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
- Title page
- Copyright page
- Preface
-
1: Problem Formulation and Model Development
- Introduction
- Algebraic Equations from Vapor–Liquid Equilibria (VLE)
- Macroscopic Balances: Lumped-Parameter Models
- Force Balances: Newton's Second Law of Motion
- Distributed Parameter Models: Microscopic Balances
- A Contrast: Deterministic Models and Stochastic Processes
- Empiricisms and Data Interpretation
- Conclusion
- Problems
- References
- 2: Algebraic Equations
- 3: Vectors and Tensors
- 4: Numerical Quadrature
-
5: Analytic Solution of Ordinary Differential Equations
- An Introductory Example
- First-Order Ordinary Differential Equations
- Nonlinear First-Order Ordinary Differential Equations
- Higher-Order Linear ODEs with Constant Coefficients
- Higher-Order Equations with Variable Coefficients
- Bessel's Equation and Bessel Functions
- Power Series Solutions of Ordinary Differential Equations
- Regular Perturbation
- Linearization
- Conclusion
- Problems
- References
-
6: Numerical Solution of Ordinary Differential Equations
- An Illustrative Example
- The Euler Method
- Runge–Kutta Methods
- Simultaneous Ordinary Differential Equations
- Limitations of Fixed Step-Size Algorithms
- Richardson Extrapolation
- Multistep Methods
- Split Boundary Conditions
- Finite-Difference Methods
- Stiff Differential Equations
- Bulirsch–Stoer Method
- Phase Space
- Summary
- Problems
- References
-
7: Analytic Solution of Partial Differential Equations
- Introduction
- Classification of Partial Differential Equations and Boundary Conditions
- Fourier Series
- The Product Method (Separation of Variables)
- Applications of the Laplace Transform
- Approximate Solution Techniques
- The Cauchy–Riemann Equations, Conformal Mapping, and Solutions for the Laplace Equation
- Conclusion
- Problems
- References
-
8: Numerical Solution of Partial Differential Equations
- Introduction
- Elliptic Partial Differential Equations
- Parabolic Partial Differential Equations
- Hyperbolic Partial Differential Equations
- Elementary Problems with Convective Transport
- A Numerical Procedure for Two-Dimensional Viscous Flow Problems
- MacCormack's Method
- Adaptive Grids
- Conclusion
- Problems
- References
-
9: Integro-Differential Equations
- Introduction
- An Example of Three-Mode Control
- Population Problems with Hereditary Influences
- An Elementary Solution Strategy
- VIM: The Variational Iteration Method
- Integro-Differential Equations and the Spread of Infectious Disease
- Examples Drawn from Population Balances
- Conclusion
- Problems
- References
- 10: Time-Series Data and the Fourier Transform
- 11: An Introduction to the Calculus of Variations and the Finite-Element Method
- Index
- End User License Agreement
Product information
- Title: Applied Mathematics for Science and Engineering
- Author(s):
- Release date: September 2014
- Publisher(s): Wiley
- ISBN: 9781118749920
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