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Solution Manual for A First Course in Mathematical Modeling, 5th Edition

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Solution Manual for A First Course in Mathematical Modeling, 5th Edition

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Offering a solid introduction to the entire modeling process, A FIRST COURSE IN MATHEMATICAL MODELING, 5th Edition delivers an excellent balance of theory and practice, and gives you relevant, hands-on experience developing and sharpening your modeling skills. Throughout, the book emphasizes key facets of modeling, including creative and empirical model construction, model analysis, and model research, and provides myriad opportunities for practice. The authors apply a proven six-step problem-solving process to enhance your problem-solving capabilities — whatever your level. In addition, rather than simply emphasizing the calculation step, the authors first help you learn how to identify problems, construct or select models, and figure out what data needs to be collected. By involving you in the mathematical process as early as possible — beginning with short projects — this text facilitates your progressive development and confidence in mathematics and modeling.

 

Table of Content:

  1. Ch 1: Modeling Change
  2. Introduction
  3. 1.1: Modeling Change with Difference Equations
  4. 1.2: Approximating Change with Difference Equations
  5. 1.3: Solutions to Dynamical Systems
  6. 1.4: Systems of Difference Equations
  7. Ch 2: The Modeling Process, Proportionality, and Geometric Similarity
  8. Introduction
  9. 2.1: Mathematical Models
  10. 2.2: Modeling Using Proportionality
  11. 2.3: Modeling Using Geometric Similarity
  12. 2.4: Automobile Gasoline Mileage
  13. 2.5: Body Weight and Height, Strength and Agility
  14. Ch 3: Model Fitting
  15. Introduction
  16. 3.1: Fitting Models to Data Graphically
  17. 3.2: Analytic Methods of Model Fitting
  18. 3.3: Applying the Least-Squares Criterion
  19. 3.4: Choosing a Best Model
  20. Ch 4: Experimental Modeling
  21. Introduction
  22. 4.1: Harvesting in the Chesapeake Bay and Other One-Term Models
  23. 4.2: High-Order Polynomial Models
  24. 4.3: Smoothing: Low-Order Polynomial Models
  25. 4.4: Cubic Spline Models
  26. Ch 5: Simulation Modeling
  27. Introduction
  28. 5.1: Simulating Deterministic Behavior: Area under a Curve
  29. 5.2: Generating Random Numbers
  30. 5.3: Simulating Probabilistic Behavior
  31. 5.4: Inventory Model: Gasoline and Consumer Demand
  32. 5.5: Queuing Models
  33. Ch 6: Discrete Probabilistic Modeling
  34. Introduction
  35. 6.1: Probabilistic Modeling with Discrete Systems
  36. 6.2: Modeling Component and System Reliability
  37. 6.3: Linear Regression
  38. Ch 7: Optimization of Discrete Models
  39. Introduction
  40. 7.1: An Overview of Optimization Modeling
  41. 7.2: Linear Programming I: Geometric Solutions
  42. 7.3: Linear Programming II: Algebraic Solutions
  43. 7.4: Linear Programming III: The Simplex Method
  44. 7.5: Linear Programming IV: Sensitivity Analysis
  45. 7.6: Numerical Search Methods
  46. Ch 8: Modeling Using Graph Theory
  47. Introduction
  48. 8.1: Graphs as Models
  49. 8.2: Describing Graphs
  50. 8.3: Graph Models
  51. 8.4: Using Graph Models to Solve Problems
  52. 8.5: Connections to Mathematical Programming
  53. Ch 9: Modeling with Decision Theory
  54. Introduction
  55. 9.1: Probability and Expected Value
  56. 9.2: Decision Trees
  57. 9.3: Sequential Decisions and Conditional Probabilities
  58. 9.4: Decisions Using Alternative Criteria
  59. Ch 10: Game Theory
  60. Introduction
  61. 10.1: Game Theory: Total Conflict
  62. 10.2: Total Conflict as a Linear Program Model: Pure and Mixed Strategies
  63. 10.3: Decision Theory Revisited: Games against Nature
  64. 10.4: Alternative Methods for Determining Pure Strategy Solutions
  65. 10.5: Alternative Shortcut Solution Methods for the 2 x 2 Total Conflict Game
  66. 10.6: Partial Conflict Games: The Classical Two-Player Games
  67. 10.7: Illustrative Modeling Examples
  68. Ch 11: Modeling with a Differential Equation
  69. Introduction
  70. 11.1: Population Growth
  71. 11.2: Prescribing Drug Dosage
  72. 11.3: Braking Distance Revisited
  73. 11.4: Graphical Solutions of Autonomous Differential Equations
  74. 11.5: Numerical Approximation Methods
  75. 11.6: Separation of Variables
  76. 11.7: Linear Equations
  77. Ch 12: Modeling with Systems of Differential Equations
  78. Introduction
  79. 12.1: Graphical Solutions of Autonomous Systems of First-Order Differential Equations
  80. 12.2: A Competitive Hunter Model
  81. 12.3: A Predator-Prey Model
  82. 12.4: Two Military Examples
  83. 12.5: Euler’s Method for Systems of Differential Equations
  84. Ch 13: Optimization of Continuous Models
  85. Introduction
  86. 13.1: An Inventory Problem: Minimizing the Cost of Delivery and Storage
  87. 13.2: Methods to Optimize Functions of Several Variables
  88. 13.3: Constrained Continuous Optimization
  89. 13.4: Managing Renewable Resources: The Fishing Industry
  90. Ch 14: Dimensional Analysis and Similitude
  91. Introduction
  92. 14.1: Dimensions as Products
  93. 14.2: The Process of Dimensional Analysis
  94. 14.3: A Damped Pendulum
  95. 14.4: Examples Illustrating Dimensional Analysis
  96. 14.5: Similitude
  97. Ch 15: Graphs of Functions as Models
  98. 15.1: An Arms Race
  99. 15.2: Modeling an Arms Race in Stages
  100. 15.3: Managing Nonrenewable Resources: The Energy Crisis
  101. 15.4: Effects of Taxation on the Energy Crisis
  102. 15.5: A Gasoline Shortage and Taxation
  103. Appendix A: Problems from the Mathematics Contest in Modeling, 1985-2012
  104. 1985: The Animal Population Problem
  105. 1985: The Strategic Reserve Problem
  106. 1986: The Hydrographic Data Problem
  107. 1986: The Emergency-Facilities Location Problem
  108. 1987: The Salt Storage Problem
  109. 1987: The Parking Lot Problem
  110. 1988: The Railroad Flatcar Problem
  111. 1988: The Drug Runner Problem
  112. 1989: The Aircraft Queuing Problem
  113. 1989: The Midge Classification Problem
  114. 1990: The Brain-Drug Problem
  115. 1991: The Water Tank Problem
  116. 1991: The Steiner Tree Problem
  117. 1992: The Emergency Power-Restoration Problem
  118. 1992: The Air-Traffic-Control Radar Problem
  119. 1993: The Coal-Tipple Operations Problem
  120. 1993: The Optimal Composting Problem
  121. 1994: The Concrete Slab Problem
  122. 1994: The Communications Network Problem
  123. 1995: The Single Helix
  124. 1995: Aluacha Balaclava College
  125. 1996: The Submarine Detection Problem
  126. 1996: The Contest Judging Problem
  127. 1997: The Velociraptor Problem
  128. 1997: Mix Well for Fruitful Discussions
  129. 1998: MRI Scanners
  130. 1998: Grade Inflation
  131. 1999: Deep Impact
  132. 1999: Unlawful Assembly
  133. 2000: Air Traffic Control
  134. 2000: Radio Channel Assignments
  135. 2001: Choosing a Bicycle Wheel
  136. 2001: Escaping a Hurricane’s Wrath
  137. 2002: Wind and Waterspray
  138. 2002: Airline Overbooking
  139. 2003: The Stunt Person
  140. 2003: Gamma Knife Treatment Planning
  141. 2004: Are Fingerprints Unique?
  142. 2004: A Faster QuickPass System
  143. 2005: Flood Planning
  144. 2005: Tollbooths
  145. 2006: Positioning and Moving Sprinkler Systems for Irrigation
  146. 2006: Wheelchair Access at Airports
  147. 2007: Gerrymandering
  148. 2007: The Airplane Seating Problem
  149. 2008: Take a Bath
  150. 2008: Creating Sudoku Puzzles
  151. 2009: Designing a Traffic Circle
  152. 2009: Energy and the Cell Phone
  153. 2010: The Sweet Spot
  154. 2010: Criminology
  155. 2011: Snowboard Course
  156. 2011: Repeater Coordination
  157. 2012: The Leaves of a Tree
  158. 2012: Camping along the Big Long River
  159. Appendix B: An Elevator Simulation Algorithm
  160. Appendix C: The Revised Simplex Method
  161. Pivoting by Matrix Inversion and Multiplication
  162. The Revised Simplex Method
  163. Appendix D: Brief Review of Integration Techniques
  164. u-Substitution
  165. Integration by Parts
  166. Rational Functions
  167. Partial Fractions
  168. Answers to Selected Problems
  169. Index

 

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