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• 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