Informal Calculus with Applications to Biological and Environmental Sciences

by Tyler Seacrest

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This book is an approachable introduction to calculus with applications to biology and environmental science. The text focuses on intuitive understanding of concepts, but still covers most of the algebra and calculations common in a survey of calculus course.

Description from LibreTexts.

Publisher
University of Montana Western
Subjects
Mathematics, Calculus
Licence
CC BY 4.0, as LibreTexts states it
Who can read
Tweens profiles and older, judged from its title and subjects

Contents

LibreTexts writes equations in TeX, and here they show as TeX; the PDF has them typeset.

  1. Front Matter
  2. TitlePage
  3. InfoPage
  4. Table of Contents
  5. Licensing
  6. 1: Algebra Tips and Tricks- Part I
  7. 1.1: Algebra Tips and Tricks Part I (Combining Terms, Distributing, Functions, Graphing)
  8. 1.2: Homework for Algebra Tips and Tricks- Part I
  9. 2: Derivative Introduction
  10. 2.1: Ball Toss Project
  11. 2.2: Position to Velocity
  12. 2.3: Homework- Position to Velocity
  13. 2.4: Algebra Tips and Tricks Part II (Piecewise Defined Functions)
  14. 2.5: Limits
  15. 2.6: Homework- Limits
  16. 2.7: Algebra Tips and Tricks Part III (Factoring)
  17. 2.8: Algebraic Limits
  18. 2.9: Homework- Algebraic Limits
  19. 2.10: Instantaneous Velocity
  20. 2.11: Homework- Instantaneous Velocity
  21. 2.12: Algebra Tips and Tricks IV (Tips for dealing with fractions)
  22. 2.13: Definition of Derivative Examples
  23. 2.14: Project- Hard Definition of Derivative Problems
  24. 2.15: Homework- Examples of the Definition of the Derivative
  25. 2.16: Project- Killdeer Migration Speed
  26. 3: Rules for Derivatives
  27. 3.1: Algebra Tips and Tricks Part V (Exponents)
  28. 3.2: Power Rule
  29. 3.3: Homework- Power Rule
  30. 3.4: Algebra Tips and Tricks Part VI (Logarithms)
  31. 3.5: Exponentials, Logarithms, and Trig Functions
  32. 3.6: Homework- Exponents, Logs, Trig Functions
  33. 3.7: Product Rule
  34. 3.8: Homework- Product Rule
  35. 3.9: Quotient Rule
  36. 3.10: Homework- Quotient Rule
  37. 3.11: Chain Rule
  38. 3.12: Homework- Chain Rule
  39. 3.13: Multirule Derivatives
  40. 3.14: Homework- Multirule Derivatives
  41. 3.15: Anti-derivatives
  42. 3.16: Homework- Anti-derivatives
  43. 4: More Derivative Intuition
  44. 4.1: Derivatives and Graphs
  45. 4.2: Homework- Derivative Graphs
  46. 4.3: Second Derivatives and Interpreting the Derivative
  47. 4.4: Homework- Second Derivatives and Interpreting the Derivative
  48. 4.5: Optimization
  49. 4.6: Homework- Optimization
  50. 4.7: Derivatives in Space
  51. 4.8: Homework- Derivatives in Space
  52. 5: Differential Equations
  53. 5.1: Recurrance Relations
  54. 5.2: Homework- Recurrence Relations
  55. 5.3: Introduction to Differential Equations
  56. 5.4: Homework- Introduction to Differential Equations
  57. 5.5: Understanding Differential Equations
  58. 5.6: Homework- Understanding Differential Equations
  59. 5.7: Initial Value Problems
  60. 5.8: Homework- Initial Value Problems
  61. 5.9: Growth and Decay
  62. 5.10: Homework- Growth and Decay
  63. 5.11: Exploring Graphs of Differential Equations
  64. 5.12: Project- Modelling with Differential Equations
  65. 6: Intuition for Integration
  66. 6.1: Introduction to Integrals
  67. 6.2: Numeric Integration Techniques
  68. 6.3: Homework- Numeric Integration Techniques
  69. 6.4: Fundamental Theorem of Calculus
  70. 6.5: Homework- The Fundamental Theorem of Calculus
  71. 6.6: Project- Measuring Streamflow
  72. 6.7: Project- Quake Lake
  73. 7: Rules for Integration
  74. 7.1: Power, exponential, trig, and logarithm rules
  75. 7.2: Homework- Power, exponential, trig, and logarithmic rules
  76. 7.3: u-substitution
  77. 7.4: Homework- u-substitution
  78. 7.5: Integral Applications
  79. 7.6: Homework- Integral Applications
  80. 7.7: Integration by Parts
  81. 7.8: Homework- Integration by Parts
  82. Back Matter
  83. Index
  84. Detailed Licensing