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Product details:
- Publisher OUP USA
- Date of Publication 13 February 2003
- ISBN 9780195153149
- Binding Hardback
- No. of pages368 pages
- Size 243x195x21 mm
- Weight 839 g
- Language English
- Illustrations numerous line figures 0
Categories
Short description:
This textbook is designed for junior/senior (3rd, 4th year) students in engineering and the physical sciences who are taking courses in mathematical modeling or applied mathematics. The text introduces the reader to setting up and solving mathematical models and physical systems based on algebraic and ordinary differential equations. Unlike the competition, it is less mathematical and focuses more on the description of physical systems. It contains numerous classical
and modern illustrations drawn from the sciences, engineering, and economics accompanied by detailed descriptions of the underlying physics and mathematics.
Long description:
The aim of this text is to provide the beginning student or professional with introduction to the topic in an easily understood student friendly manner. It is based on the premise that modeling is as much art as it is science and that mastering the art can only be achieved by sustained practice. To provide that practice, the text contains some 100 odd worked examples as well as numerous practice problems drawn from variety of disciplines. They range from classical
examples such as Euler's treatment of the buckling of the strut, to the contemporary topics of silicon chip manufacturing and the dynamics of the human immunodeficiency virus (HIV). Other examples are drawn from mechanical, electrical, chemical and environmental engineering disciplines as well as
from the fields of economics, physics and chemistry.
The mathematics required are confined to simple treatment of vector algebra, matrix operations and the solutions of ordinary differential equations. Both analytical and numerical methods are taken up and are described in sufficient detail to serve as a learning tool for the beginner or as a refresher for the informed reader.
The text is designed for 3rd and 4th yr students in all engineering disciplines as well as mathematics, physics and chemistry. It should also serve as a welcome addition to libraries of practicing professionals.
Table of Contents:
Preface
Notation
1. Getting Started and Beyond
When Not to Model
The Challenger Space Shuttle Disaster
Loss of Blood Vessel Patency
Some Initial Tools and Steps
Closure
Discharge of Plant Effluent into a River
Electrical Field Due to a Dipole
Design of a Thermocouple
Newton's Law for Systems of Variable Mass: A False Start and the Remedy
Release of a Substance into a Flowing Fluid. Determination of a Mass Transfer Coefficient
Practice Problems
2. Some Mathematical Tools
Vector Algebra
Definition of a Vector
Vector Equality
Vector Addition and Subtraction
Multiplication by a Scalar
The Scalar or Dot Product
The Vector or Cross Product
Distance of a Point from a Plane
Shortest Distance Between Two Lines
Work as an Application of the Scalar Product
Extension of the Scalar Product to n Dimensions. A Sale of Stocks
A Model Economy
Matrices
Types of Matrices
The Echelon Form. Rank r
Matrix Equality
Matrix Addition
Acquisition Costs
Multiplication by a Scalar
Matrix Multiplication
The Product of Two Matrices
Matrix-Vector Representation of Linear Algebraic Equation
Elementary Row Operations
Application of Elementary Row Operation. Algebraic Equivalence
Solution of Sets of Linear Algebraic Equations. Gaussian Elimination
An Overspecified System of Equations with a Unique Solution
A Normal System of Equations with no Solutions
Ordinary Differential Equations
A Population Model
Newton's Law of Cooling
Order of an ODE
Linear and Non-linear ODE's
Boundary and Initial Conditions
Classification of ODE's and Boundary Conditions
Equivalent Systems
Equivalence of Vibrating Mechanical Systems and an Electrical RLC Circuit
Analytical Methods
Solution by Separation of Variables
Solution of Non-Linear ODE's by Separation of Variables
The D-Operator and Eigenvalue Methods. Particular Integrals
Mass on a Spring Subjected to a Sinusoidal Forcing Function
The Laplace Transformation
Application of Inversion Procedures
The Mass-Spring System Revisited. Resonance
Practice Problems
3. Geometrical Concepts
Introduction
A Simple Geometry Problem: Crossing of a River
The Formation of Quasi Crystals and Tilings from Two Quadrilateral Polygons
Charting of Market Price Dynamics: The Japanese Candlestick Method
Surveying: The Join Calculation. The Triangulation Intersection
The Global Positioning System (GPS)
The Orthocenter of a Triangle
Relative Velocity and the Wind Triangle
Interception of an Airplane
Path of Pursuit
Trilinear Coordinates. The Three Jug Problem
Inflecting Production Rates and Multiple Steady States. The Van Heerden Diagram
Linear Programming: A Geometrical Construction
Stagewise Adsorption Purification of Liquids. The Operating Diagram
Supercoiled DNA
Practice Problems
4. The Effect of Forces
Introduction
The Stress-Strain Relation. Stored Strain Energy. Stress Due to the Impact of a Falling Mass
Bending of Beams. Euler's Formula for the Buckling of a Strut
Electrical and Magnetic Forces. Thomson's Determination of e/m
Pressure of a Gas in Terms of its Molecular Properties. Boyle's Law and the Ideal Gas Law. Velocity of Gas Molecules
Path of a Projectile
The Law of Universal Gravitation. Escape Velocity. The Synchronous Satellite
Fluid Forces. Bernoulli's Equation and Its Applications. The Continuity Equation
Lift Capacity of a Hot Air Balloon
Work and Energy. Compression of a Gas. Power Output of a Bumblebee Practice Problems
5. Compartmental Models
Introduction
Measurement of Plasma Volume and Cardiac Output by the Dye Dilution Method
The Continuous Stirred Tank Reactor (CSTR). Model and Optimum Size
Modeling of a Bioreactor. Monod Kinetics. The Optimum Dilution Rate
Non-Idealities in a Stirred Tank. Residence-Time Distributions from Tracer Experiments
A Moving Boundary Problem: The Shrinking Core Model and the Quasi-Steady State
More on Moving Boundaries. The Crystallization Process
Moving Boundaries in Medicine: Controlled Release Drug Delivery
Evaporation of a Pollutant into the Atmosphere
Ground Penetration from an Oil Spill
Concentration Variations in Stratified Layers
One-Compartment Pharmocokinetics
Deposition of Platelets from Flowing Blood
Dynamics of the Human Immunodeficiency Virus (HIV)
Practice Problems
6. One-Dimensional Distributed Systems
Introduction
The Hypsometric Formula
Poiseuille's Equation for Laminar Flow in a Pipe
Compressible Laminar Flow in a Horizontal Pipe
Conduction of Heat Through Various Geometries
Conduction in Systems with Heat Sources
The Countercurrent Heat Exchanger
Diffusion and Reaction in a Catalyst Pellet. The Effectiveness Factor
The Heat Exchanger Fin
Polymer Sheet Extrusion. The Uniformity Index
The Streeter-Phelps River Pollution Model. The Oxygen Sag Curve
Conduction in a Thin Wire Carrying an Electrical Current
Electrical Potential Due to a Charged Disk
Production of Silicon Crystals: Getting Lost and Staging a Recovery
Practice Problems
7. Some Simple Networks
Introduction
A Thermal Network: External Heating of a Stirred Tank
A Chemical Reaction Network. The Radioactive Decay Series
Hydraulic Networks
An Electrical Network: Hitting a Brick Wall and Going Around It
A Mechanical Network. Resonance of Two Vibrating Masses
Application of Matrix Methods to Stoichiometric Calculations
Diagnosis of a Plant Flow Sheet
Manufacturing Costs. Use of Matrix-Vector Products
More About Electrical Circuits. The Electrical Ladder Networks
Networks in Plant Physiology: Photosynthesis and Respiration
Practice Problems
8. More Mathematical Tools: Dimensional Analysis and Numerical Methods
Dimensional Analysis
Introduction
Time of Swing of a Simple Pendulum
Vibration of a One-Dimensional Structure
Systems with More Variables than Dimensions. The Buckingham ? Theorem
Heat Transfer to a Fluid in Turbulent Flow
Drag on Submerged Bodies. Horsepower of a Car
Design of a Depth Charge
Practice Problems
Numerical Methods
Introduction
Numerical Software Packages
Numerical Solution of Simultaneous Linear Algebraic Equations. Gaussian Elimination
The Global Positioning System Revisited: Gaussian Elimination Using the MATHEMATICA Package
Numerical Solution of Single Nonlinear Equations. Newton's Method
Chemical Equilibrium: The Synthesis of Ammonia by the Haber Process
Numerical Solution of Simultaneous, Non-Linear Equations. The Newton-Raphson Method
More Chemical Equilibria: Producing Silicon Films by Chemical Vapor Deposition (CVD)
Numerical Solution of Ordinary Differential Equations. The Euler and Runge-Kutta Methods
The Effect of Drag on the Trajectory of an Artillery Piece
Practice Problems
Index
