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MATH 2200: Calculus for Scientists II

Nguồn ngoài

MATH 2200: Calculus for Scientists II

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.

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