Elementary Functions and Analytic Geometry

Preface

Chapter 1 Functions and Graphs


1. Introduction


2. Real Numbers


3. Coordinates on the Line and Plane


4. Functions


5. Construction of Functions

Tests

Chapter 2 Linear and Quadratic Functions


1. Linear Functions


2. Quadratic Functions


3. Some Applications


4. Tips on Graphing

Tests

Chapter 3 Polynomial Functions


1. Algebra of Polynomials


2. Graphs of Polynomials


3. Zeros and Roots


4. Zeros of Higher Degree Polynomials


5. Graphs of Factored Polynomials

Tests

Chapter 4 Rational Functions


1. Basic Properties


2. Algebraic Operations


3. Graphs of Rational Functions


4. Division with Remainder


5. Partial Fractions

Tests

Chapter 5 Exponential and Logarithm Functions


1. Review of Exponents


2. Exponential Functions


3. Logarithm Functions


4. Accuracy and Tables [Optional]


5. Log Tables [Optional]


6. Computations with Logarithms [Optional]


7. Power Functions

Tests

Chapter 6 Trigonometric Functions


1. Introduction


2. Distances and Angles


3. Sine and Cosine


4. Other Trigonometric Functions


5. Graphs of Sine and Cosine


6. Graphs of the Other Functions

Tests

Chapter 7 Identities and Inverse Functions


1. Identities


2. Further Identities


3. Inverse Functions


4. Trigonometric Equations

Tests

Chapter 8 Trigonometry


1. Right Triangles


2. Laws of Cosines and Sines


3. Oblique Triangles [Optional]

Tests

Chapter 9 Vectors


1. Vector Algebra


2. Lines


3. Length and Inner Product


4. Normal Form

Tests

Chapter 10 Analytic Geometry


1. Translation of Axes


2. The Circle


3. Tangents and Loci


4. Polar Coordinates


5. Conics: The Parabola


6. The Ellipse


7. The Hyperbola


8. Rotation of Axes [Optional]


9. Additional Exercises on Conics [Optional]

Tests

Chapter 11 Solid Analytic Geometry


1. Coordinates and Vectors


2. Lines and Planes


5. Linear Systems and Intersections


4. Polynomials in Several Variables


5. Quadric Surfaces


6. Cylinders and Cones

Tests

Chapter 12 Complex Numbers


1. Complex Arithmetic


2. The Complex Plane


3. Zeros of Polynomials


4. De Moivre's Theorem and Roots of Unity

Tests

Chapter 13 Induction and the Binomial Theorem


1. Mathematical Induction


2. Binomial Coefficients


3. Binomial Theorem

Tests

Answers to Odd-Numbered Exercises

Tables


1. 4-Place Logarithm


2. 4-Place Antilogarithm


3. Powers and Roots


4. Trigonometric (Degrees)


5. Trigonometric (Radians)


6. Log-Trig (Degrees)


7. Trigonometric (π Radians)

Index