InhaltsangabePreface.- A Computer Algebra Systems.- B The Spiral Staircase to Learning.- C How to Climb the Spiral Staircase.- I The Appetizers.- 1 The Pictures of Science.- 1.1 Introduction.- 1.2 Data and Function Plots.- 1.2.1 Correcting for Inflation.- 1.2.2 The Plummeting Badminton Bird.- 1.2.3 Minimizing the Travel Time.- 1.3 Log-Log (Power Law) Plots.- 1.3.1 Chimpanzee Brain Size.- 1.3.2 Scaling Arguments and Gulliver's Travels.- 1.4 Contour and Gradient Plots.- 1.4.1 The Secret Message.- 1.4.2 Designing a Ski Hill.- 1.5 Animated Plots.- 1.5.1 Waves Are Dynamic.- 1.5.2 The Sands of Time.- 2 Deriving Model Equations.- 2.1 Introduction.- 2.2 Linear Correlation.- 2.2.1 What Is Linear Correlation?.- 2.2.2 The Corn Palace.- 2.3 Least Squares Derivations.- 2.3.1 Regression Analysis.- 2.3.2 Will You Be Better Off Than Your Parents?.- 2.3.3 What Was the Heart Rate of a Brachiosaurus?.- 2.3.4 Senate Renewal.- 2.3.5 Bikini Sales and the Logistic Curve.- 2.3.6 Following the Dow Jones Index.- 2.3.7 Variation of "g" with Latitude.- 2.3.8 Finding Romeo a Juhet.- 2.4 Multiple Regression Equations.- 2.4.1 Real Estate Appraisals.- 2.4.2 And the Winner Is?.- 3 Algebraic Models.- 3.1 Introduction.- 3.2 Algebraic Examples.- 3.2.1 Bombs Versus Schools.- 3.2.2 Kirchhoff Rules the Electrical World.- 3.2.3 The Window Washer's Secret.- 3.2.4 The Science Student's Summer Job Interview.- 3.2.5 Envelope of Safety.- 3.2.6 Rainbow County.- 3.3 Integral Examples.- 3.3.1 The Great Pyramid of Cheops.- 3.3.2 Noah's Ark.- 3.4 Vector Examples.- 3.4.1 Vectoria's Mathematical Heritage.- 3.4.2 Ain't She Sweet.- 3.4.3 Born Curl Free.- 3.4.4 Of Flux and Circulation and Coordinates Too.- 4 Monte Carlo Methods.- 4.1 Introduction.- 4.2 Random Walks.- 4.2.1 The Concept.- 4.2.2 The Soccer Fan's Drunken Walk.- 4.2.3 Blowin' in the Wind.- 4.2.4 Flight of Penelope Jitter Bug.- 4.2.5 That Meandering Perfume Molecule.- 4.3 Monte Carlo Integration.- 4.3.1 Standard Numerical Integration Algorithms.- 4.3.2 Monte Carlo Integration.- 4.3.3 Wait and Buy Later!.- 4.3.4 Wait and Buy Later! The Sequel.- 4.3.5 Estimating ?.- 4.3.6 Chariot of Fire and Destruction.- 4.4 Probability Distributions.- 4.4.1 Of Nuts and Bolts and Hospital Beds Too.- 4.4.2 The Ice Wines of Rainbow County.- 4.5 Monte Carlo Statistical Distributions.- 4.5.1 Estimating e.- 4.5.2 Vapor Deposition.- II The Entrees.- 5 Phase-Plane Portraits.- 5.1 Introduction.- 5.2 Phase-Plane Portraits.- 5.2.1 Stationary or Singular Points.- 5.3 Linear ODE Models.- 5.3.1 Tenure Policy at Erehwon University.- 5.3.2 Vectoria Investigates the RLC Circuit.- 5.4 Nonlinear ODE Models.- 5.4.1 Classification of Stationary Points.- 5.4.2 Rabbits and Foxes.- 5.4.3 The Mona Lisa of Nonlinear Science.- 5.4.4 Mike Creates a Higher-Order Singular Point.- 5.4.5 The Gnus and Sung of Erehwon.- 5.5 Nonautonomous ODEs.- 5.5.1 Can an Unstable Spring Find Stability?.- 5.5.2 The Period Doubling Route to Chaos.- 6 Linear ODE Models.- 6.1 Introduction.- 6.2 Solving Linear ODEs with Maple.- 6.3 First-Order ODE Models.- 6.3.1 There Goes Louie's Alibi.- 6.3.2 The Water Skier.- 6.4 Second-Order ODE Models.- 6.4.1 Shrinking the Safety Envelope.- 6.4.2 Halley's Comet.- 6.4.3 Frank N Stein Is Not Heartless.- 6.4.4 Vectoria Feels the Force and Hits the Bottle.- 6.5 Bessel and Legendre ODE Models.- 6.5.1 Introduction to Special Functions.- 6.5.2 The Vibrating Bungee Cord.- 6.5.3 Wheel of misFortune.- 6.5.4 TheWeedeater.- 7 Nonlinear ODE Models.- 7.1 Introduction.- 7.2 First-Order Models.- 7.2.1 The Nonlinear Diode.- 7.2.2 The Bad Bird Equation.- 7.2.3 The Struggle for Existence.- 7.3 Second-Order Models.- 7.3.1 Pirates of the Caribbean.- 7.3.2 Oh What Sounds We Hear!.- 7.3.3 Those Lennard-Jones Vibrational Blues.- 7.3.4 Golf Is Such an "Uplifting" Experience.- 7.3.5 This Would Be a Great Amusement Park Ride.- 7.4 Limit Cycles.- 7.4.1 The Bizarre World of the Tunnel Diode Oscillator.- 7.4.2 Follow That Rabbit.- 8 Difference Equation Models.- 8.1 Introduction.- 8.2 Linear D

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InhaltsangabePreface.- A Computer Algebra Systems.- B The Spiral Staircase to Learning.- C How to Climb the Spiral Staircase.- I The Appetizers.- 1 The Pictures of Science.- 1.1 Introduction.- 1.2 Data and Function Plots.- 1.2.1 Correcting for Inflation.- 1.2.2 The Plummeting Badminton Bird.- 1.2.3 Minimizing the Travel Time.- 1.3 Log-Log (Power Law) Plots.- 1.3.1 Chimpanzee Brain Size.- 1.3.2 Scaling Arguments and Gulliver's Travels.- 1.4 Contour and Gradient Plots.- 1.4.1 The Secret Message.- 1.4.2 Designing a Ski Hill.- 1.5 Animated Plots.- 1.5.1 Waves Are Dynamic.- 1.5.2 The Sands of Time.- 2 Deriving Model Equations.- 2.1 Introduction.- 2.2 Linear Correlation.- 2.2.1 What Is Linear Correlation?.- 2.2.2 The Corn Palace.- 2.3 Least Squares Derivations.- 2.3.1 Regression Analysis.- 2.3.2 Will You Be Better Off Than Your Parents?.- 2.3.3 What Was the Heart Rate of a Brachiosaurus?.- 2.3.4 Senate Renewal.- 2.3.5 Bikini Sales and the Logistic Curve.- 2.3.6 Following the Dow Jones Index.- 2.3.7 Variation of "g" with Latitude.- 2.3.8 Finding Romeo a Juhet.- 2.4 Multiple Regression Equations.- 2.4.1 Real Estate Appraisals.- 2.4.2 And the Winner Is?.- 3 Algebraic Models.- 3.1 Introduction.- 3.2 Algebraic Examples.- 3.2.1 Bombs Versus Schools.- 3.2.2 Kirchhoff Rules the Electrical World.- 3.2.3 The Window Washer's Secret.- 3.2.4 The Science Student's Summer Job Interview.- 3.2.5 Envelope of Safety.- 3.2.6 Rainbow County.- 3.3 Integral Examples.- 3.3.1 The Great Pyramid of Cheops.- 3.3.2 Noah's Ark.- 3.4 Vector Examples.- 3.4.1 Vectoria's Mathematical Heritage.- 3.4.2 Ain't She Sweet.- 3.4.3 Born Curl Free.- 3.4.4 Of Flux and Circulation and Coordinates Too.- 4 Monte Carlo Methods.- 4.1 Introduction.- 4.2 Random Walks.- 4.2.1 The Concept.- 4.2.2 The Soccer Fan's Drunken Walk.- 4.2.3 Blowin' in the Wind.- 4.2.4 Flight of Penelope Jitter Bug.- 4.2.5 That Meandering Perfume Molecule.- 4.3 Monte Carlo Integration.- 4.3.1 Standard Numerical Integration Algorithms.- 4.3.2 Monte Carlo Integration.- 4.3.3 Wait and Buy Later!.- 4.3.4 Wait and Buy Later! The Sequel.- 4.3.5 Estimating ?.- 4.3.6 Chariot of Fire and Destruction.- 4.4 Probability Distributions.- 4.4.1 Of Nuts and Bolts and Hospital Beds Too.- 4.4.2 The Ice Wines of Rainbow County.- 4.5 Monte Carlo Statistical Distributions.- 4.5.1 Estimating e.- 4.5.2 Vapor Deposition.- II The Entrees.- 5 Phase-Plane Portraits.- 5.1 Introduction.- 5.2 Phase-Plane Portraits.- 5.2.1 Stationary or Singular Points.- 5.3 Linear ODE Models.- 5.3.1 Tenure Policy at Erehwon University.- 5.3.2 Vectoria Investigates the RLC Circuit.- 5.4 Nonlinear ODE Models.- 5.4.1 Classification of Stationary Points.- 5.4.2 Rabbits and Foxes.- 5.4.3 The Mona Lisa of Nonlinear Science.- 5.4.4 Mike Creates a Higher-Order Singular Point.- 5.4.5 The Gnus and Sung of Erehwon.- 5.5 Nonautonomous ODEs.- 5.5.1 Can an Unstable Spring Find Stability?.- 5.5.2 The Period Doubling Route to Chaos.- 6 Linear ODE Models.- 6.1 Introduction.- 6.2 Solving Linear ODEs with Maple.- 6.3 First-Order ODE Models.- 6.3.1 There Goes Louie's Alibi.- 6.3.2 The Water Skier.- 6.4 Second-Order ODE Models.- 6.4.1 Shrinking the Safety Envelope.- 6.4.2 Halley's Comet.- 6.4.3 Frank N Stein Is Not Heartless.- 6.4.4 Vectoria Feels the Force and Hits the Bottle.- 6.5 Bessel and Legendre ODE Models.- 6.5.1 Introduction to Special Functions.- 6.5.2 The Vibrating Bungee Cord.- 6.5.3 Wheel of misFortune.- 6.5.4 TheWeedeater.- 7 Nonlinear ODE Models.- 7.1 Introduction.- 7.2 First-Order Models.- 7.2.1 The Nonlinear Diode.- 7.2.2 The Bad Bird Equation.- 7.2.3 The Struggle for Existence.- 7.3 Second-Order Models.- 7.3.1 Pirates of the Caribbean.- 7.3.2 Oh What Sounds We Hear!.- 7.3.3 Those Lennard-Jones Vibrational Blues.- 7.3.4 Golf Is Such an "Uplifting" Experience.- 7.3.5 This Would Be a Great Amusement Park Ride.- 7.4 Limit Cycles.- 7.4.1 The Bizarre World of the Tunnel Diode Oscillator.- 7.4.2 Follow That Rabbit.- 8 Difference Equation Models.- 8.1 Introduction.- 8.2 Linear D