Essentials of Mathematical Methods in Science and Engineering, 2nd Edition

Essentials of Mathematical Methods in Science and Engineering, 2nd Edition

by Selcuk S. Bayin
Released December 2019
Publisher(s): Wiley
ISBN: 9781119580249

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Book description

A comprehensive introduction to the multidisciplinary applications of mathematical methods, revised and updated

The second edition of Essentials of Mathematical Methods in Science and Engineering offers an introduction to the key mathematical concepts of advanced calculus, differential equations, complex analysis, and introductory mathematical physics for students in engineering and physics research. The book’s approachable style is designed in a modular format with each chapter covering a subject thoroughly and thus can be read independently.

This updated second edition includes two new and extensive chapters that cover practical linear algebra and applications of linear algebra as well as a computer file that includes Matlab codes. To enhance understanding of the material presented, the text contains a collection of exercises at the end of each chapter. The author offers a coherent treatment of the topics with a style that makes the essential mathematical skills easily accessible to a multidisciplinary audience. This important text:

•    Includes derivations with sufficient detail so that the reader can follow them without searching for results in other parts of the book

•    Puts the emphasis on the analytic techniques

•    Contains two new chapters that explore linear algebra and its applications

•    Includes Matlab codes that the readers can use to practice with the methods introduced in the book

Written for students in science and engineering, this new edition of Essentials of Mathematical Methods in Science and Engineering maintains all the successful features of the first edition and includes new information.

Table of contents

  1. Cover
  2. Preface
    1. About the Second Edition
    2. Summary of the Book
    3. Course Suggestions
  3. Acknowledgments
  4. CHAPTER 1: FUNCTIONAL ANALYSIS
    1. 1.1 CONCEPT OF FUNCTION
    2. 1.2 CONTINUITY AND LIMITS
    3. 1.3 PARTIAL DIFFERENTIATION
    4. 1.4 TOTAL DIFFERENTIAL
    5. 1.5 TAYLOR SERIES
    6. 1.6 MAXIMA AND MINIMA OF FUNCTIONS
    7. 1.7 EXTREMA OF FUNCTIONS WITH CONDITIONS
    8. 1.8 DERIVATIVES AND DIFFERENTIALS OF COMPOSITE FUNCTIONS
    9. 1.9 IMPLICIT FUNCTION THEOREM
    10. 1.10 INVERSE FUNCTIONS
    11. 1.11 INTEGRAL CALCULUS AND THE DEFINITE INTEGRAL
    12. 1.12 RIEMANN INTEGRAL
    13. 1.13 IMPROPER INTEGRALS
    14. 1.14 CAUCHY PRINCIPAL VALUE INTEGRALS
    15. 1.15 INTEGRALS INVOLVING A PARAMETER
    16. 1.16 LIMITS OF INTEGRATION DEPENDING ON A PARAMETER
    17. 1.17 DOUBLE INTEGRALS
    18. 1.18 PROPERTIES OF DOUBLE INTEGRALS
    19. 1.19 TRIPLE AND MULTIPLE INTEGRALS
    20. REFERENCES
    21. PROBLEMS
  5. CHAPTER 2: VECTOR ANALYSIS
    1. 2.1 VECTOR ALGEBRA: GEOMETRIC METHOD
    2. 2.2 VECTOR ALGEBRA: COORDINATE REPRESENTATION
    3. 2.3 LINES AND PLANES
    4. 2.4 VECTOR DIFFERENTIAL CALCULUS
    5. 2.5 GRADIENT OPERATOR
    6. 2.6 DIVERGENCE AND CURL OPERATORS
    7. 2.7 VECTOR INTEGRAL CALCULUS IN TWO DIMENSIONS
    8. 2.8 CURL OPERATOR AND STOKES'S THEOREM
    9. 2.9 MIXED OPERATIONS WITH THE DEL OPERATOR
    10. 2.10 POTENTIAL THEORY
    11. REFERENCES
    12. PROBLEMS
  6. CHAPTER 3: GENERALIZED COORDINATES AND TENSORS
    1. 3.1 TRANSFORMATIONS BETWEEN CARTESIAN COORDINATES
    2. 3.2 CARTESIAN TENSORS
    3. 3.3 GENERALIZED COORDINATES
    4. 3.4 GENERAL TENSORS
    5. 3.5 DIFFERENTIAL OPERATORS IN GENERALIZED COORDINATES
    6. 3.6 ORTHOGONAL GENERALIZED COORDINATES
    7. REFERENCES
    8. PROBLEMS
  7. CHAPTER 4: DETERMINANTS AND MATRICES
    1. 4.1 BASIC DEFINITIONS
    2. 4.2 OPERATIONS WITH MATRICES
    3. 4.3 SUBMATRIX AND PARTITIONED MATRICES
    4. 4.4 SYSTEMS OF LINEAR EQUATIONS
    5. 4.5 GAUSS'S METHOD OF ELIMINATION
    6. 4.6 DETERMINANTS
    7. 4.7 PROPERTIES OF DETERMINANTS
    8. 4.8 CRAMER'S RULE
    9. 4.9 INVERSE OF A MATRIX
    10. 4.10 HOMOGENEOUS LINEAR EQUATIONS
    11. REFERENCES
    12. PROBLEMS
  8. CHAPTER 5: LINEAR ALGEBRA
    1. 5.1 FIELDS AND VECTOR SPACES
    2. 5.2 LINEAR COMBINATIONS, GENERATORS, AND BASES
    3. 5.3 COMPONENTS
    4. 5.4 LINEAR TRANSFORMATIONS
    5. 5.5 MATRIX REPRESENTATION OF TRANSFORMATIONS
    6. 5.6 ALGEBRA OF TRANSFORMATIONS
    7. 5.7 CHANGE OF BASIS
    8. 5.8 INVARIANTS UNDER SIMILARITY TRANSFORMATIONS
    9. 5.9 EIGENVALUES AND EIGENVECTORS
    10. 5.10 MOMENT OF INERTIA TENSOR
    11. 5.11 INNER PRODUCT SPACES
    12. 5.12 THE INNER PRODUCT
    13. 5.13 ORTHOGONALITY AND COMPLETENESS
    14. 5.14 GRAM–SCHMIDT ORTHOGONALIZATION
    15. 5.15 EIGENVALUE PROBLEM FOR REAL SYMMETRIC MATRICES
    16. 5.16 PRESENCE OF DEGENERATE EIGENVALUES
    17. 5.17 QUADRATIC FORMS
    18. 5.18 HERMITIAN MATRICES
    19. 5.19 MATRIX REPRESENTATION OF HERMITIAN OPERATORS
    20. 5.20 FUNCTIONS OF MATRICES
    21. 5.21 FUNCTION SPACE AND HILBERT SPACE
    22. 5.22 DIRAC'S BRA AND KET VECTORS
    23. REFERENCES
    24. PROBLEMS
  9. CHAPTER 6: PRACTICAL LINEAR ALGEBRA
    1. 6.1 SYSTEMS OF LINEAR EQUATIONS
    2. 6.2 NUMERICAL METHODS OF LINEAR ALGEBRA
    3. REFERENCES
    4. PROBLEMS
  10. CHAPTER 7: APPLICATIONS OF LINEAR ALGEBRA
    1. 7.1 CHEMISTRY AND CHEMICAL ENGINEERING
    2. 7.2 LINEAR PROGRAMMING
    3. 7.3 LEONTIEF INPUT–OUTPUT MODEL OF ECONOMY
    4. 7.4 APPLICATIONS TO GEOMETRY
    5. 7.5 ELIMINATION THEORY
    6. 7.6 CODING THEORY
    7. 7.7 CRYPTOGRAPHY
    8. 7.8 GRAPH THEORY
    9. REFERENCES
    10. PROBLEMS
  11. CHAPTER 8: SEQUENCES AND SERIES
    1. 8.1 SEQUENCES
    2. 8.2 INFINITE SERIES
    3. 8.3 ABSOLUTE AND CONDITIONAL CONVERGENCE
    4. 8.4 OPERATIONS WITH SERIES
    5. 8.5 SEQUENCES AND SERIES OF FUNCTIONS
    6. 8.6 ‐TEST FOR UNIFORM CONVERGENCE
    7. 8.7 PROPERTIES OF UNIFORMLY CONVERGENT SERIES
    8. 8.8 POWER SERIES
    9. 8.9 TAYLOR SERIES AND MACLAURIN SERIES
    10. 8.10 INDETERMINATE FORMS AND SERIES
    11. REFERENCES
    12. PROBLEMS
  12. CHAPTER 9: COMPLEX NUMBERS AND FUNCTIONS
    1. 9.1 THE ALGEBRA OF COMPLEX NUMBERS
    2. 9.2 ROOTS OF A COMPLEX NUMBER
    3. 9.3 INFINITY AND THE EXTENDED COMPLEX PLANE
    4. 9.4 COMPLEX FUNCTIONS
    5. 9.5 LIMITS AND CONTINUITY
    6. 9.6 DIFFERENTIATION IN THE COMPLEX PLANE
    7. 9.7 ANALYTIC FUNCTIONS
    8. 9.8 HARMONIC FUNCTIONS
    9. 9.9 BASIC DIFFERENTIATION FORMULAS
    10. 9.10 ELEMENTARY FUNCTIONS
    11. REFERENCES
    12. PROBLEMS
  13. CHAPTER 10: COMPLEX ANALYSIS
    1. 10.1 CONTOUR INTEGRALS
    2. 10.2 TYPES OF CONTOURS
    3. 10.3 THE CAUCHY–GOURSAT THEOREM
    4. 10.4 INDEFINITE INTEGRALS
    5. 10.5 SIMPLY AND MULTIPLY CONNECTED DOMAINS
    6. 10.6 THE CAUCHY INTEGRAL FORMULA
    7. 10.7 DERIVATIVES OF ANALYTIC FUNCTIONS
    8. 10.8 COMPLEX POWER SERIES
    9. 10.9 CONVERGENCE OF POWER SERIES
    10. 10.10 CLASSIFICATION OF SINGULAR POINTS
    11. 10.11 RESIDUE THEOREM
    12. REFERENCES
    13. PROBLEMS
  14. CHAPTER 11: ORDINARY DIFFERENTIAL EQUATIONS
    1. 11.1 BASIC DEFINITIONS FOR ORDINARY DIFFERENTIAL EQUATIONS
    2. 11.2 FIRST‐ORDER DIFFERENTIAL EQUATIONS
    3. 11.3 SECOND‐ORDER DIFFERENTIAL EQUATIONS
    4. 11.4 LINEAR DIFFERENTIAL EQUATIONS OF HIGHER ORDER
    5. 11.5 INITIAL VALUE PROBLEM AND UNIQUENESS OF THE SOLUTION
    6. 11.6 SERIES SOLUTIONS: FROBENIUS METHOD
    7. REFERENCES
    8. PROBLEMS
  15. CHAPTER 12: SECOND‐ORDER DIFFERENTIAL EQUATIONS AND SPECIAL FUNCTIONS
    1. 12.1 LEGENDRE EQUATION
    2. 12.2 HERMITE EQUATION
    3. 12.3 LAGUERRE EQUATION
    4. REFERENCES
    5. PROBLEMS
  16. CHAPTER 13: BESSEL'S EQUATION AND BESSEL FUNCTIONS
    1. 13.1 BESSEL'S EQUATION AND ITS SERIES SOLUTION
    2. 13.2 ORTHOGONALITY AND THE ROOTS OF BESSEL FUNCTIONS
    3. REFERENCES
    4. PROBLEMS
  17. CHAPTER 14: PARTIAL DIFFERENTIAL EQUATIONS AND SEPARATION OF VARIABLES
    1. 14.1 SEPARATION OF VARIABLES IN CARTESIAN COORDINATES
    2. 14.2 SEPARATION OF VARIABLES IN SPHERICAL COORDINATES
    3. 14.3 SEPARATION OF VARIABLES IN CYLINDRICAL COORDINATES
    4. REFERENCES
    5. PROBLEMS
  18. CHAPTER 15: FOURIER SERIES
    1. 15.1 ORTHOGONAL SYSTEMS OF FUNCTIONS
    2. 15.2 FOURIER SERIES
    3. 15.3 EXPONENTIAL FORM OF THE FOURIER SERIES
    4. 15.4 CONVERGENCE OF FOURIER SERIES
    5. 15.5 SUFFICIENT CONDITIONS FOR CONVERGENCE
    6. 15.6 THE FUNDAMENTAL THEOREM
    7. 15.7 UNIQUENESS OF FOURIER SERIES
    8. 15.8 EXAMPLES OF FOURIER SERIES
    9. 15.9 FOURIER SINE AND COSINE SERIES
    10. 15.10 CHANGE OF INTERVAL
    11. 15.11 INTEGRATION AND DIFFERENTIATION OF FOURIER SERIES
    12. REFERENCES
    13. PROBLEMS
  19. CHAPTER 16: FOURIER AND LAPLACE TRANSFORMS
    1. 16.1 TYPES OF SIGNALS
    2. 16.2 SPECTRAL ANALYSIS AND FOURIER TRANSFORMS
    3. 16.3 CORRELATION WITH COSINES AND SINES
    4. 16.4 CORRELATION FUNCTIONS AND FOURIER TRANSFORMS
    5. 16.5 INVERSE FOURIER TRANSFORM
    6. 16.6 FREQUENCY SPECTRUMS
    7. 16.7 DIRAC‐DELTA FUNCTION
    8. 16.8 A CASE WITH TWO COSINES
    9. 16.9 GENERAL FOURIER TRANSFORMS AND THEIR PROPERTIES
    10. 16.10 BASIC DEFINITION OF LAPLACE TRANSFORM
    11. 16.11 DIFFERENTIAL EQUATIONS AND LAPLACE TRANSFORMS
    12. 16.12 TRANSFER FUNCTIONS AND SIGNAL PROCESSORS
    13. 16.13 CONNECTION OF SIGNAL PROCESSORS
    14. REFERENCES
    15. PROBLEMS
  20. CHAPTER 17: CALCULUS of VARIATIONS
    1. 17.1 A SIMPLE CASE
    2. 17.2 VARIATIONAL ANALYSIS
    3. 17.3 ALTERNATE FORM OF EULER EQUATION
    4. 17.4 VARIATIONAL NOTATION
    5. 17.5 A MORE GENERAL CASE
    6. 17.6 HAMILTON'S PRINCIPLE
    7. 17.7 LAGRANGE'S EQUATIONS OF MOTION
    8. 17.8 DEFINITION OF LAGRANGIAN
    9. 17.9 PRESENCE OF CONSTRAINTS IN DYNAMICAL SYSTEMS
    10. 17.10 CONSERVATION LAWS
    11. REFERENCES
    12. PROBLEMS
  21. CHAPTER 18: PROBABILITY THEORY AND DISTRIBUTIONS
    1. 18.1 INTRODUCTION TO PROBABILITY THEORY
    2. 18.2 PERMUTATIONS AND COMBINATIONS
    3. 18.3 APPLICATIONS TO STATISTICAL MECHANICS
    4. 18.4 STATISTICAL MECHANICS AND THERMODYNAMICS
    5. 18.5 RANDOM VARIABLES AND DISTRIBUTIONS
    6. 18.6 DISTRIBUTION FUNCTIONS AND PROBABILITY
    7. 18.7 EXAMPLES OF CONTINUOUS DISTRIBUTIONS
    8. 18.8 DISCRETE PROBABILITY DISTRIBUTIONS
    9. 18.9 FUNDAMENTAL THEOREM OF AVERAGES
    10. 18.10 MOMENTS OF DISTRIBUTION FUNCTIONS
    11. 18.11 CHEBYSHEV'S THEOREM
    12. 18.12 LAW OF LARGE NUMBERS
    13. REFERENCES
    14. PROBLEMS
  22. CHAPTER 19: INFORMATION THEORY
    1. 19.1 ELEMENTS OF INFORMATION PROCESSING MECHANISMS
    2. 19.2 CLASSICAL INFORMATION THEORY
    3. 19.3 QUANTUM INFORMATION THEORY
    4. REFERENCES
    5. PROBLEMS
  23. Further Reading
    1. MATHEMATICAL METHODS TEXTBOOKS:
    2. MATHEMATICAL METHODS WITH COMPUTERS:
    3. CALCULUS/ADVANCED CALCULUS:
    4. LINEAR ALGEBRA AND ITS APPLICATIONS:
    5. COMPLEX CALCULUS:
    6. DIFFERENTIAL EQUATIONS:
    7. CALCULUS OF VARIATIONS:
    8. FOURIER SERIES, INTEGRAL TRANSFORMS AND SIGNAL PROCESSING:
    9. SERIES AND SPECIAL FUNCTIONS:
    10. MATHEMATICAL TABLES:
    11. CLASSICAL MECHANICS:
    12. QUANTUM MECHANICS:
    13. ELECTROMAGNETIC THEORY:
    14. PROBABILITY THEORY:
    15. INFORMATION THEORY:
  24. INDEX
  25. End User License Agreement

Product information

  • Title: Essentials of Mathematical Methods in Science and Engineering, 2nd Edition
  • Author(s): Selcuk S. Bayin
  • Release date: December 2019
  • Publisher(s): Wiley
  • ISBN: 9781119580249