribution<br/><br/>24.7 Binomial, Poisson, and Hypergeometric Distributions<br/><br/>24.8 Normal Distribution<br/><br/>24.9 Distributions of Several Random Variables<br/><br/>Sustainability and Ethical Considerations<br/><br/>Chapter 24 Review Questions and Problems<br/><br/>Summary of Chapter 24<br/><br/> <br/><br/>CHAPTER 25 Mathematical Statistics<br/><br/>25.1 Introduction. Random Sampling<br/><br/>25.2 Point Estimation of Parameters<br/><br/>25.3 Confidence Intervals<br/><br/>25.4 Testing Hypotheses. Decisions<br/><br/>25.5 Quality Control<br/><br/>25.6 Acceptance Sampling<br/><br/>25.7 Goodness of Fit. χ2-Test<br/><br/>25.8 Nonparametric Tests<br/><br/>25.9 Regression. Fitting Straight Lines. Correlation<br/><br/>Sustainability and Ethical Considerations<br/><br/>Chapter 25 Review Questions and Problems<br/><br/>Summary of Chapter 25<br/><br/> <br/><br/>PROJECTs<br/><br/> <br/><br/>APPENDIX 1 References<br/><br/> <br/><br/>APPENDIX 2 Answers to Odd-Numbered Problems (available online)<br/><br/> <br/><br/>APPENDIX 3 Auxiliary Material<br/><br/>A3.1 Formulas for Special Functions<br/><br/>A3.2 Partial Derivatives<br/><br/>A3.3 Sequences and Series<br/><br/>A3.4 Grad, Div, Curl, in Curvilinear Coordinates<br/><br/> <br/><br/>APPENDIX 4 Additional Proofs<br/><br/> <br/><br/>APPENDIX 5 Tables<br/><br/> <br/><br/>APPENDIX 6 Emerging Topics in Applied Mathematics<br/><br/> <br/><br/>INDEX |
| 700 1# - ADDED ENTRY--PERSONAL NAME |
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| Personal name |
Kreyszig, Herbert. |
| 700 1# - ADDED ENTRY--PERSONAL NAME |
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| Personal name |
Norminton, E. J. |
| Fuller form of name |
(Edward J.) |
| 856 42 - ELECTRONIC LOCATION AND ACCESS |
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| Materials specified |
Publisher description |
| Uniform Resource Identifier |
<a href="http://www.loc.gov/catdir/enhancements/fy1114/2011287100-d.html">http://www.loc.gov/catdir/enhancements/fy1114/2011287100-d.html</a> |
| 856 41 - ELECTRONIC LOCATION AND ACCESS |
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| Materials specified |
Table of contents only |
| Uniform Resource Identifier |
<a href="http://www.loc.gov/catdir/enhancements/fy1114/2011287100-t.html">http://www.loc.gov/catdir/enhancements/fy1114/2011287100-t.html</a> |
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Dewey Decimal Classification |
| Suppress in OPAC |
No |