Mathematical Modeling: Applications with GeoGebra

Lýsing:A logical problem-based introduction to the use of GeoGebra for mathematical modeling and...
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Mathematical Modeling: Applications with GeoGebra

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Rafbók til leigu í 1 ár. Útgáfa: 1

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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