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Applied Mathematics for Science and Engineering

Book Description

Prepare students for success in using applied mathematics for engineering practice and post-graduate studies

  • moves from one mathematical method to the next sustaining reader interest and easing the application of the techniques

  • Uses different examples from chemical, civil, mechanical and various other engineering fields

  • Based on a decade's worth of the authors lecture notes detailing the topic of applied mathematics for scientists and engineers

  • Concisely writing with numerous examples provided including historical perspectives as well as a solutions manual for academic adopters

  • Table of Contents

    1. Title page
    2. Copyright page
    3. Preface
    4. 1: Problem Formulation and Model Development
      1. Introduction
      2. Algebraic Equations from Vapor–Liquid Equilibria (VLE)
      3. Macroscopic Balances: Lumped-Parameter Models
      4. Force Balances: Newton's Second Law of Motion
      5. Distributed Parameter Models: Microscopic Balances
      6. A Contrast: Deterministic Models and Stochastic Processes
      7. Empiricisms and Data Interpretation
      8. Conclusion
      9. Problems
      10. References
    5. 2: Algebraic Equations
      1. Introduction
      2. Elementary Methods
      3. Simultaneous Linear Algebraic Equations
      4. Simultaneous Nonlinear Algebraic Equations
      5. Algebraic Equations with Constraints
      6. Conclusion
      7. Problems
      8. References
    6. 3: Vectors and Tensors
      1. Introduction
      2. Manipulation of Vectors
      3. Green's Theorem
      4. Stokes' Theorem
      5. Conclusion
      6. Problems
      7. References
    7. 4: Numerical Quadrature
      1. Introduction
      2. Trapezoid Rule
      3. Simpson's Rule
      4. Newton–Cotes Formulae
      5. Roundoff and Truncation Errors
      6. Romberg Integration
      7. Adaptive Integration Schemes
      8. Integrating Discrete Data
      9. Multiple Integrals (Cubature)
      10. Conclusion
      11. Problems
      12. References
    8. 5: Analytic Solution of Ordinary Differential Equations
      1. An Introductory Example
      2. First-Order Ordinary Differential Equations
      3. Nonlinear First-Order Ordinary Differential Equations
      4. Higher-Order Linear ODEs with Constant Coefficients
      5. Higher-Order Equations with Variable Coefficients
      6. Bessel's Equation and Bessel Functions
      7. Power Series Solutions of Ordinary Differential Equations
      8. Regular Perturbation
      9. Linearization
      10. Conclusion
      11. Problems
      12. References
    9. 6: Numerical Solution of Ordinary Differential Equations
      1. An Illustrative Example
      2. The Euler Method
      3. Runge–Kutta Methods
      4. Simultaneous Ordinary Differential Equations
      5. Limitations of Fixed Step-Size Algorithms
      6. Richardson Extrapolation
      7. Multistep Methods
      8. Split Boundary Conditions
      9. Finite-Difference Methods
      10. Stiff Differential Equations
      11. Bulirsch–Stoer Method
      12. Phase Space
      13. Summary
      14. Problems
      15. References
    10. 7: Analytic Solution of Partial Differential Equations
      1. Introduction
      2. Classification of Partial Differential Equations and Boundary Conditions
      3. Fourier Series
      4. The Product Method (Separation of Variables)
      5. Applications of the Laplace Transform
      6. Approximate Solution Techniques
      7. The Cauchy–Riemann Equations, Conformal Mapping, and Solutions for the Laplace Equation
      8. Conclusion
      9. Problems
      10. References
    11. 8: Numerical Solution of Partial Differential Equations
      1. Introduction
      2. Elliptic Partial Differential Equations
      3. Parabolic Partial Differential Equations
      4. Hyperbolic Partial Differential Equations
      5. Elementary Problems with Convective Transport
      6. A Numerical Procedure for Two-Dimensional Viscous Flow Problems
      7. M<span xmlns="http://www.w3.org/1999/xhtml" xmlns:m="http://www.w3.org/1998/Math/MathML" xmlns:svg="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:ibooks="http://vocabulary.itunes.apple.com/rdf/ibooks/vocabulary-extensions-1.0" xmlns:epub="http://www.idpf.org/2007/ops" style="font-variant:small-caps">ac</span>Cormack's MethodCormack's Method
      8. Adaptive Grids
      9. Conclusion
      10. Problems
      11. References
    12. 9: Integro-Differential Equations
      1. Introduction
      2. An Example of Three-Mode Control
      3. Population Problems with Hereditary Influences
      4. An Elementary Solution Strategy
      5. VIM: The Variational Iteration Method
      6. Integro-Differential Equations and the Spread of Infectious Disease
      7. Examples Drawn from Population Balances
      8. Conclusion
      9. Problems
      10. References
    13. 10: Time-Series Data and the Fourier Transform
      1. Introduction
      2. A Nineteenth-Century Idea
      3. The Autocorrelation Coefficient
      4. A Fourier Transform Pair
      5. The Fast Fourier Transform
      6. Aliasing and Leakage
      7. Smoothing Data by Filtering
      8. Modulation (Beats)
      9. Some Familiar Examples
      10. Conclusion and Some Final Thoughts
      11. Problems
      12. References
    14. 11: An Introduction to the Calculus of Variations and the Finite-Element Method
      1. Some Preliminaries
      2. Notation for the Calculus of Variations
      3. Brachistochrone Problem
      4. Other Examples
      5. A Contemporary COV Analysis of an Old Structural Problem
      6. Systems with Surface Tension
      7. The Connection between COV and the Finite-Element Method (FEM)
      8. Conclusion
      9. Problems
      10. Note
      11. References
    15. Index
    16. End User License Agreement