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| Preface | |
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| Notation | |
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| Getting Started and Beyond | |
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| When Not to Model | |
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| The Challenger Space Shuttle Disaster | |
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| Loss of Blood Vessel Patency | |
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| Some Initial Tools and Steps | |
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| Closure | |
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| Discharge of Plant Effluent into a River | |
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| Electrical Field Due to a Dipole | |
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| Design of a Thermocouple | |
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| Newton's Law for Systems of Variable Mass: A False Start and the Remedy | |
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| Release of a Substance into a Flowing Fluid: Determination of a Mass Transfer Coefficient | |
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| Practice Problems | |
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| Some Mathematical Tools | |
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| Vector Algebra | |
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| Definition of a Vector | |
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| Vector Equality | |
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| Vector Addition and Subtraction | |
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| Multiplication by a Scalar m | |
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| The Scalar or Dot Product | |
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| The Vector or Cross Product | |
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| Distance of a Point from a Plane | |
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| Shortest Distance Between Two Lines | |
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| Work as an Application of the Scalar Product | |
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| Extension of the Scalar Product to n Dimensions: A Sale of Stocks | |
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| A Simple Model Economy | |
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| Matrices | |
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| Types of Matrix | |
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| The Echelon Form, Rank r | |
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| Matrix Equality | |
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| Matrix Addition | |
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| Acquisition Costs | |
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| Multiplication by a Scalar | |
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| Matrix Multiplication | |
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| The Product of Two Matrices | |
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| Matrix-Vector Representation of Linear Algebraic Equations | |
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| Elementary Row Operations | |
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| Application of Elementary Row Operations: Algebraic Equivalence | |
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| Solution of Sets of Linear Algebraic Equations: Gaussian Elimination | |
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| An Overspecified System of Equations with a Unique Solution | |
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| A Normal System of Equations with no Solutions | |
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| Ordinary Differential Equations (ODEs) | |
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| A Population Model | |
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| Newton's Law of Cooling | |
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| Order of an ODE | |
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| Linear and Nonlinear ODEs | |
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| Boundary and Initial Conditions | |
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| Classification of ODEs and Boundary Conditions | |
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| Equivalent Systems | |
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| Example 2.15 | |
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| Analytical Solution Methods | |
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| Solution of NonLinear ODEs by Separation of Variables | |
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| Mass on a Spring Subjected to a Sinusoidal Forcing Function | |
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| Application of Inversion Procedures | |
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| The Mass-Spring System Revisited: Resonance | |
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| Practice Problems | |
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| Geometrical Concepts | |
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| A Simple Geometry Problem: Crossing of a River | |
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| The Formation of Quasi Crystals and Tilings from Two Quadrilateral Polygons | |
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| Charting of Market Price Dynamics: The Japanese Candlestick Method | |
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| Surveying: The Join Calculation and the Triangulation Intersection | |
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| The Global Positioning System (GPS) | |
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| The Orthocenter of a Triangle | |
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| Relative Velocity and the Wind Triangle | |
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| Interception of an Airplane | |
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| Path of Pursuit | |
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| Trilinear Coordinates: The Three-Jug Problem | |
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| Inflecting Production Rates and Multiple Steady States: The van Heerden Diagram | |
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| Linear Programming: A Geometrical Construction | |
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| Stagewise Adsorption Purification of Liquids: The Operating Diagram | |
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| Supercoiled DNA Practice Problems | |
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| The Effect of Forces | |
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| Introduction | |
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| The Stress-Strain Relation: Stored Strain Energy and Stress Due to the Impact of a Falling Mass | |
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| Bending of Beams: Euler's Formula for the Buckling of a Strut | |
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| Electrical and Magnetic Forces: Thomson's Determination of e/m | |
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| Pressure of a Gas in Terms of Its Molecular Properties: Boyle's Law and the Ideal Gas Law, Velocity of Gas Molecules | |
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| Path of a Projectile | |
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| The Law of Universal Gravitation: Escape Velocity and Geosynchronous Satellites | |
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| Fluid Forces: Bernoulli's Equation and the Continuity Equation | |
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| Lift Capacity of a Hot Air Balloon | |
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| Work and Energy: Compression of a Gas and Power Output of a Bumblebee | |
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| Practice Problems | |
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| Compa | |