MATH 1200: Calculus for Scientists I

by Pamini Thangarajah

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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.

Description from LibreTexts.

Publisher
Mount Royal University
Subjects
Mathematics
Licence
CC BY-NC-SA, as LibreTexts states it. Non-commercial use only.
Who can read
Tweens profiles and older, judged from its title and subjects

Contents

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  1. Front Matter
  2. TitlePage
  3. InfoPage
  4. Table of Contents
  5. Licensing
  6. Preface
  7. 0: Pre-Calculus Refresher
  8. 0.1: Real numbers
  9. 0.2: Analytic geometry
  10. 0.3: Trigonometry
  11. 0.4: Logarithms and Exponents
  12. 0E: Exercises
  13. Common Mistakes
  14. 1: Functions and Graphs
  15. 1.0: Prelude to Functions and Graphs
  16. 1.1: Review of Functions
  17. 1.1E: Exercises for Section 1.1
  18. 1.2: Basic Classes of Functions
  19. 1.2E: Exercises for Section 1.2
  20. 1.3: Trigonometric Functions
  21. 1.3E: Exercises for Section 1.3
  22. 1.4: Inverse Functions
  23. 1.4E: Exercises for Section 1.4
  24. 2: Limit and Continuity of Functions
  25. 2.0: Library of functions
  26. 2.0E: Exercises
  27. 2.1: Introduction to concept of a limit
  28. 2.1E: Exercises
  29. 2.2: One sided Limits and Vertical Asymptotes
  30. 2.2E: Exercises
  31. 2.3: Limit calculations for algebraic expressions
  32. 2.3E: Exercises
  33. 2.5: Formal Definition of a Limit (optional)
  34. 2.5E: Exercises
  35. 2.6: Continuity and the Intermediate Value Theorem
  36. 2.6E: Excercises
  37. 2.7: Limit of Trigonometric functions
  38. 2.7E: Exercises
  39. 2.8: Limits and continuity of Inverse Trigonometric functions
  40. 2.9: Limit of Exponential Functions and Logarithmic Functions
  41. 2.9E: Exercises
  42. 2.R: Chapter 2 Review Exercises
  43. 2E: Limit Review Exercises
  44. 3: Derivatives
  45. 3.0: Tangent lines and Rates of change
  46. 3.0E: Exercises
  47. 3.1: Derivative as a Function
  48. 3.1E: Exercises
  49. 3.2: Techniques of differentiation
  50. 3.2E: Exercises
  51. 3.3: Derivative as a rate of Change
  52. 3.3E: Exercises
  53. 3.4: Derivatives of Trigonometric functions
  54. 3.4E: Exercises
  55. 3.5: Chain Rule
  56. 3.5E: Exercises
  57. 3.6: Implicit Differentiation
  58. 3.6E: Exercises
  59. 3.7: Derivatives of Inverse Trigonometric Functions
  60. 3.7E: Exercises
  61. 3.8: Derivatives of Exponential and Logarithmic functions
  62. 3.8E: Exercises
  63. 3.R: Chapter 3 Review Exercises
  64. 4: Applications of Derivatives
  65. 4.0: Introduction to applications of Derivative
  66. 4.1: Related Rates
  67. 4.1E: Exercises
  68. 4.2 Linear approximations and Differentials
  69. 4.2E: Exercises
  70. 4.3: Extremas
  71. 4.3E: Exercises
  72. 4.4 The Mean Value Theorem
  73. 4.4E: Exercises
  74. 4.5: Derivatives and the Shape of a Graph
  75. 4.5E: Exercises
  76. 4.6: Limits at Infinity and Horizontal Asymptotes : End Behavior
  77. 4.6E: Exercises
  78. 4.7: Applied Optimization Problems
  79. 4.7E: Exercises
  80. 4.8: L'Hôpital's Rule
  81. 4.8E: Exercises
  82. 4.9: Newton's Method
  83. 4.9E: Exercises
  84. 4.R: Chapter 4 Review Exercises
  85. 4. 10: Anti derivatives and Rectilinear Motion
  86. 4.10E: Exercises
  87. 5: Integration
  88. 4.1: Integration by Substitution
  89. 4.1E: Exercises
  90. 4.7: Definite integrals by substitution.
  91. 4.7E: Exercises
  92. 4.9: Applications of definite integrals
  93. 4.9E: Exercises
  94. 5.0: Antidervatives and Indefinite Integration (Revisited)
  95. 5.0E: Exercises
  96. 5.0: Prelude to Integration
  97. 5.1: Approximating Areas
  98. 4.3E: Exercises
  99. 5.1E: Exercises for Section 5.1
  100. 5.2: The Definite Integral
  101. 5.2E: Exercises for Section 5.2
  102. 5.2A: Definite Integral_Introduction
  103. 4.2E: Exercises
  104. 5.3: The Fundamental Theorem of Calculus
  105. 5.3E: Exercises
  106. 5.3 E: Exercises for Section 5.3
  107. 5.4: Integration Formulas and the Net Change Theorem
  108. 5.4E: Exercises
  109. 5.5: Substitution
  110. 5.6E: Exercises for Section 5.6
  111. 5.5: Substitution
  112. 5.7: Integrals Resulting in Inverse Trigonometric Functions
  113. 5.7E: Exercises for Section 5.7
  114. 5E: Exercises
  115. 6: Applications of Integration
  116. 6.0: Prelude to Applications of Integration
  117. 6.1: Area between curves
  118. 6.1E: Exercises for Section 6.1
  119. Mock Exams (Celebration of Learning) and Review Exercises
  120. 0E:Precalculus Review
  121. 2E: Limit Review Exercises
  122. 3E: Derivatives Review Exercises
  123. 4E: Applications of Derivatives Exercises
  124. 5E: Integrals Review Exercises
  125. 6E: Applications of Integration Exercises
  126. Test 1
  127. Test 1A
  128. Test 1B
  129. Test 2
  130. Test 2A
  131. Test 2W
  132. Test 3 (Mock Exam)
  133. Additional Resources
  134. Glossary
  135. Key equations
  136. Notations
  137. Table of Derivatives
  138. Table of Integrals
  139. Table of limits
  140. Back Matter
  141. Index
  142. Glossary
  143. Detailed Licensing
  144. 5.3E: Exercises for Section 5.3