Calculus 4th Edition Smith Test Bank

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Now in its 4th edition, Smith/Minton, Calculus offers students and instructors a mathematically sound text, robust exercise sets and elegant presentation of calculus concepts. When packaged with ALEKS Prep for Calculus, the most effective remediation tool on the market, Smith/Minton offers a complete package to ensure students success in calculus.The new edition has been updated with a reorganization of the exercise sets, making the range of exercises more transparent. Additionally, over 1,000 new classic calculus problems were added.

 

Table of Content:

  1. CHAPTER 0 Preliminaries
  2. 0.1 The Real Numbers and the Cartesian Plane
  3. The Real Number System and Inequalities
  4. The Cartesian Plane
  5. 0.2 Lines and Functions
  6. Equations of Lines
  7. Functions
  8. 0.3 Graphing Calculators and Computer Algebra Systems
  9. 0.4 Trigonometric Functions
  10. 0.5 Transformations of Functions
  11. CHAPTER 1 Limits and Continuity
  12. 1.1 A Brief Preview of Calculus: Tangent Lines and the Length of a Curve
  13. 1.2 The Concept of Limit
  14. 1.3 Computation of Limits
  15. 1.4 Continuity and Its Consequences
  16. The Method of Bisections
  17. 1.5 Limits Involving Infinity; Asymptotes
  18. Limits at Infinity
  19. 1.6 Formal Definition of the Limit
  20. Exploring the Definition of Limit Graphically
  21. Limits Involving Infinity
  22. 1.7 Limits and Loss-of-Significance Errors
  23. Computer Representation of Real Numbers
  24. CHAPTER 2 Differentiation
  25. 2.1 Tangent Lines and Velocity
  26. The General Case
  27. Velocity
  28. 2.2 The Derivative
  29. Alternative Derivative Notations
  30. Numerical Differentiation
  31. 2.3 Computation of Derivatives: The Power Rule
  32. The Power Rule
  33. General Derivative Rules
  34. Higher Order Derivatives
  35. Acceleration
  36. 2.4 The Product and Quotient Rules
  37. Product Rule
  38. Quotient Rule
  39. Applications
  40. 2.5 The Chain Rule
  41. 2.6 Derivatives of Trigonometric Functions
  42. Applications
  43. 2.7 Implicit Differentiation
  44. 2.8 The Mean Value Theorem
  45. CHAPTER 3 Applications of Differentiation
  46. 3.1 Linear Approximations and Newton’s Method
  47. Linear Approximations
  48. Newton’s Method
  49. 3.2 Maximum and Minimum Values
  50. 3.3 Increasing and Decreasing Functions
  51. What You See May Not Be What You Get
  52. 3.4 Concavity and the Second Derivative Test
  53. 3.5 Overview of Curve Sketching
  54. 3.6 Optimization
  55. 3.7 Related Rates
  56. 3.8 Rates of Change in Economics and the Sciences
  57. CHAPTER 4 Integration
  58. 4.1 Antiderivatives
  59. 4.2 Sums and Sigma Notation
  60. Principle of Mathematical Induction
  61. 4.3 Area
  62. 4.4 The Definite Integral
  63. Average Value of a Function
  64. 4.5 The Fundamental Theorem of Calculus
  65. 4.6 Integration by Substitution
  66. Substitution in Definite Integrals
  67. 4.7 Numerical Integration
  68. Simpson’s Rule
  69. Error Bounds for Numerical Integration
  70. CHAPTER 5 Applications of the Definite Integral
  71. 5.1 Area Between Curves
  72. 5.2 Volume: Slicing, Disks and Washers
  73. Volumes by Slicing
  74. The Method of Disks
  75. The Method of Washers
  76. 5.3 Volumes by Cylindrical Shells
  77. 5.4 Arc Length and Surface Area
  78. Arc Length
  79. Surface Area
  80. 5.5 Projectile Motion
  81. 5.6 Applications of Integration to Physics and Engineering
  82. CHAPTER 6 Exponentials, Logarithms and Other Transcendental Functions
  83. 6.1 The Natural Logarithm
  84. Logarithmic Differentiation
  85. 6.2 Inverse Functions
  86. 6.3 The Exponential Function
  87. Derivative of the Exponential Function
  88. 6.4 The Inverse Trigonometric Functions
  89. 6.5 The Calculus of the Inverse Trigonometric Functions
  90. Integrals Involving the Inverse Trigonometric Functions
  91. 6.6 The Hyperbolic Functions
  92. The Inverse Hyperbolic Functions
  93. Derivation of the Catenary
  94. CHAPTER 7 Integration Techniques
  95. 7.1 Review of Formulas and Techniques
  96. 7.2 Integration by Parts
  97. 7.3 Trigonometric Techniques of Integration
  98. Integrals Involving Powers of Trigonometric Functions
  99. Trigonometric Substitution
  100. 7.4 Integration of Rational Functions Using Partial Fractions
  101. Brief Summary of Integration Techniques
  102. 7.5 Integration Tables and Computer Algebra Systems
  103. Using Tables of Integrals
  104. Integration Using a Computer Algebra System
  105. 7.6 Indeterminate Forms and L‘Hôpital’s Rule
  106. Other Indeterminate Forms
  107. 7.7 Improper Integrals
  108. Improper Integrals with a Discontinuous Integrand
  109. Improper Integrals with an Infinite Limit of Integration
  110. A Comparison Test
  111. 7.8 Probability
  112. CHAPTER 8 First-Order Differential Equations
  113. 8.1 Modeling with Differential Equations
  114. Growth and Decay Problems
  115. Compound Interest
  116. 8.2 Separable Differential Equations
  117. Logistic Growth
  118. 8.3 Direction Fields and Euler’s Method
  119. 8.4 Systems of First-Order Differential Equations
  120. Predator-Prey Systems
  121. CHAPTER 9 Infinite Series
  122. 9.1 Sequences of Real Numbers
  123. 9.2 Infinite Series
  124. 9.3 The Integral Test and Comparison Tests
  125. Comparison Tests
  126. 9.4 Alternating Series
  127. Estimating the Sum of an Alternating Series
  128. 9.5 Absolute Convergence and the Ratio Test
  129. The Ratio Test
  130. The Root Test
  131. Summary of Convergence Tests
  132. 9.6 Power Series
  133. 9.7 Taylor Series
  134. Representation of Functions as Power Series
  135. Proof of Taylor’s Theorem
  136. 9.8 Applications of Taylor Series
  137. The Binomial Series
  138. 9.9 Fourier Series
  139. Functions of Period Other Than 2π
  140. Fourier Series and Music Synthesizers
  141. CHAPTER 10 Parametric Equations and Polar Coordinates
  142. 10.1 Plane Curves and Parametric Equations
  143. 10.2 Calculus and Parametric Equations
  144. 10.3 Arc Length and Surface Area in Parametric Equations
  145. 10.4 Polar Coordinates
  146. 10.5 Calculus and Polar Coordinates
  147. 10.6 Conic Sections
  148. Parabolas
  149. Ellipses
  150. Hyperbolas
  151. 10.7 Conic Sections in Polar Coordinates
  152. CHAPTER 11 Vectors and the Geometry of Space
  153. 11.1 Vectors in the Plane
  154. 11.2 Vectors in Space
  155. Vectors in R3
  156. 11.3 The Dot Product
  157. Components and Projections
  158. 11.4 The Cross Product
  159. 11.5 Lines and Planes in Space
  160. Planes in R3
  161. 11.6 Surfaces in Space
  162. Cylindrical Surfaces
  163. Quadric Surfaces
  164. An Application
  165. CHAPTER 12 Vector-Valued Functions
  166. 12.1 Vector-Valued Functions
  167. Arc Length in R3
  168. 12.2 The Calculus of Vector-Valued Functions
  169. 12.3 Motion in Space
  170. Equations of Motion
  171. 12.4 Curvature
  172. 12.5 Tangent and Normal Vectors
  173. Tangential and Normal Components of Acceleration
  174. Kepler’s Laws
  175. 12.6 Parametric Surfaces
  176. CHAPTER 13 Functions of Several Variables and Partial Differentiation
  177. 13.1 Functions of Several Variables
  178. 13.2 Limits and Continuity
  179. 13.3 Partial Derivatives
  180. 13.4 Tangent Planes and Linear Approximations
  181. Increments and Differentials
  182. 13.5 The Chain Rule
  183. Implicit Differentiation
  184. 13.6 The Gradient and Directional Derivatives
  185. 13.7 Extrema of Functions of Several Variables
  186. Proof of the Second Derivatives Test
  187. 13.8 Constrained Optimization and Lagrange Multipliers
  188. CHAPTER 14 Multiple Integrals
  189. 14.1 Double Integrals
  190. Double Integrals over a Rectangle
  191. Double Integrals over General Regions
  192. 14.2 Area, Volume and Center of Mass
  193. Moments and Center of Mass
  194. 14.3 Double Integrals in Polar Coordinates
  195. 14.4 Surface Area
  196. 14.5 Triple Integrals
  197. Mass and Center of Mass
  198. 14.6 Cylindrical Coordinates
  199. 14.7 Spherical Coordinates
  200. Triple Integrals in Spherical Coordinates
  201. 14.8 Change of Variables in Multiple Integrals
  202. CHAPTER 15 Vector Calculus
  203. 15.1 Vector Fields
  204. 15.2 Line Integrals
  205. 15.3 Independence of Path and Conservative Vector Fields
  206. 15.4 Green’s Theorem
  207. 15.5 Curl and Divergence
  208. 15.6 Surface Integrals
  209. Parametric Representation of Surfaces
  210. 15.7 The Divergence Theorem
  211. 15.8 Stokes’ Theorem
  212. 15.9 Applications of Vector Calculus
  213. CHAPTER 16 Second-Order Differential Equations
  214. 16.1 Second-Order Equations with Constant Coefficients
  215. 16.2 Nonhomogeneous Equations: Undetermined Coefficients
  216. 16.3 Applications of Second-Order Equations
  217. 16.4 Power Series Solutions of Differential Equations
  218. Appendix A: Proofs of Selected Theorems
  219. Appendix B: Answers to Odd-Numbered Exercises
  220. Credits
  221. Subject Index

 

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