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MATH 1200: Calculus for Scientists I

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MATH 1200: Calculus for Scientists I

This course provides an introduction to calculus with exposure to applications in sciences. The main concepts covered are limits, derivatives, and integrals. Derivatives of transcendental functions are used to solve optimization, linear approximation, and related rates problems. Studying calculus will expose students to a variety of important mathematical ideas and help students develop their critical thinking and problem solving skills.

Mathematics
Author
Pamini Thangarajah
Publisher
Mount Royal University
Source
LibreTexts
License
CC BY-NC-SA
Language
EN
Category
Basic Sciences
Read online Download PDF (open licence)
Contents· 137 sections
  1. 0: Pre-Calculus Refresher
  2. 0.1: Real numbers
  3. 0.2: Analytic geometry
  4. 0.3: Trigonometry
  5. 0.4: Logarithms and Exponents
  6. 0E: Exercises
  7. Common Mistakes
  8. 1: Functions and Graphs
  9. 1.0: Prelude to Functions and Graphs
  10. 1.1: Review of Functions
  11. 1.1E: Exercises for Section 1.1
  12. 1.2: Basic Classes of Functions
  13. 1.2E: Exercises for Section 1.2
  14. 1.3: Trigonometric Functions
  15. 1.3E: Exercises for Section 1.3
  16. 1.4: Inverse Functions
  17. 1.4E: Exercises for Section 1.4
  18. 2: Limit and Continuity of Functions
  19. 2.0: Library of functions
  20. 2.0E: Exercises
  21. 2.1: Introduction to concept of a limit
  22. 2.1E: Exercises
  23. 2.2: One sided Limits and Vertical Asymptotes
  24. 2.2E: Exercises
  25. 2.3: Limit calculations for algebraic expressions
  26. 2.3E: Exercises
  27. 2.5: Formal Definition of a Limit (optional)
  28. 2.5E: Exercises
  29. 2.6: Continuity and the Intermediate Value Theorem
  30. 2.6E: Excercises
  31. 2.7: Limit of Trigonometric functions
  32. 2.7E: Exercises
  33. 2.8: Limits and continuity of Inverse Trigonometric functions
  34. 2.9: Limit of Exponential Functions and Logarithmic Functions
  35. 2.9E: Exercises
  36. 2.R: Chapter 2 Review Exercises
  37. 2E: Limit Review Exercises
  38. 3: Derivatives
  39. 3.0: Tangent lines and Rates of change
  40. 3.0E: Exercises
  41. 3.1: Derivative as a Function
  42. 3.1E: Exercises
  43. 3.2: Techniques of differentiation
  44. 3.2E: Exercises
  45. 3.3: Derivative as a rate of Change
  46. 3.3E: Exercises
  47. 3.4: Derivatives of Trigonometric functions
  48. 3.4E: Exercises
  49. 3.5: Chain Rule
  50. 3.5E: Exercises
  51. 3.6: Implicit Differentiation
  52. 3.6E: Exercises
  53. 3.7: Derivatives of Inverse Trigonometric Functions
  54. 3.7E: Exercises
  55. 3.8: Derivatives of Exponential and Logarithmic functions
  56. 3.8E: Exercises
  57. 3.R: Chapter 3 Review Exercises
  58. 4: Applications of Derivatives
  59. 4. 10: Anti derivatives and Rectilinear Motion
  60. 4.10E: Exercises
  61. 4.0: Introduction to applications of Derivative
  62. 4.1: Related Rates
  63. 4.1E: Exercises
  64. 4.2 Linear approximations and Differentials
  65. 4.2E: Exercises
  66. 4.3: Extremas
  67. 4.3E: Exercises
  68. 4.4 The Mean Value Theorem
  69. 4.4E: Exercises
  70. 4.5: Derivatives and the Shape of a Graph
  71. 4.5E: Exercises
  72. 4.6: Limits at Infinity and Horizontal Asymptotes : End Behavior
  73. 4.6E: Exercises
  74. 4.7: Applied Optimization Problems
  75. 4.7E: Exercises
  76. 4.8: L'Hôpital's Rule
  77. 4.8E: Exercises
  78. 4.9: Newton's Method
  79. 4.9E: Exercises
  80. 4.R: Chapter 4 Review Exercises
  81. 5: Integration
  82. 4.1: Integration by Substitution
  83. 4.1E: Exercises
  84. 4.7: Definite integrals by substitution.
  85. 4.7E: Exercises
  86. 4.9: Applications of definite integrals
  87. 4.9E: Exercises
  88. 5.0: Antidervatives and Indefinite Integration (Revisited)
  89. 5.0E: Exercises
  90. 5.0: Prelude to Integration
  91. 5.1: Approximating Areas
  92. 4.3E: Exercises
  93. 5.1E: Exercises for Section 5.1
  94. 5.2: The Definite Integral
  95. 5.2E: Exercises for Section 5.2
  96. 5.2A: Definite Integral Introduction
  97. 4.2E: Exercises
  98. 5.3: The Fundamental Theorem of Calculus
  99. 5.3 E: Exercises for Section 5.3
  100. 5.3E: Exercises
  101. 5.4: Integration Formulas and the Net Change Theorem
  102. 5.4E: Exercises
  103. 5.5: Substitution
  104. 5.5: Substitution
  105. 5.5E: Exercises for Section 5.5
  106. 5.6: Integrals Involving Exponential and Logarithmic Functions
  107. 5.6E: Exercises for Section 5.6
  108. 5.5: Substitution
  109. 5.7: Integrals Resulting in Inverse Trigonometric Functions
  110. 5.7E: Exercises for Section 5.7
  111. 5E: Exercises
  112. 5.3E: Exercises for Section 5.3
  113. 6: Applications of Integration
  114. 6.0: Prelude to Applications of Integration
  115. 6.1: Area between curves
  116. 6.1E: Exercises for Section 6.1
  117. Additional Resources
  118. Glossary
  119. Key equations
  120. Notations
  121. Table of Derivatives
  122. Table of Integrals
  123. Table of limits
  124. Mock Exams (Celebration of Learning) and Review Exercises
  125. 0E:Precalculus Review
  126. 2E: Limit Review Exercises
  127. 3E: Derivatives Review Exercises
  128. 4E: Applications of Derivatives Exercises
  129. 5E: Integrals Review Exercises
  130. 6E: Applications of Integration Exercises
  131. Test 1
  132. Test 1A
  133. Test 1B
  134. Test 2
  135. Test 2A
  136. Test 2W
  137. Test 3 (Mock Exam)