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Analysis

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Analysis

MathematicsK-12 Education
Author
CK-Foundation
Publisher
LibreTexts
Source
LibreTexts
License
CK-12
Language
EN
Category
Basic Sciences
Read online Download PDF (open licence)
Contents· 195 sections
  1. 01: Analyzing Functions
  2. 1.01: Relations and Functions
  3. 1.1.01: Relations and Functions
  4. 1.1.02: Intervals and Interval Notation
  5. 1.1.03: Symmetry
  6. 1.1.04: Zeroes and Intercepts
  7. 1.02: Average Rate of Change
  8. 1.2.01: Minimums and Maximums
  9. 1.2.02: Discrete and Continuous Functions
  10. 1.2.03: Increasing and Decreasing Functions
  11. 1.03: Limits
  12. 1.3.01: Limits and Asymptotes
  13. 1.3.02: Infinite and Non-Existent Limits
  14. 1.04: Function Families
  15. 1.4.01: Linear and Absolute Value Function Families
  16. 1.4.02: Square and Cube Function Families
  17. 1.4.03: Graphing Cube Root Functions
  18. 1.05: Transformations
  19. 1.5.01: Vertical and Horizontal Transformations
  20. 1.5.02: Stretching and Reflecting Transformations
  21. 1.5.03: Combining Transformations
  22. 1.5.04: Notation for Transformations
  23. 1.06: Operations on Functions
  24. 1.6.01: Composition of Functions
  25. 1.07: Models of Functions
  26. 1.7.01: Linear and Quadratic Models
  27. 1.7.02: Cubic Models
  28. 02: Polynomial and Rational Functions
  29. 2.01: Quadratic Functions
  30. 2.1.01: Methods for Solving Quadratic Functions
  31. 2.1.02: Graphs of Quadratic Functions
  32. 2.02: Graphing Polynomials
  33. 2.2.01: Graphs of Polynomials Using Transformations
  34. 2.2.02: Graphs of Polynomials Using Zeros
  35. 2.2.03: Graphing Calculator to Analyze Polynomial Functions
  36. 2.03: Analysis of Graphs of Rational Functions
  37. 2.3.01: Graphs of Basic Rational Functions
  38. 2.3.02: Graphs of Rational Functions when the Degrees are Equal
  39. 2.3.03: Graphs of Rational Functions when the Degrees are not Equal
  40. 2.3.04: Sign Test for Rational Function Graphs
  41. 2.04: Analysis of Rational Functions
  42. 2.4.01: Holes in Rational Functions
  43. 2.4.02: Vertical Asymptotes
  44. 2.4.03: Horizontal Asymptotes
  45. 2.4.3.01: Oblique Asymptotes of Rational Functions
  46. 2.4.04: Solving Rational Equations
  47. 2.05: Forms of Inequalities
  48. 2.5.01: Quadratic Inequalities
  49. 2.5.02: Polynomial and Rational Inequalities
  50. 2.06: Finding Zeros of Polynomials
  51. 2.6.01: Long Division of Polynomials
  52. 2.6.02: Synthetic Division of Polynomials
  53. 2.6.03: Real Zeros of Polynomials
  54. 2.6.04: Intermediate Value Theorem
  55. 2.6.05: Fundamental Theorem of Algebra
  56. 03: Exponential and Logarithmic Functions
  57. 3.01: Functions and Inverses
  58. 3.1.01: One-to-One Functions and Their Inverses
  59. 3.02: Basic Exponential Functions
  60. 3.2.01: Solving Exponential Equations
  61. 3.03: Properties of Logarithms
  62. 3.3.01: Product and Quotient Properties of Logarithms
  63. 3.3.02: Power Property of Logarithms
  64. 3.3.03: Inverse Properties of Logarithms
  65. 3.04: Logarithmic Functions
  66. 3.4.01: Graphs of Logarithmic Functions
  67. 3.4.02: Common and Natural Logarithms
  68. 3.4.03: Solving Logarithmic Equations
  69. 3.4.04: Change of Base
  70. 3.05: Exponential and Logarithmic Models
  71. 3.5.01: Exponential Models
  72. 3.5.02: Logarithmic Models
  73. 3.5.03: Simple and Compound Interest
  74. 3.5.04: The Number e
  75. 3.5.05: Logistic Functions
  76. 04: Polar Equations and Complex Numbers
  77. 4.01: Logarithmic Functions
  78. 4.1.01: Graphs of Logarithmic Functions
  79. 4.1.02: Common and Natural Logarithms
  80. 4.1.03: Solving Logarithmic Equations
  81. 4.1.04: Change of Base
  82. 4.02: Exponential and Logarithmic Models
  83. 4.2.01: Exponential Models
  84. 4.2.02: Logarithmic Models
  85. 4.2.03: Simple and Compound Interest
  86. 4.2.04: The Number e
  87. 4.2.05: Logistic Functions
  88. 4.03: Exponential and Logarithmic Functions
  89. 4.3.01: Basic Exponential Functions
  90. 4.3.1.01: Solving Exponential Equations
  91. 4.3.02: Properties of Logarithms
  92. 4.3.2.01: Product and Quotient Properties of Logarithms
  93. 4.3.2.02: Power Property of Logarithms
  94. 4.3.2.03: Inverse Properties of Logarithms
  95. 4.3.03: Functions and Inverses
  96. 4.3.3.01: One-to-One Functions and Their Inverses
  97. 4.04: Polar Equations
  98. 4.4.01: Polar Coordinates
  99. 4.4.02: Polar and Cartesian Transformation
  100. 4.4.03: Systems of Polar Equations
  101. 4.4.04: Polar Equations of Conics
  102. 4.05: Imaginary Numbers and Complex Numbers
  103. 4.5.01: Imaginary Numbers
  104. 4.5.02: Complex Numbers
  105. 4.5.03: Quadratic Formula and Complex Sums
  106. 4.5.04: Products and Quotients of Complex Numbers
  107. 4.5.05: Polar Form of Complex Numbers
  108. 4.5.06: Product and Quotient Theorems
  109. 4.5.07: Powers and Roots of Complex Numbers
  110. 05: Vector Analysis
  111. 5.01: Two- and Three- Dimension Positions
  112. 5.1.01: Positions and Midpoints in Two Dimensions
  113. 5.1.02: Three-Dimensional Positions
  114. 5.02: Vector Calculations
  115. 5.2.01: Dot Products
  116. 5.2.02: Scalar Projections
  117. 5.2.03: Cross Products
  118. 5.2.04: Vector Projection
  119. 5.03: Planes in Space
  120. 5.3.01: Distance Between a Point and a Plane
  121. 5.3.02: Vector Direction
  122. 5.04: Vector Equations and Applications
  123. 5.4.01: Vector Equation of a Line
  124. 5.4.02: Vector Analysis Applications
  125. 06: Conic Sections
  126. 6.01: Ellipses
  127. 6.1.01: Ellipses Centered at the Origin
  128. 6.1.02: Equation of an Ellipse
  129. 6.1.03: Ellipses Not Centered at the Origin
  130. 6.1.04: Focal Property of Ellipses
  131. 6.02: Parabolas
  132. 6.2.01: Parabolas with Vertex at the Origin
  133. 6.2.02: Parabolas and the Distance Formula
  134. 6.2.03: Parabolas with any Vertex
  135. 6.2.04: Parabolas and Analytic Geometry
  136. 6.2.05: Applications of Parabolas
  137. 6.03: Hyperbolas
  138. 6.3.01: Graphs of Hyperbolas Centered at the Origin
  139. 6.3.02: Equations of Hyperbolas Centered at the Origins
  140. 6.3.03: Hyperbolas with any Center
  141. 6.3.04: Hyperbola Equations and the Focal Property
  142. 6.3.05: Hyperbolas and Asymptotes
  143. 6.04: Equations of Circles
  144. 6.4.01: Circles Centered at the Origin
  145. 6.4.02: Circles Not Centered at the Origin
  146. 6.05: Conic Sections and Degenerate Conics
  147. 6.5.01: Conic Sections and Dandelin Spheres
  148. 6.5.02: Classifying Conic Sections
  149. 6.5.03: Degenerate Conics
  150. 6.5.04: Solving Systems of Lines Quadratics and Conics
  151. 07: Sequences Series and Mathematical Induction
  152. 7.01: Formulas and Notation for Sequences and Series
  153. 7.1.01: Recursive Formulas
  154. 7.1.02: Explicit Formulas
  155. 7.1.03: Sum Notation and Properties of Sigma
  156. 7.02: Series Sums
  157. 7.2.01: Partial Sums
  158. 7.2.02: Series Sums and Gauss' Formula
  159. 7.2.03: Problem Solving with Series Sums
  160. 7.03: Mathematical Induction
  161. 7.3.01: Inductive Reasoning from Patterns
  162. 7.3.1.01: Inductive Proofs
  163. 7.3.02: Induction and Factors
  164. 7.3.03: Induction and Inequalities
  165. 7.04: Sums of Geometric Series
  166. 7.4.01: Sums of Finite Geometric Series
  167. 7.4.02: Sums of Infinite Geometric Series
  168. 7.05: Factorials and Combinations
  169. 7.5.01: Binomial Theorem and Expansions
  170. 7.06: Arithmetic Sequences
  171. 7.6.01: Finding the nth Term Given the Common Difference and a Term
  172. 7.6.02: Finding the nth Term Given Two Terms for an Arithmetic Sequence
  173. 7.07: Geometric Sequences
  174. 7.7.01: Finding the nth Term Given the Common Ratio and the First Term
  175. 7.7.02: Finding the nth Term Given Two Terms for a Geometric Sequence
  176. 7.08: Sums of Arithmetic Series
  177. 7.8.01: Sums of Finite Arithmetic Series
  178. 08: Introduction to Calculus
  179. 8.01: Limits in Calculus
  180. 8.1.01: Definition of a Limit
  181. 8.1.02: One-Sided Limits
  182. 8.1.03: Infinite Limits
  183. 8.1.04: Polynomial Function Limits
  184. 8.1.05: Tables to Find Limits
  185. 8.02: Lines Tangent to a Curve
  186. 8.2.01: Tangents to a Curve
  187. 8.2.02: Instantaneous Rates of Change
  188. 8.03: Derivatives
  189. 8.3.01: Constant Derivatives and the Power Rule
  190. 8.3.02: Derivatives of Sums and Differences
  191. 8.3.03: Quotient Rule and Higher Derivatives
  192. 8.04: Integrals
  193. 8.4.01: Area Under the Curve
  194. 8.05: Anti-Derivative
  195. 8.5.01: Fundamental Theorem of Calculus