Introduction | p. xi |
Geometry | p. 1 |
Lines and Angles | p. 2 |
Polygons | p. 8 |
Triangles | p. 11 |
Quadrilaterals (Four-Sided Polygons) | p. 16 |
Circles | p. 20 |
Perimeter and Area of Planar Two-Dimensional Shapes | p. 26 |
Volume and Surface Area of Three-Dimensional Objects | p. 32 |
Vectors | p. 38 |
Trigonometry | p. 41 |
Introduction | p. 42 |
General Trigonometric Functions | p. 43 |
Addition, Subtraction, and Multiplication of Two Angles | p. 50 |
Oblique Triangles | p. 51 |
Graphs of Cosine, Sine, Tangent, Secant, Cosecant, and Cotangent | p. 52 |
Relationship Between Trigonometric and Exponential Functions | p. 56 |
Hyperbolic Functions | p. 57 |
Sets and Functions | p. 59 |
Sets | p. 59 |
Functions | p. 62 |
Sequences, Progressions, and Series | p. 67 |
Sequences | p. 68 |
Arithmetic Progressions | p. 69 |
Geometric Progressions | p. 70 |
Series | p. 71 |
Infinite Series: Convergence and Divergence | p. 74 |
Tests for Convergence of Infinite Series | p. 77 |
The Power Series | p. 83 |
Expanding Functions into Series | p. 84 |
The Binomial Expansion | p. 89 |
Limits | p. 91 |
Introduction to Limits | p. 91 |
Limits and Continuity | p. 95 |
Introduction to the Derivative | p. 101 |
Definition | p. 102 |
Evaluating Derivatives | p. 107 |
Differentiating Multivariable Functions | p. 109 |
Differentiating Polynomials | p. 110 |
Derivatives and Graphs of Functions | p. 110 |
Adding and Subtracting Derivatives of Functions | p. 113 |
Multiple or Repeated Derivatives of a Function | p. 114 |
Derivatives of Products and Powers of Functions | p. 115 |
Derivatives of Quotients of Functions | p. 120 |
The Chain Rule for Differentiating Complicated Functions | p. 122 |
Differentiation of Implicit vs. Explicit Functions | p. 125 |
Using Derivatives to Determine the Shape of the Graph of a Function (Minimum and Maximum Points) | p. 128 |
Other Rules of Differentiation | p. 136 |
An Application of Differentiation: Curvilinear Motion | p. 137 |
Introduction to the Integral | p. 141 |
Definition of the Antiderivative or Indefinite Integral | p. 142 |
Properties of the Antiderivative or Indefinite Integral | p. 144 |
Examples of Common Indefinite Integrals | p. 147 |
Definition and Evaluation of the Definite Integral | p. 148 |
The Integral and the Area Under the Curve in Graphs of Functions | p. 151 |
Integrals and Volume | p. 155 |
Even Functions, Odd Functions, and Symmetry | p. 158 |
Properties of the Definite Integral | p. 160 |
Methods for Evaluating Complex Integrals: Integration by Parts, Substitution, and Tables | p. 161 |
Index | p. 165 |
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