Efnisyfirlit

• COVER
• TITLE PAGE
• PREFACE
• INTRODUCTION
  • ABOUT THIS BOOK
  • ABOUT MATHEMATICAL MODELING
  • ABOUT MATHEMATICAL MODELING TECHNIQUES
  • ABOUT BEING A GOOD MODELER
  • ABOUT THE MODELING PROBLEMS
  • ABOUT GEOGEBRA
  • ABOUT WOLFRAM ALPHA
  • ABOUT TYPOGRAPHY
  • ABOUT THE DIGITAL MATERIAL FOR THE BOOK
  • ABOUT THE AUTHORS
  • REFERENCES
• ABOUT THE COMPANION WEBSITE
• 1 SOME INTRODUCTORY PROBLEMS
  • 1.1 TICKET PRICES
  • 1.2 HOW LONG WILL THE PASTURE LAST IN A FIELD?
  • 1.3 A BIT OF CHEMISTRY
  • 1.4 SYDNEY HARBOR BRIDGE
  • 1.5 PERSPECTIVE
  • 1.6 LAKE ERIE’S AREA
  • 1.7 ZEBRA CROSSING
  • 1.8 THE SECURITY CASE
  • 1.9 PERSONAL MEASUREMENTS
  • 1.10 HEIGHT OF THE BODY
  • 1.11 LAMP POLE
  • 1.12 THE SKYSCRAPER
  • 1.13 THE FENCE
  • 1.14 THE CORRIDOR
  • 1.15 BIRD FEEDERS
  • 1.16 GOLF
• 2 LINEAR MODELS
  • 2.1 ARE WOMEN FASTER THAN MEN?
  • 2.2 TAXI COMPANIES
  • 2.3 CRIME DEVELOPMENT
  • 2.4 THE METAL WIRE
  • 2.5 OPTIONS TRADING
  • 2.6 FLYING FOXES
  • 2.7 KNOTS ON A ROPE
  • 2.8 THE CANDLE
  • 2.9 HOOKE’S LAW
  • 2.10 RANKING
  • 2.11 DOLBEAR'S LAW
  • 2.12 MAN AT OFFICE
  • 2.13 A STACK OF PAPER
  • 2.14 MILK PRODUCTION IN COWS
• 3 NONLINEAR EMPIRICAL MODELS I
  • 3.1 GALAXY ROTATION
  • 3.2 OLYMPIC POLE VAULTING
  • 3.3 KEPLER’S THIRD LAW
  • 3.4 DENSITY
  • 3.5 YEAST
  • 3.6 COOLING I
  • 3.7 MODELING THE POPULATION OF IRELAND
  • 3.8 THE RULE OF 72
  • 3.9 THE FISH FARM I
  • 3.10 NEW ORLEANS TEMPERATURES
  • 3.11 THE RECORD MILE
  • 3.12 THE ROCKET
  • 3.13 STOPPING DISTANCES
  • 3.14 A BOTTLE WITH HOLES
  • 3.15 THE PENDULUM
  • 3.16 RADIO RANGE
  • 3.17 RUNNING 400 METERS
  • 3.18 BLUE WHALE
  • 3.19 USED CARS
  • 3.20 TEXTS
• 4 NONLINEAR EMPIRICAL MODELS II
  • 4.1 COOLING II
  • 4.2 BODY SURFACE AREA
  • 4.3 WARM‐BLOODED ANIMALS
  • 4.4 CONTROL OF INSECT PESTS
  • 4.5 SELLING MAGAZINES FOR CHRISTMAS
  • 4.6 TUMOR
  • 4.7 FREE FALL
  • 4.8 CONCENTRATION
  • 4.9 AIR CURRENT
  • 4.10 TIDES
  • 4.11 FITNESS
  • 4.12 LIFE EXPECTANCY VERSUS AVERAGE INCOME
  • 4.13 STOCKHOLM CENTER
  • 4.14 WORKFORCE
  • 4.15 POPULATION OF SWEDEN
  • 4.16 WHO KILLED THE LION?
  • 4.17 AIDS IN UNITED STATES
  • 4.18 THERMAL COMFORT
  • 4.19 WATTS AND LUMEN
  • 4.20 THE BEAUFORT SCALE
  • 4.21 THE VON BERTALANFFY GROWTH EQUATION
• 5 MODELING WITH CALCULUS
  • 5.1 THE FISH FARM II
  • 5.2 TITRATION
  • 5.3 THE BOWL
  • 5.4 THE AIRCRAFT WING
  • 5.5 THE GATEWAY ARCH IN ST. LOUIS
  • 5.6 VOLUME OF A PEAR
  • 5.7 STORM FLOOD
  • 5.8 EXERCISE
  • 5.9 BICYCLE REFLECTORS
  • 5.10 CARDIAC OUTPUT
  • 5.11 MEDICATION
  • 5.12 NEW SONG ON SPOTIFY
  • 5.13 TEMPERATURE CHANGE
  • 5.14 TAR
  • 5.15 BICYCLE REFLECTORS REVISITED
  • 5.16 GAS PRESSURE
  • 5.17 AIRBORNE ATTACKS
  • 5.18 RAILROAD TRACKS
  • 5.19 COBB–DOUGLAS PRODUCTION FUNCTIONS
  • 5.20 FUTURE CARBON DIOXIDE EMISSIONS
  • 5.21 OVERTAKING
  • 5.22 POPULATION DYNAMICS OF INDIA
  • 5.23 DRAG RACING
  • 5.24 SUPER EGGS
  • 5.25 MEASURING STICKS
  • 5.26 THE LECTURE HALL
  • 5.27 PROGRESSIVE BRAKING DISTANCES
  • 5.28 CYLINDER IN A CONE
• 6 USING DIFFERENTIAL EQUATIONS
  • 6.1 COOLING III
  • 6.2 MOOSE HUNTING
  • 6.3 THE WATER CONTAINER
  • 6.4 SKYDIVING
  • 6.5 FLU EPIDEMICS
  • 6.6 USA’S POPULATION
  • 6.7 PREDATORS AND PREY
  • 6.8 SMOKE
  • 6.9 ALCOHOL CONSUMPTION
  • 6.10 WHO KILLED THE MATHEMATICS TEACHER
  • 6.11 RIVER CLAMS
  • 6.12 CONTAMINATION
  • 6.13 DAMPED OSCILLATION
  • 6.14 THE POTASSIUM–ARGON METHOD
  • 6.15 BARIUM, LANTHANUM, AND CERIUM
  • 6.16 IODINE
  • 6.17 ENDEMIC EPIDEMICS
  • 6.18 WAR
  • 6.19 FARMERS, BANDITS, AND RULERS
  • 6.20 EPIDEMICS WITHOUT IMMUNITY
  • 6.21 ZOMBIE APOCALYPSE I
  • 6.22 ZOMBIE APOCALYPSE II
• 7 GEOMETRICAL MODELS
  • 7.1 THE LOOPING PEN
  • 7.2 COMPARING AREAS
  • 7.3 CROSSING LINES
  • 7.4 POINTS IN A TRIANGLE
  • 7.5 TRISECTED AREA
  • 7.6 SPIROGRAPH
  • 7.7 CONNECTED LP PLAYERS
  • 7.8 FOLDING PAPER
  • 7.9 THE LOCOMOTIVE
  • 7.10 MAXIMUM VOLUME
  • 7.11 PASCAL’S SNAIL OR LIMAÇON
  • 7.12 EQUILATERAL TRIANGLE DISSECTION
  • 7.13 DIVIDING THE SIDES OF A TRIANGLE
  • 7.14 THE PEDAL TRIANGLE
  • 7.15 THE INFINITY DIAGRAM
  • 7.16 DISSECTING A CIRCULAR SEGMENT
  • 7.17 NEUBERG CUBIC ART
  • 7.18 PHASE PLOTS FOR TRIANGLES
  • 7.19 THE JOUKOWSKI AIRFOIL
• 8 DISCRETE MODELS
  • 8.1 THE CABINETMAKER
  • 8.2 WEATHER
  • 8.3 Squirrels
  • 8.4 CHLORINE
  • 8.5 THE DEER FARM
  • 8.6 ANALYZING A NUMBER SEQUENCE
  • 8.7 INNER AREAS IN A SQUARE
  • 8.8 INNER AREAS IN A TRIANGLE
  • 8.9 A CLIMATE MODEL BASED ON ALBEDO
  • 8.10 TRAFFIC JAM
  • 8.11 WILDFIRE
  • 8.12 A MODERN CARPENTER
  • 8.13 CONWAY'S GAME OF LIFE
  • 8.14 MATRIX TAXIS
  • 8.15 THE CAR PARK
  • 8.16 SELECTING A COLLAGE
  • 8.17 APPORTIONMENT
  • 8.18 STEINER TREES FOR REGULAR POLYGONS
  • 8.19 HUGS AND HIGH FIVES
  • 8.20 PYTHAGOREAN TRIPLES
  • 8.21 CREDITS
  • 8.22 THE PIANO
• 9 MODELING IN THE CLASSROOM
  • 9.1 THE TEACHER CREATING DIAGRAMS
  • 9.2 STUDENT’S LAB REPORTS
  • 9.3 MAKING SCREENCAST INSTRUCTIONS
  • 9.4 DEMONSTRATIONS
  • 9.5 STUDENTS INVESTIGATING CONSTRUCTIONS
  • 9.6 WORKING IN GROUPS
  • 9.7 STUDENTS CONSTRUCTING MODELS
  • 9.8 BROADER ASSIGNMENTS
  • 9.9 THE SAME OR DIFFERENT ASSIGNMENTS
  • 9.10 PREVIOUS ASSIGNMENTS
  • 9.11 THE CONSULTANCY BUREAU
• 10 ASSESSING MODELING
  • 10.1 TO EVALUATE MATHEMATICAL MODELING ASSIGNMENTS
  • 10.2 CONCRETIZING GRADING CRITERIA
  • 10.3 EVALUATING STUDENTS’ WORK
• 11 ASSESSING MODELS
  • 11.1 RELATIVE ERROR
  • 11.2 CORRELATION
  • 11.3 SUM OF SQUARED ERRORS
  • 11.4 SIMPLE LINEAR REGRESSION
  • 11.5 MULTIPLE REGRESSION ANALYSIS
  • 11.6 NONLINEAR REGRESSION
  • 11.7 CONFIDENCE INTERVALS
  • 11.8 2D CONFIDENCE INTERVAL TOOLS
• 12 INTERPRETING MODELS
  • 12.1 MATHEMATICAL REPRESENTATIONS
  • 12.2 GRAPHICAL REPRESENTATIONS
  • 12.3 A SAMPLE MODEL INTERPRETED
  • 12.4 CREATING THE MODEL
• APPENDIX A: INTRODUCTION TO GEOGEBRA
  • A.1 GEOGEBRATUBE AND THE ECOSYSTEM
  • A.2 GEOGEBRABOOKS
  • A.3 GEOGEBRA ON DIFFERENT DEVICES
  • A.4 THE USER INTERFACE
  • A.5 CUSTOMIZING GEOGEBRA
  • A.6 SLIDERS
  • A.7 BASIC SKILLS AND EXERCISES
  • A.8 WRITING INSTRUCTIONS
  • A.9 REMEMBER
• APPENDIX B: FUNCTION LIBRARY
  • B.1 DIFFERENT FUNCTIONS AND THEIR PARAMETRIZATIONS
  • B.2 LINEAR TRANSFORMATIONS IN GENERAL
  • B.3 DRAGGING A FUNCTION IN GEOGEBRA
  • B.4 GEOGEBRA'S GENERIC FITTING COMMANDS
  • B.5 EXAMPLE OF A GENERIC FIT
• INTEGER PROPERTIES
• INDEX
• LIST OF PROBLEMS BY NAME
• END USER LICENSE AGREEMENT

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