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Math 370: Precalculus

This course improves upon the foundational mathematics and critical thinking skills required in the calculus sequence for STEM majors. Course content includes a rigorous treatment of the properties of polynomial, rational, exponential, logarithmic, and trigonometric functions. Additional topics include systems of linear and non-linear equations and inequalities, conic sections, sequences and series, analytic geometry, vectors, parametric equations, and polar equations.

Mathematics
Author
Carl Stitz & Jeff Zeager
Publisher
Lakeland Community College & Lorain County Community College
Source
LibreTexts
License
CC BY-NC-SA
Language
EN
Category
Basic Sciences
Read online Download PDF (open licence)
Contents· 119 sections
  1. 01: Relations and Functions
  2. 1.01: Sets of Real Numbers and the Cartesian Coordinate Plane
  3. 1.1E: Exercises
  4. 1.02: Relations
  5. 1.2E: Exercises
  6. 1.03: Introduction to Functions
  7. 1.3E: Exercises
  8. 1.04: Function Notation
  9. 1.4E: Exercises
  10. 1.05: Function Arithmetic
  11. 1.5E: Exercises
  12. 1.06: Graphs of Functions
  13. 1.6E: Exercises
  14. 1.07: Transformations
  15. 1.7E: Exercises
  16. 02: Linear and Quadratic Functions
  17. 2.01: Linear Functions
  18. 2.1E: Exercises
  19. 2.02: Absolute Value Functions
  20. 2.2E: Exercises
  21. 2.03: Quadratic Functions
  22. 2.3E: Exercises
  23. 2.04: Inequalities with Absolute Value and Quadratic Functions
  24. 2.4E: Exercises
  25. 03: Polynomial Functions
  26. 3.01: Graphs of Polynomials
  27. 3.1E: Exercises
  28. 3.02: The Factor and Remainder Theorems
  29. 3.2E: Exercises
  30. 3.03: Real Zeros of Polynomials
  31. 3.3E: Exercises
  32. 3.04: Complex Zeros and the Fundamental Theorem of Algebra
  33. 3.4E: Exercises
  34. 04: Rational Functions
  35. 4.01: Introduction to Rational Functions
  36. 4.1E: Exercises
  37. 4.02: Graphs of Rational Functions
  38. 4.2E: Exercises
  39. 4.03: Rational Inequalities and Applications
  40. 4.3E: Exercises
  41. 05: Further Topics in Functions
  42. 5.01: Function Composition
  43. 5.1E: Exercises
  44. 5.02: Inverse Functions
  45. 5.2E: Exercises
  46. 5.03: Other Algebraic Functions
  47. 5.3E: Exercises
  48. 5.4: Algebraic Simplifications Necessary for Calculus
  49. 06: Exponential and Logarithmic Functions
  50. 6.01: Introduction to Exponential and Logarithmic Functions
  51. 6.1E: Exercises
  52. 6.02: Properties of Logarithms
  53. 6.2E: Exercises
  54. 6.03: Exponential Equations and Inequalities
  55. 6.3E: Exercises
  56. 6.04: Logarithmic Equations and Inequalities
  57. 6.4E: Exercises
  58. 6.05: Applications of Exponential and Logarithmic Functions
  59. 6.5E: Exercises
  60. 07: Sequences and the Binomial Theorem
  61. 7.01: Sequences
  62. 7.1E: Exercises
  63. 7.02: Summation Notation
  64. 7.2E: Exercises
  65. 7.03: Mathematical Induction
  66. 7.3E: Exercises
  67. 7.04: The Binomial Theorem
  68. 7.4E: Exercises
  69. 08: Hooked on Conics
  70. 8.01: Introduction to Conics
  71. 8.02: Circles
  72. 8.2E: Exercises
  73. 8.03: Parabolas
  74. 8.3E: Exercises
  75. 8.04: Ellipses
  76. 8.4E: Exercises
  77. 8.05: Hyperbolas
  78. 8.5E: Exercises
  79. 09: Systems of Equations and Inequalities
  80. 9.01: Systems of Linear Equations - Gaussian Elimination
  81. 9.1E: Exercises
  82. 9.02: Systems of Linear Equations - Augmented Matrices
  83. 9.2E: Exercises
  84. 9.03: Systems of Non-Linear Equations and Inequalities
  85. 9.3E: Exercises
  86. 10: Foundations of Trigonometry
  87. 10.01: Angles and their Measure
  88. 10.1E: Exercises
  89. 10.02: The Unit Circle - Cosine and Sine
  90. 10.2E: Exercises
  91. 10.03: The Six Circular Functions and Fundamental Identities
  92. 10.3E: Exercises
  93. 10.04: Trigonometric Identities
  94. 10.4E: Exercises
  95. 10.05: Graphs of the Trigonometric Functions
  96. 10.5E: Exercises
  97. 10.06: The Inverse Trigonometric Functions
  98. 10.6E: Exercises
  99. 10.07: Trigonometric Equations and Inequalities
  100. 10.7E: Exercises
  101. 11: Applications of Trigonometry
  102. 11.01: Applications of Sinusoids
  103. 11.1E: Exercises
  104. 11.02: The Law of Sines
  105. 11.2E: Exercises
  106. 11.03: The Law of Cosines
  107. 11.3E: Exercises
  108. 11.04: Polar Coordinates
  109. 11.4E: Exercises
  110. 11.05: Graphs of Polar Equations
  111. 11.5E: Exercises
  112. 11.06: Hooked on Conics Again
  113. 11.6E: Exercises
  114. 11.07: Polar Form of Complex Numbers
  115. 11.7E: Exercises
  116. 11.08: Vectors
  117. 11.8E: Exercises
  118. 11.09: Parametric Equations
  119. 11.9E: Exercises