MAT 1350: Precalculus Part I

by Jay Abramson

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Algebra is the study of mathematical symbols and the rules for manipulating these symbols. It is a unifying thread of almost all of mathematics. Elementary algebra is generally considered to be essential for any study of mathematics, science, or engineering, as well as such applications as medicine and economics. Elementary algebra differs from arithmetic in the use of abstractions, such as using letters to stand for numbers that are either unknown or allowed to take on many values.

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Publisher
Prince George's Community College
Subjects
Mathematics
Licence
CC BY 4.0, as LibreTexts states it
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. 1: Prerequisites
  7. 1.0: Prelude to Prerequisites
  8. 1.1: Real Numbers - Algebra Essentials
  9. 1.2: Exponents and Scientific Notation
  10. 1.3: Radicals and Rational Expressions
  11. 1.4: Polynomials
  12. 1.5: Factoring Polynomials
  13. 1.6: Rational Expressions
  14. 2: Equations and Inequalities
  15. 2.0: Prelude to Equations and Inequalities
  16. 2.1: The Rectangular Coordinate Systems and Graphs
  17. 2.2: Linear Equations in One Variable
  18. 2.3: Models and Applications
  19. 2.4: Complex Numbers
  20. 2.5: Quadratic Equations
  21. 2.6: Other Types of Equations
  22. 2.7: Linear Inequalities and Absolute Value Inequalities
  23. 2.8: Circles
  24. 3: Functions
  25. 3.0: Prelude to Functions
  26. 3.1: Functions and Function Notation
  27. 3.2: Domain and Range
  28. 3.3: Rates of Change and Behavior of Graphs
  29. 3.4: Composition of Functions
  30. 3.5: Transformation of Functions
  31. 3.6: Absolute Value Functions
  32. 3.7: Inverse Functions
  33. 3.8: Linear Functions
  34. 3.8.0: Introduction to Linear Functions
  35. 3.8.1: Linear Functions
  36. 3.8.2: Modeling with Linear Functions
  37. 3.8.3: Fitting Linear Models to Data
  38. 4: Linear Functions
  39. 4.0: Introduction to Linear Functions
  40. 4.1: Linear Functions
  41. 4.2: Modeling with Linear Functions
  42. 4.3: Fitting Linear Models to Data
  43. 5: Polynomial and Rational Functions
  44. 5.0: Prelude to Polynomial and Rational Functions
  45. 5.1: Quadratic Functions
  46. 5.2: Power Functions and Polynomial Functions
  47. 5.3: Graphs of Polynomial Functions
  48. 5.4: Dividing Polynomials
  49. 5.5: Zeros of Polynomial Functions
  50. 5.6: Rational Functions
  51. 5.7: Inverses and Radical Functions
  52. 5.8: Modeling Using Variation
  53. 5.9: Solving Quadratic Inequalities
  54. 5.10: Solving Polynomial and Rational Inequalities
  55. 6: Exponential and Logarithmic Functions
  56. 6.0: Prelude to Exponential and Logarithmic Functions
  57. 6.1: Exponential Functions
  58. 6.2: Graphs of Exponential Functions
  59. 6.3: Logarithmic Functions
  60. 6.4: Graphs of Logarithmic Functions
  61. 6.5: Logarithmic Properties
  62. 6.6: Exponential and Logarithmic Equations
  63. 6.7: Exponential and Logarithmic Models
  64. 6.8: Fitting Exponential Models to Data
  65. 7: The Unit Circle - Sine and Cosine Functions
  66. 7.0: Introduction to The Unit Circle- Sine and Cosine Functions
  67. 7.1: Angles
  68. 7.2: Right Triangle Trigonometry
  69. 7.3: Unit Circle
  70. 7.4: The Other Trigonometric Functions
  71. 8: Periodic Functions
  72. 8.0: 8.1 Introduction to Periodic Functions
  73. 8.1: Graphs of the Sine and Cosine Functions
  74. 8.2: Graphs of the Other Trigonometric Functions
  75. 8.3: Inverse Trigonometric Functions
  76. 9: Trigonometric Identities and Equations
  77. 9.0: Prelude to Trigonometric Identities and Equations
  78. 9.1: Solving Trigonometric Equations with Identities
  79. 9.2: Sum and Difference Identities
  80. 9.3: Double-Angle, Half-Angle, and Reduction Formulas
  81. 9.4: Sum-to-Product and Product-to-Sum Formulas
  82. 9.5: Solving Trigonometric Equations
  83. 10: Further Applications of Trigonometry
  84. 10.0: Prelude to Further Applications of Trigonometry
  85. 10.1: Non-right Triangles - Law of Sines
  86. 10.2: Non-right Triangles - Law of Cosines
  87. 10.3: Polar Coordinates
  88. 10.4: Polar Coordinates - Graphs
  89. 10.5: Polar Form of Complex Numbers
  90. 10.6: Parametric Equations
  91. 10.7: Parametric Equations- Graphs
  92. 10.8: Vectors
  93. 11: Systems of Equations and Inequalities
  94. 11.0: Prelude to Systems of Equations and Inequalities
  95. 11.1: Systems of Linear Equations - Two Variables
  96. 11.2: Systems of Linear Equations with Three Variables
  97. 11.3: Systems of Nonlinear Equations and Inequalities - Two Variables
  98. 11.4: Partial Fractions
  99. 11.5: Matrices and Matrix Operations
  100. 11.6: Solving Systems with Gaussian Elimination
  101. 11.7: Solving Systems with Inverses
  102. 11.8: Solving Systems with Cramer's Rule
  103. 12: Analytic Geometry
  104. 12.0: Prelude to Analytic Geometry
  105. 12.1: The Ellipse
  106. 12.2: The Hyperbola
  107. 12.3: The Parabola
  108. 12.4: Rotation of Axes
  109. 12.5: Conic Sections in Polar Coordinates
  110. 13: Sequences, Probability, and Counting Theory
  111. 13.0: Prelude to Sequences, Probability and Counting Theory
  112. 13.1: Sequences and Their Notations
  113. 13.2: Arithmetic Sequences
  114. 13.3: Geometric Sequences
  115. 13.4: Series and Their Notations
  116. 13.5: Counting Principles
  117. 13.6: Binomial Theorem
  118. 13.7: Probability
  119. Back Matter
  120. Index
  121. Glossary
  122. Glossary
  123. Detailed Licensing