PREFACE ; NOTATION ; 1. GETTING STARTED AND BEYOND ; 1.1 When Not to Model ; Illustration 1.1 The Challenger Space Shuttle Disaster ; Illustration 1.2 Loss of Blood Vessel Patency ; 1.2 Some Initial Tools and Steps ; 1.3 Closure ; Illustration 1.3 Discharge of Plant Effluent into a River ; Illustration 1.4 Electrical Field Due to a Dipole ; Illustration 1.5 Design of a Thermocouple ; Illustration 1.6 Newton's Law for Systems of Variable Mass: A False Start and the Remedy ; Illustration 1.7 Release of a Substance into a Flowing Fluid. Determination of a Mass Transfer Coefficient ; Practice Problems ; 2. SOME MATHEMATICAL TOOLS ; 2.1 Vector Algebra ; 2.1.1 Definition of a Vector ; 2.1.2 Vector Equality ; 2.1.3 Vector Addition and Subtraction ; 2.1.4 Multiplication by a Scalar ; 2.1.5 The Scalar or Dot Product ; 2.1.6 The Vector or Cross Product ; Illustration 2.1 Distance of a Point from a Plane ; Illustration 2.2 Shortest Distance Between Two Lines ; Illustration 2.3 Work as an Application of the Scalar Product ; Illustration 2.4 Extension of the Scalar Product to n Dimensions. A Sale of Stocks ; Illustration 2.5 A Model Economy ; 2.2 Matrices ; 2.2.1 Types of Matrices ; 2.2.2 The Echelon Form. Rank r ; 2.2.3 Matrix Equality ; 2.2.4 Matrix Addition ; Illustration 2.6 Acquisition Costs ; 2.2.5 Multiplication by a Scalar ; 2.2.6 Matrix Multiplication ; Illustration 2.7 The Product of Two Matrices ; Illustration 2.8 Matrix-Vector Representation of Linear Algebraic Equation ; 2.2.7 Elementary Row Operations ; Illustration 2.9 Application of Elementary Row Operation. Algebraic Equivalence ; 2.2.8 Solution of Sets of Linear Algebraic Equations. Gaussian Elimination ; Illustration 2.10 An Overspecified System of Equations with a Unique Solution ; Illustration 2.11 A Normal System of Equations with no Solutions ; 2.3 Ordinary Differential Equations ; Illustration 2.12 A Population Model ; Illustration 2.13 Newton's Law of Cooling ; 2.3.1 Order of an ODE ; 2.3.2 Linear and Non-linear ODE's ; 2.3.3 Boundary and Initial Conditions ; Illustration 2.14 Classification of ODE's and Boundary Conditions ; 2.3.4 Equivalent Systems ; Illustration 2.15 Equivalence of Vibrating Mechanical Systems and an Electrical RLC Circuit ; 2.3.5 Analytical Methods ; A. Solution by Separation of Variables ; Illustration 2.16 Solution of Non-Linear ODE's by Separation of Variables ; B. The D-Operator and Eigenvalue Methods. Particular Integrals ; Illustration 2.17 Mass on a Spring Subjected to a Sinusoidal Forcing Function ; C. The Laplace Transformation ; Illustration 2.18 Application of Inversion Procedures ; Illustration 2.19 The Mass-Spring System Revisited. Resonance ; Practice Problems ; 3. GEOMETRICAL CONCEPTS ; 3.1 Introduction ; Illustration 3.1 A Simple Geometry Problem: Crossing of a River ; Illustration 3.2 The Formation of Quasi Crystals and Tilings from Two Quadrilateral Polygons ; Illustration 3.3 Charting of Market Price Dynamics: The Japanese Candlestick Method ; Illustration 3.4 Surveying: The Join Calculation. The Triangulation Intersection ; Illustration 3.5 The Global Positioning System (GPS) ; Illustration 3.6 The Orthocenter of a Triangle ; Illustration 3.7 Relative Velocity and the Wind Triangle ; Illustration 3.8 Interception of an Airplane ; Illustration 3.9 Path of Pursuit ; Illustration 3.10 Trilinear Coordinates. The Three Jug Problem ; Illustration 3.11 Inflecting Production Rates and Multiple Steady States. The Van Heerden Diagram ; Illustration 3.12 Linear Programming: A Geometrical Construction ; Illustration 3.13 Stagewise Adsorption Purification of Liquids. The Operating Diagram ; Illustration 3.14 Supercoiled DNA ; Practice Problems ; 4. THE EFFECT OF FORCES ; 4.1 Introduction ; Illustration 4.1 The Stress-Strain Relation. Stored Strain Energy. Stress Due to the Impact of a Falling Mass ; Illustration 4.2 Bending of Beams. Euler's Formula for the Buckling of a Strut ; Illustration 4.3 Electrical and Magnetic Forces. Thomson's Determination of e/m ; Illustration 4.4 Pressure of a Gas in Terms of its Molecular Properties. Boyle's Law and the Ideal Gas Law. Velocity of Gas Molecules ; Illustration 4.5 Path of a Projectile ; Illustration 4.6 The Law of Universal Gravitation. Escape Velocity. The Synchronous Satellite ; Illustration 4.7 Fluid Forces. Bernoulli's Equation and Its Applications. The Continuity Equation ; Illustration 4.8 Lift Capacity of a Hot Air Balloon ; Illustration 4.9 Work and Energy. Compression of a Gas. Power Output of a Bumblebee Practice Problems ; 5. COMPARTMENTAL MODELS ; 5.1 Introduction ; Illustration 5.1 Measurement of Plasma Volume and Cardiac Output by the Dye Dilution Method ; Illustration 5.2 The Continuous Stirred Tank Reactor (CSTR). Model and Optimum Size ; Illustration 5.3 Modeling of a Bioreactor. Monod Kinetics. The Optimum Dilution Rate ; Illustration 5.4 Non-Idealities in a Stirred Tank. Residence-Time Distributions from Tracer Experiments ; Illustration 5.5 A Moving Boundary Problem: The Shrinking Core Model and the Quasi-Steady State ; Illustration 5.6 More on Moving Boundaries. The Crystallization Process ; Illustration 5.7 Moving Boundaries in Medicine: Controlled Release Drug Delivery ; Illustration 5.8 Evaporation of a Pollutant into the Atmosphere ; Illustration 5.9 Ground Penetration from an Oil Spill ; Illustration 5.10 Concentration Variations in Stratified Layers ; Illustration 5.11 One-Compartment Pharmocokinetics ; Illustration 5.12 Deposition of Platelets from Flowing Blood ; Illustration 5.13 Dynamics of the Human Immunodeficiency Virus (HIV) ; Practice Problems ; 6. ONE-DIMENSIONAL DISTRIBUTED SYSTEMS ; 6.1 Introduction ; Illustration 6.1 The Hypsometric Formula ; Illustration 6.2 Poiseuille's Equation for Laminar Flow in a Pipe ; Illustration 6.3 Compressible Laminar Flow in a Horizontal Pipe ; Illustration 6.4 Conduction of Heat Through Various Geometries ; Illustration 6.5 Conduction in Systems with Heat Sources ; Illustration 6.6 The Countercurrent Heat Exchanger ; Illustration 6.7 Diffusion and Reaction in a Catalyst Pellet. The Effectiveness Factor ; Illustration 6.8 The Heat Exchanger Fin ; Illustration 6.9 Polymer Sheet Extrusion. The Uniformity Index ; Illustration 6.10 The Streeter-Phelps River Pollution Model. The Oxygen Sag Curve ; Illustration 6.11 Conduction in a Thin Wire Carrying an Electrical Current ; Illustration 6.12 Electrical Potential Due to a Charged Disk ; Illustration 6.13 Production of Silicon Crystals: Getting Lost and Staging a Recovery ; Practice Problems ; 7. SOME SIMPLE NETWORKS ; 7.1 Introduction ; Illustration 7.1 A Thermal Network: External Heating of a Stirred Tank ; Illustration 7.2 A Chemical Reaction Network. The Radioactive Decay Series ; Illustration 7.3 Hydraulic Networks ; Illustration 7.4 An Electrical Network: Hitting a Brick Wall and Going Around It ; Illustration 7.5 A Mechanical Network. Resonance of Two Vibrating Masses ; Illustration 7.6 Application of Matrix Methods to Stoichiometric Calculations ; Illustration 7.7 Diagnosis of a Plant Flow Sheet ; Illustration 7.8 Manufacturing Costs. Use of Matrix-Vector Products ; Illustration 7.9 More About Electrical Circuits. The Electrical Ladder Networks ; Illustration 7.10 Networks in Plant Physiology: Photosynthesis and Respiration ; Practice Problems ; 8. MORE MATHEMATICAL TOOLS: DIMENSIONAL ANALYSIS AND NUMERICAL METHODS ; 8.1 Dimensional Analysis ; 8.1.1 Introduction ; Illustration 8.1 Time of Swing of a Simple Pendulum ; Illustration 8.2 Vibration of a One-Dimensional Structure ; 8.1.2 Systems with More Variables than Dimensions. The Buckingham pi Theorem ; Illustration 8.3 Heat Transfer to a Fluid in Turbulent Flow ; Illustration 8.4 Drag on Submerged Bodies. Horsepower of a Car ; Illustration 8.5 Design of a Depth Charge ; Practice Problems ; 8.2 Numerical Methods ; 8.2.1 Introduction ; 8.2.2 Numerical Software Packages ; 8.2.3 Numerical Solution of Simultaneous Linear Algebraic Equations. Gaussian Elimination ; Illustration 8.6 The Global Positioning System Revisited: Gaussian Elimination Using the MATHEMATICA Package ; 8.2.4 Numerical Solution of Single Nonlinear Equations. Newton's Method ; Illustration 8.7 Chemical Equilibrium: The Synthesis of Ammonia by the Haber Process ; 8.2.5 Numerical Solution of Simultaneous, Non-Linear Equations. The Newton-Raphson Method ; Illustration 8.8 More Chemical Equilibria: Producing Silicon Films by Chemical Vapor Deposition (CVD) ; 8.2.6 Numerical Solution of Ordinary Differential Equations. The Euler and Runge-Kutta Methods ; Illustration 8.9 The Effect of Drag on the Trajectory of an Artillery Piece ; Practice Problems ; Index

show more