Mathematical Modeling: Applications with GeoGebra

TITLE PAGE
COPYRIGHT PAGE
CONTENTS
PREFACE
INTRODUCTION
ABOUT THE COMPANION WEBSITE
CHAPTER 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
CHAPTER 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
CHAPTER 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
CHAPTER 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
CHAPTER 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
CHAPTER 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
CHAPTER 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
CHAPTER 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
CHAPTER 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
CHAPTER 10 ASSESSING MODELING
10.1 TO EVALUATE MATHEMATICAL MODELING ASSIGNMENTS
10.2 CONCRETIZING GRADING CRITERIA
10.3 EVALUATING STUDENTS’ WORK
CHAPTER 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
CHAPTER 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 GEOGEBRABOKS
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 G EOGEBRA’S GENERIC FITTING COMMANDS
B.5 EXAMPLE OF A GENERIC FIT
INTEGER PROPERTIES
INDEX
LIST OF PROBLEMS BY NAME
EULA