The art of modeling in science and engineering with Mathematica.
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| Author / Creator: | Basmadjian, Diran. |
|---|---|
| Edition: | 2nd ed. / Diran Basmadjian and Ramin Farnood. |
| Imprint: | Boca Raton : Chapman & Hall/CRC, c2007. |
| Description: | 509 p. : ill. ; 25 cm. |
| Language: | English |
| Subject: | |
| Format: | Print Book |
| URL for this record: | http://pi.lib.uchicago.edu/1001/cat/bib/6104642 |
Table of Contents:
- Chapter 1. A First Look at Modeling
- 1.1. The Physical Laws
- 1.1.1. Conservation Laws
- 1.1.2. Auxiliary Relations
- 1.1.3. The Balance Space and Its Geometry
- 1.2. The Rate of the Variables: Dependent and Independent Variables
- 1.3. The Role of Balance Space: Differential and Integral Balances
- 1.4. The Role of Time: Unsteady State and Steady State Balances
- 1.5. Information Derived from Model Solutions
- 1.6. Choosing a Model
- 1.7. Kick-Starting the Modeling Process
- 1.8. Solution Analysis
- Practice Problems
- Chapter 2. Analytical Tools: The Solution of Ordinary Differential Equations
- 2.1. Definitions and Classifications
- 2.1.1. Order of an ODE
- 2.1.2. Linear and Nonlinear ODEs
- 2.1.3. ODEs with Variable Coefficients
- 2.1.4. Homogeneous and Nonhomogeneous ODEs
- 2.1.5. Autonomous ODEs
- 2.2. Boundary and Initial Conditions
- 2.2.1. Some Useful Hints on Boundary Conditions
- 2.3. Analytical Solutions of ODEs
- 2.3.1. Separation of Variables
- 2.3.2. The D-Operator Method. Solution of Linear n-th-Order ODEs with Constant Coefficients
- 2.3.3. Nonhomogeneous Linear Second-Order ODEs with Constant Coefficients
- 2.3.4. Series Solutions of Linear ODEs with Variable Coefficients
- 2.3.5. Other Methods
- 2.4. Nonlinear Analysis
- 2.4.1. Phase Plane Analysis: Critical Points
- 2.5. Laplace Transformation
- 2.5.1. General Properties of the Laplace Transform
- 2.5.2. Application to Differential Equations
- Practice Problems
- Chapter 3. The Use of Mathematica in Modeling Physical Systems
- 3.1. Handling Algebraic Expressions
- 3.2. Algebraic Equations
- 3.2.1. Analytical Solution to Algebraic Equations
- 3.2.2. Numerical Solution to Algebraic Equations
- 3.3. Integration
- 3.4. Ordinary Differential Equations
- 3.4.1. Analytical Solution to ODEs
- 3.4.2. Numerical Solution to Ordinary Differential Equation
- 3.5. Partial Differential Equations
- Practice Problems
- Chapter 4. Elementary Applications of the Conservation Laws
- 4.1. Application of Force Balances
- 4.2. Applications of Mass Balances
- 4.2.1. Compartmental Models
- 4.2.2. Distributed Systems
- 4.3. Applications of Energy Balances
- 4.3.1. Compartmental Models
- 4.3.2. Distributed Models
- 4.4. Simultaneous Applications of the Conservation Laws
- Practice Problems
- Chapter 5. Partial Differential Equations: Classification, Types, and Properties - Some Simple Transformations
- 5.1. Properties and Classes of PDEs
- 5.1.1. Order of a PDE
- 5.1.1.1. First-Order PDEs
- 5.1.1.2. Second-Order PDEs
- 5.1.1.3. Higher-Order PDEs
- 5.1.2. Homogeneous PDEs and BCs
- 5.1.3. PDEs with Variable Coefficients
- 5.1.4. Linear and Nonlinear PDEs: A New Category - Quasilinear PDEs
- 5.1.5. Another New Category: Elliptic, Parabolic, and Hyperbolic PDEs
- 5.1.6. Boundary and Initial Conditions
- 5.2. PDEs of Major Importance
- 5.2.1. First-Order Partial Differential Equations
- 5.2.2. Second-Order PDEs
- 5.3. Useful Simplifications and Transformations
- 5.3.1. Elimination of Independent Variables: Reduction to ODEs
- 5.3.2. Elimination of Dependent Variables: Reduction of Number of Equations
- 5.3.3. Elimination of Nonhomogeneous Terms
- 5.3.4. Change in Independent Variables: Reduction to Canonical Form
- 5.3.5. Simplification of Geometry
- 5.3.5.1. Reduction of a Radial Spherical Configuration into a Planar One
- 5.3.5.2. Reduction of a Radial Circular or Cylindrical Configuration into a Planar One
- 5.3.5.3. Reduction of a Radial Circular or Cylindrical Configuration to a Semi-Infinite One
- 5.3.5.4. Reduction of a Planar Configuration to a Semi-Infinite One
- 5.3.6. Nondimensionalization
- 5.4. PDEs PDQ: Locating Solutions in the Literature
- Practice Problems
- Chapter 6. Solution of Linear Systems by Superposition Methods
- 6.1. Superposition by Addition of Simple Flows: Solutions in Search of a Problem
- 6.2. Superposition by Multiplication: The Neumann Product Solutions
- 6.3. Solution of Source Problems: Superposition by Integration
- 6.4. More Superposition by Integration: Duhamel's Integral and the Superposition of Danckwerts
- Practice Problems
- Chapter 7. Vector Calculus: Generalized Transport Equations
- 7.1. Vector Notation and Vector Calculus
- 7.1.1. Differential Operators and Vector Calculus
- 7.1.2. Integral Theorems of Vector Calculus
- 7.2. Superposition Revisited: Green's Functions and the Solution of PDEs by Green's Functions
- 7.3. Transport of Mass
- 7.4. Transport of Energy
- 7.4.1. Steady state Temperatures and Heat Flux in Multidimensional Geometries: The Shape Factor
- 7.5. Transport of Momentum
- Practice Problems
- Chapter 8. Analytical Solutions of Partial Differential Equations
- 8.1. Separation of Variables
- 8.1.1. Orthogonal Functions and Fourier Series
- 8.1.1.1. Orthogonal and Orthonormal Functions. The Sturm-Liouville Theorem
- 8.1.2. Historical Note
- 8.2. Laplace Transformation and Other Integral Transforms
- 8.2.1. General Properties
- 8.2.2. The Role of the Kernel
- 8.2.3. Pros and Cons of Integral Transforms
- 8.2.3.1. Advantages
- 8.2.3.2. Disadvantages
- 8.2.4. The Laplace Transformation of PDEs
- Historical Note
- 8.3. The Method of Characteristics
- 8.3.1. General Properties
- 8.3.2. The Characteristics
- Practice Problems
- Selected References
- Index
