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Calculus Using Mathematica: Scientific Projects and Mathematical Background is a companion to the core text, Calculus Using Mathematica. The book contains projects that illustrate applications of calculus to a variety of practical situations.
The text consists of 14 chapters of various projects on how to apply the concepts and methodologies of calculus. Chapters are devoted to epidemiological applications; log and exponential functions in science; applications to mechanics, optics, economics, and ecology. Applications of linear differential equations; forced linear equations; differential equations from vector geometry; and to chemical reactions are presented as well.
College students of calculus will find this book very helpful.
Chapter 1 Introduction to the Scientific Projects
Project 1. Linear Approximation of CO2 Data
Chapter 2 Epidemiological Applications
Project 2. Review of The S-I-R Model
Project 3. The 1968-69 New York Hong Kong Flu Epidemic
Project 4. Vaccination for Herd Immunity
Project 5. A Model for S-I-S Diseases and The Endemic Limit
Chapter 3 Applications of The Increment Approximation R(t + δt) = R(t) + R'(t) St + εδt
Project 6. A Derivation of Hubble's Law
Chapter 4 The Role of Rules for Derivatives
Project 7. The Expanding Economy
Project 8. The Expanding House
8.1. Volume Expansion Explained by Calculus
Chapter 5 Log and Exponential Functions in Science
Project 9. Drug Concentration and "Bi-Exponential" Functions
Project 10. Measurement of Kidney Function by Drug Concentration
Chapter 6 Applications to Mechanics
Project 11. The Falling Ladder (or Dad's Disaster)
Project 12. Falling with Air Resistance: Data and A Linear Model
Project 13. Bungee Diving and Nonlinear Airresistance
Chapter 7 Optics
Project 14. Fermat's Principle Implies SnelPs Law
Chapter 8 Applications in Economics
Project 15. Monopoly Pricing
Project 16. Discrete Dynamics of Price Adjustment
Project 17. Continuous Production and Exchange
Chapter 9 Applications in Ecology
Project 18. Sustained Harvest of Sei Whales
Project 19. A Journey to The Sogapalag Islands
Project 20. Competition and Cooperation Between Species
Chapter 10 Applications of Linear Differential Equations
Project 21. Lanchester's Combat Models
Project 22. Drug Dynamics and Pharmacokinetics
Chapter 11 Forced Linear Equations
Project 23. Forced Vibration - Non-autonomous Equations
Project 24. Resonance - Maximal Response to Forcing
Project 25. A Notch Filter - Minimal Response to Forcing
Chapter 12 Differential Equations from Vector Geometry
Project 26. The Perfecto Skier
Project 27. Low Level Bombing
Project 28. The Pendulum
Project 29. Using Jupiter as a Slingshot
Chapter 13 Chemical Reactions
Project 30. Stability of a Tank Reaction
Project 31. Enzyme Reactions: Beer, Coke & Vitamin C
Chapter 14 More Projects
- No. of pages:
- © Academic Press 1993
- 1st January 1993
- Academic Press
- eBook ISBN:
Department of Mathematics, The University of Iowa Iowa City. Iowa
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