Introductory College Mathematics - 1st Edition - ISBN: 9780122596605, 9781483262956

Introductory College Mathematics

1st Edition

with Linear Algebra and Finite Mathematics

Authors: Harley Flanders Justin J. Price
eBook ISBN: 9781483262956
Imprint: Academic Press
Published Date: 1st January 1973
Page Count: 486
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Introductory College Mathematics: With Linear Algebra and Finite Mathematics is an introduction to college mathematics, with emphasis on linear algebra and finite mathematics. It aims to provide a working knowledge of basic functions (polynomial, rational, exponential, logarithmic, and trigonometric); graphing techniques and the numerical aspects and applications of functions; two- and three-dimensional vector methods; the fundamental ideas of linear algebra; and complex numbers, elementary combinatorics, the binomial theorem, and mathematical induction.

Comprised of 15 chapters, this book begins with a discussion on functions and graphs, paying particular attention to quantities measured in the real number system. The next chapter deals with linear and quadratic functions as well as some of their applications. Tips on graphing are offered. Subsequent chapters focus on polynomial functions, along with graphs of factored polynomials; rational functions; exponential and logarithm functions; and trigonometric functions. Identities and inverse functions, vectors and matrices, and trigonometry are also explored, together with complex numbers, linear transformations, and the geometry of space. The book concludes by considering finite mathematics, with particular reference to mathematical induction and the binomial theorem.

This monograph will be a useful resource for undergraduate students of mathematics and algebra.

Table of Contents


Chapter 1 Functions and Graphs

1. Introduction

2. Real Numbers

3. Coordinates on the Line and Plane

4. Functions

5. Construction of Functions


Chapter 2 Linear and Quadratic Functions

1. Linear Functions

2. Quadratic Functions

3. Some Applications

4. Tips on Graphing


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


Chapter 4 Rational Functions

1. Basic Properties

2. Algebraic Operations

3. Graphs of Rational Functions

4. Division with Remainder

5. Partial Fractions


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


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


Chapter 7 Identities and Inverse Functions

1. Identities

2. Further Identities

3. Inverse Functions

4. Trigonometric Equations


Chapter 8 Trigonometry

1. Right Triangles

2. Laws of Cosines and Sines

3. Oblique Triangles [Optional]


Chapter 9 Vectors

1. Vector Algebra

2. Lines

3. Length and Inner Product

4. Normal Form


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]


Chapter 11 Vectors and Matrices

1. Column Vectors and Inner Products

2. Matrices

3. 3x3 Matrices

4. Determinants

5. Linear Systems

6. Inverses and Cramer's Rule


Chapter 12 Geometry of Space

1. Lines and Planes

2. The Cross Product

3. Linear Independence

4. Some Applications

5. Polynomials in Several Variables

6. Quadric Surfaces

7. Cylinders and Cones


Chapter 13 Linear Transformations

1. Basic Properties

2. Examples in the Plane

3. Rotations and Reflections

4. Examples in Space


Chapter 14 Complex Numbers

1. Complex Arithmetic

2. The Complex Plane

3. Zeros of Polynomials

4. De Moivre's Theorem and Roots of Unity

5. Complex Matrices [Optional]


Chapter 15 Finite Mathematics

1. Sequences

2. Evaluation of Sums

3. Counting

4. Permutations and Combinations

5. Binomial Theorem

6. Mathematical Induction


Answers to Odd-Numbered Exercises


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)



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© Academic Press 1973
Academic Press
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About the Author

Harley Flanders

Affiliations and Expertise

Purdue University Lafayette, Indiana

Justin J. Price

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