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Differential Calculus for the Life Sciences

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Differential Calculus for the Life Sciences

Calculus arose as a tool for solving practical scientific problems through the centuries. However, it is often taught as a technical subject with rules and formulas (and occasionally theorems), devoid of its connection to applications. In this course, the applications form an important focal point, with emphasis on life sciences. This places the techniques and concepts into practical context, as well as motivating quantitative approaches to biology taught to undergraduates.

CalculusMathematics
Author
Leah Edelstein-Keshet
Publisher
University of British Columbia
Source
LibreTexts
License
CC BY-NC-SA
Language
EN
Category
Basic Sciences
Read online Download PDF (open licence)
Contents· 111 sections
  1. 01: Power functions as building blocks
  2. 1.01: Power Functions
  3. 1.02: How big can a cell be A model for nutrient balance
  4. 1.03: Sustainability and energy balance on Earth
  5. 1.04: First steps in graph sketching
  6. 1.05: Rate of an enzyme-catalyzed reaction
  7. 1.06: Predator Response
  8. 1.07: Summary
  9. 1.08: Exercises
  10. 02: Average rates of change average velocity and the secant line
  11. 2.01: Time-dependent data and rates of change
  12. 2.02: The slope of a straight line is a rate of change
  13. 2.03: The slope of a secant line is the average rate of change
  14. 2.04: From average to instantaneous rate of change
  15. 2.05: Introduction to the derivative
  16. 2.06: Summary
  17. 2.07: Exercises
  18. 03: Three Faces of the Derivative - Geometric Analytic and Computational
  19. 3.01: The Geometric View - Zooming into the Graph of a Function
  20. 3.02: The analytic view- calculating the derivative
  21. 3.03: The computational view- software to the rescue
  22. 3.04: Summary
  23. 3.05: Exercises
  24. 04: Differentiation rules simple antiderivatives and applications
  25. 4.01: Rules of Differentiation
  26. 4.02: Application of the Second Derivative to Acceleration
  27. 4.03: Sketching the First and Second Derivative and the Anti-Derivatives
  28. 4.04: Summary
  29. 4.05: Exercises
  30. 05: Tangent lines Linear Approximation and Newtons Method
  31. 5.01: The Equation of a Tangent Line
  32. 5.02: Generic Tangent line Equation and Properties
  33. 5.03: Approximating a Function by its Tangent Line
  34. 5.04: Tangent Lines for Finding Zeros of a Function - Newtons Method
  35. 5.05: Aphids and Ladybugs revisited
  36. 5.06: Harder problems- finding the point of tangency
  37. 5.07: Summary
  38. 5.08: Exercises
  39. 06: Sketching the Graph of a Function using Calculus Tools
  40. 6.01: Overall Shape of the Graph of a Function
  41. 6.02: Special Points on the Graph of a Function
  42. 6.03: Sketching the Graph of a Function
  43. 6.04: Summary
  44. 6.05: Exercises
  45. 07: Optimization
  46. 7.01: Simple Biological Optimization Problems
  47. 7.02: Optimization with a constraint
  48. 7.03: Checking Endpoints
  49. 7.04: Optimal Foraging
  50. 7.05: Summary
  51. 7.06: Exercises
  52. 08: Introducing the Chain Rule
  53. 8.01: The Chain Rule
  54. 8.02: The chain rule applied to optimization problems
  55. 8.03: Summary
  56. 8.04: Exercises
  57. 09: Chain rule applied to related rates and implicit differentiation
  58. 9.01: Applications of the chain rule to related rates
  59. 9.02: Implicit Differentiation
  60. 9.03: The Power Rule for Fractional Powers
  61. 9.04: Summary
  62. 9.05: Exercises
  63. 10: Exponential Functions
  64. 10.01: Unlimited Growth and Doubling
  65. 10.02: Derivatives of Exponential Functions
  66. 10.03: Inverse Functions and Logarithms
  67. 10.04: Applications of the Logarithm
  68. 10.05: Summary
  69. 10.06: Exercises
  70. 11: Differential equations for exponential growth and decay
  71. 11.01: Introducing a new kind of equation
  72. 11.02: Differential equation for unlimited population growth
  73. 11.03: Radioactivity
  74. 11.04: Deriving a differential equation for the growth of cell mass
  75. 11.05: Summary
  76. 11.06: Exercises
  77. 12: Solving Differential Equations
  78. 12.01: Verifying that a Function is a Solution
  79. 12.02: Equations of the Form- y'(t) aby
  80. 12.03: Eulers Method and Numerical Solutions
  81. 12.04: Summary
  82. 12.05: Exercises
  83. 13: Qualitative Methods for Differential Equations
  84. 13.01: Linear and Nonlinear Differential Equations
  85. 13.02: The Geometry of Change
  86. 13.03: Applying qualitative analysis to biological models
  87. 13.04: Summary
  88. 13.05: Exercises
  89. 14: Periodic and Trigonometric Functions
  90. 14.01: Basic Trigonometry
  91. 14.02: Periodic Functions
  92. 14.03: Inverse trigonometric functions
  93. 14.04: Summary
  94. 14.05: Exercises
  95. 15: Cycles Periods and Rates of Change
  96. 15.01: Derivatives of Trigonometric Functions
  97. 15.02: Changing Angles and Related Rates
  98. 15.03: The Zebra Danios Escape Responses
  99. 15.04: Summary
  100. 15.05: Exercises
  101. 16: Additional Exercises
  102. 16.01: Exercises
  103. 17: Appendices
  104. 17.01: Appendix A- A review of Straight Lines
  105. 17.02: Appendix B- A precalculus review
  106. 17.03: Appendix C- A Review of Simple Functions
  107. 17.04: Appendix D- Limits
  108. 17.05: Appendix E- Proofs
  109. 17.06: Appendix F- Trigonometry Review
  110. 17.07: Appendix G- For Further Study
  111. 17.08: Appendix H- Short Answers to Problems