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Solution Manual for Biocalculus Calculus for Life Sciences, 1st Edition

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Solution Manual for Biocalculus Calculus for Life Sciences, 1st Edition

Product details:

  • ISBN-10 ‏ : ‎ 1133109632
  • ISBN-13 ‏ : ‎ 978-1133109631
  • Author: James Stewart

The chief goal in this textbook is to show students how calculus relates to biology, with a style that maintains rigor without being overly formal. The text motivates and illustrates the topics of calculus with examples drawn from many areas of biology, including genetics, biomechanics, medicine, pharmacology, physiology, ecology, epidemiology, and evolution, to name a few. Particular attention has been paid to ensuring that all applications of the mathematics are genuine, and references to the primary biological literature for many of these has been provided so that students and instructors can explore the applications in greater depth. Although the focus is on the interface between mathematics and the life sciences, the logical structure of the book is motivated by the mathematical material. Students will come away from a course based on this book with a sound knowledge of mathematics and an understanding of the importance of mathematical arguments. Equally important, they will also come away with a clear understanding of how these mathematical concepts and techniques are central in the life sciences.

Table contents:

  1. Ch 1: Functions and Sequences
  2. 1.1: Four Ways to Represent a Function
  3. 1.2: A Catalog of Essential Functions
  4. 1.3: New Functions from Old Functions
  5. 1.4: Exponential Functions
  6. 1.5: Logarithms; Semilog and Log-Log Plots
  7. 1.6: Sequences and Difference Equations
  8. Chapter 1: Review
  9. Ch 2: Limits
  10. 2.1: Limits of Sequences
  11. 2.2: Limits of Functions at Infinity
  12. 2.3: Limits of Functions at Finite Numbers
  13. 2.4: Limits: Algebraic Methods
  14. 2.5: Continuity
  15. Chapter 2: Review
  16. Ch 3: Derivatives
  17. 3.1: Derivatives and Rates of Change
  18. 3.2: The Derivative as a Function
  19. 3.3: Basic Differentiation Formulas
  20. 3.4: The Product and Quotient Rules
  21. 3.5: The Chain Rule
  22. 3.6: Exponential Growth and Decay
  23. 3.7: Derivatives of the Logarithmic and Inverse Tangent Functions
  24. 3.8: Linear Approximations and Taylor Polynomials
  25. Chapter 3: Review
  26. Ch 4: Applications of Derivatives
  27. 4.1: Maximum and Minimum Values
  28. 4.2: How Derivatives Affect the Shape of a Graph
  29. 4.3: L’Hospital’s Rule: Comparing Rates of Growth
  30. 4.4: Optimization Problems
  31. 4.5: Recursions: Equilibria and Stability
  32. 4.6: Antiderivatives
  33. Chapter 4: Review
  34. Ch 5: Integrals
  35. 5.1: Areas, Distances, and Pathogenesis
  36. 5.2: The Definite Integral
  37. 5.3: The Fundamental Theorem of Calculus
  38. 5.4: The Substitution Rule
  39. 5.5: Integration by Parts
  40. 5.6: Partial Fractions
  41. 5.7: Integration Using Tables and Computer Algebra Systems
  42. 5.8: Improper Integrals
  43. Chapter 5: Review
  44. Ch 6: Applications of Integrals
  45. 6.1: Areas between Curves
  46. 6.2: Average Values
  47. 6.3: Further Applications to Biology
  48. 6.4: Volumes
  49. Chapter 6: Review
  50. Ch 7: Differential Equations
  51. 7.1: Modeling with Differential Equations
  52. 7.2: Phase Plots, Equilibria, and Stability
  53. 7.3: Direction Fields and Euler’s Method
  54. 7.4: Separable Equations
  55. 7.5: Systems of Differential Equations
  56. 7.6: Phase Plane Analysis
  57. Chapter 7: Review
  58. Ch 8: Vectors and Matrix Models
  59. 8.1: Coordinate Systems
  60. 8.2: Vectors
  61. 8.3: The Dot Product
  62. 8.4: Matrix Algebra
  63. 8.5: Matrices and the Dynamics of Vectors
  64. 8.6: The Inverse and Determinant of a Matrix
  65. 8.7: Eigenvectors and Eigenvalues
  66. 8.8: Iterated Matrix Models
  67. Chapter 8: Review
  68. Ch 9: Multivariable Calculus
  69. 9.1: Functions of Several Variables
  70. 9.2: Partial Derivatives
  71. 9.3: Tangent Planes and Linear Approximations
  72. 9.4: The Chain Rule
  73. 9.5: Directional Derivatives and the Gradient Vector
  74. 9.6: Maximum and Minimum Values
  75. Chapter 9: Review
  76. Ch 10: Systems of Linear Differential Equations
  77. 10.1: Qualitative Analysis of Linear Systems
  78. 10.2: Solving Systems of Linear Differential Equations
  79. 10.3: Applications
  80. 10.4: Systems of Nonlinear Differential Equations
  81. Chapter 10: Review
  82. Ch 11: Descriptive Statistics
  83. 11.1: Numerical Descriptions of Data
  84. 11.2: Graphical Descriptions of Data
  85. 11.3: Relationships between Variables
  86. 11.4: Populations, Samples, and Inference
  87. Chapter 11: Review
  88. Ch 12: Probability
  89. 12.1: Principles of Counting
  90. 12.2: What is Probability?
  91. 12.3: Conditional Probability
  92. 12.4: Discrete Random Variables
  93. 12.5: Continuous Random Variables
  94. Chapter 12: Review
  95. Ch 13: Inferential Statistics
  96. 13.1: The Sampling Distribution
  97. 13.2: Confidence Intervals
  98. 13.3: Hypothesis Testing
  99. 13.4: Contingency Table Analysis
  100. Chapter 13: Review
  101. Appendixes
  102. A: Intervals, Inequalities, and Absolute Values
  103. B: Coordinate Geometry
  104. C: Trigonometry
  105. D: Precise Definitions of Limits
  106. E: A Few Proofs
  107. F: Sigma Notation
  108. G: Complex Numbers
  109. H: Statistical Tables
  110. Glossary of Biological Terms
  111. Answers to Odd-Numbered Exercises
  112. Biological Index
  113. Index
  114. Concept Check Answers

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