MATH 2200: Calculus for Scientists II

by Pamini Thangarajah

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In this course, students will learn advanced methods of integration, partial differentiation, introduction to first and second-order linear differential equations and a variety of applications. The main concepts of multivariable calculus will also be introduced.

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. 1: Applications of Integration
  8. 1.1: Volumes of solids of revolution -cross-sections
  9. 1.1E: Exercises
  10. 1.2: Volumes of solids of revolution - cylindrical shells
  11. 1.2E: Exercises
  12. 1.3: Surface area (surfaces of revolution)
  13. 1.3E: Exercises
  14. 1.4: Other applications: Work, centroid, and center of mass
  15. 1.4E: Exercises
  16. 1.5: Moments and Centers of Mass
  17. 1.5E: Exercises
  18. 1.7: Calculus of the Hyperbolic Functions
  19. 1.7E: Exercises
  20. 1.E: Chapter Review Exercises
  21. 2: Techniques of Integration
  22. 2.1: Integration by parts
  23. 2.1E: Exercises
  24. 2.2: Integrals of Trigonometric functions
  25. 2.2E: Exercises
  26. 2.3: Trigonometric Substitutions
  27. 2.3E: Exercises
  28. 2.4: Partial Fraction Decomposition
  29. 2.4E: Exercises
  30. 2.5: Numerical Integration - Midpoint, Trapezoid, Simpson's rule
  31. 2.5E: Exercises
  32. 2.6: Improper Integrals
  33. 2.6E: Exercises
  34. 2.7: Other Strategies for Integration
  35. 2.7E: Exercises
  36. 2.E: Chapter Review Exercises
  37. 3: Introduction to Differential equations
  38. 3.0: Prelude to Differential Equations
  39. 3.1: Basics of Differential equations
  40. 3.1E: Exercises
  41. 3.2: Direction Fields and Numerical Methods
  42. 3.2E: Exercises
  43. 3.3: Separable differential Equations
  44. 3.3E: Excercises
  45. 3.4: The Logistic Equation
  46. 3.4E: Exercises
  47. 3.5: First-order Linear Differential Equations
  48. 3.5E: Exercises
  49. 3E:Review Exercises
  50. 4: Sequences and Series
  51. 4.0: Introduction
  52. 4.1: Sequences
  53. 4.1 E: Exercises
  54. 4.2: Series
  55. 4.2 E: Exercises
  56. 4.3 : The Divergence and Integral Tests
  57. 4.3E: Exercises
  58. 4.4: Convergence Tests - Comparison Test
  59. 4.4E: Excersieses
  60. 4.5: Alternating Series
  61. 4.5E: Exercises
  62. 4.6: Ratio and Root Tests
  63. 4.6E: Exercises
  64. 8E: Chapter Review Excercises
  65. 5: Power Series
  66. 5.0: Prelude to Power Series
  67. 5.1 : Power Series and Functions
  68. 5.1E: Exercises
  69. 5.2: Properties of Power Series
  70. 5.2E: Excercises
  71. 5.3: Taylor and Maclaurin Series
  72. 5.3E: Exercises
  73. 5.4: Working with Taylor Series
  74. 5.4E: Excercises
  75. 5E: Review Exercises
  76. 6: Parametric Equations and Polar Coordinates
  77. 6.0: Prelude to Parametric Equations and Polar Coordinates
  78. 6.1: Parametric equations - Tangent lines and arc length
  79. 6.1E: Excercises
  80. 6.2: Calculus of Parametric Curves
  81. 6.2E: Excercises
  82. 6.3: Polar coordinates: definitions, arc length, and area for polar curves
  83. 6.3E: Excersises
  84. 6.4: Area and Arc Length in Polar Coordinates
  85. 6.4E: Excercises
  86. 6.5: Conic Sections
  87. 6.5E: Exercises
  88. 6E: Chapter Exercises
  89. 7: Vector Spaces
  90. 5.2: Vectors in Three Dimensions
  91. 5.2E: Excersies
  92. 5.3: The Dot Product
  93. 5.3E: Excersies
  94. 5.4: The Cross Product
  95. 5.4E: Excersies
  96. 5.5: Equations of Lines and Planes in Space
  97. 5.5E: Excersies
  98. 5.6: Quadratic Surfaces
  99. 5.6E: Excersies
  100. 5.7: Cylindrical and Spherical Coordinates
  101. 5.7E: Excersies
  102. 5E: Chapter Review Exercises
  103. 7.1: Vectors in the Plane
  104. 7.1E: Excersies
  105. 8: Mulitvariable Calculus
  106. 6.1: Functions of Several Variables
  107. 6.1E: Exercises
  108. 6.2: Limits and Continuity
  109. 6.2E: Excercises
  110. 6.3: Partial Derivatives
  111. 6.3E: Exercises
  112. 6.4: Chain Rule
  113. 6.4E: Exercises
  114. 6E: Review Excersies
  115. 9: Multiple Integration
  116. 9.1 Double Integrals over Rectangular Regions
  117. 9.1E: Exercises
  118. 9.2: Double Integrals over General Regions
  119. 9.2E: Exercises
  120. 9.3: Double Integrals in Polar Coordinates
  121. 9.3E: Exercises
  122. 9.4: Triple Integrals
  123. 9.4E:Exercises
  124. 9.5: Triple Integrals in Cylindrical and Spherical Coordinates
  125. 9.5E: Excersies
  126. 9.6: Calculating Centers of Mass and Moments of Inertia
  127. 9.6E: Exercises
  128. 9.7: Change of Variables in Multiple Integrals
  129. 9.7E: Exercises
  130. 9E: Chapter Review Exercises
  131. Mock Exams (Celebration of Learning)
  132. Test (Final) (Mock Exam)
  133. Test 1(Mock Exam)
  134. Test 2(Mock Exam)
  135. Back Matter
  136. Index
  137. Glossary
  138. Detailed Licensing
  139. Summary Tables
  140. Convergence Tests
  141. Integration tables
  142. Table of Derivatives
  143. Table of Limits
  144. Solutions and Visuals using Python
  145. Chapter 2
  146. Chapter 1
  147. Partial Fraction Solver(not operational)
  148. Partial fraction Solver
  149. Appendix
  150. A1: Introduction to Differential Equations
  151. 3.0: Some Applications Leading to Differential Equation
  152. 3.1: Basic Concepts
  153. 3.1E: Exercises
  154. 3.2: First order linear equations
  155. 3.2E: Exercises
  156. 3.3: Direction Fields for First Order Equations
  157. 3.3E: Exercises
  158. 3.4: Separable Differential Equations
  159. 3.4E: Exersices
  160. 3.5: Existence and Uniqueness of Solutions of Nonlinear Equations
  161. 3.5E: Excersies
  162. 3.6: First Order Equations: Transformation of Nonlinear Equations into Separable Equations
  163. 3.7: Exact Equations
  164. 3.7E: Excercises
  165. 3.8: Integrating Factors
  166. 3.8E: Excercises
  167. 3.9: Applications
  168. 3.9E: Excercises
  169. 3.E: Chapter Review Excercises