Introductory College Mathematics
with Linear Algebra and Finite Mathematics
- 1st Edition - January 1, 1973
- Imprint: Academic Press
- Authors: Harley Flanders, Justin J. Price
- Language: English
- eBook ISBN:9 7 8 - 1 - 4 8 3 2 - 6 2 9 5 - 6
Introductory College Mathematics: With Linear Algebra and Finite Mathematics is an introduction to college mathematics, with emphasis on linear algebra and finite mathematics. It… Read more
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Request a sales quoteIntroductory 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.
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 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
Tests
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
Tests
Chapter 13 Linear Transformations
1. Basic Properties
2. Examples in the Plane
3. Rotations and Reflections
4. Examples in Space
Tests
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]
Tests
Chapter 15 Finite Mathematics
1. Sequences
2. Evaluation of Sums
3. Counting
4. Permutations and Combinations
5. Binomial Theorem
6. Mathematical Induction
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
- Edition: 1
- Published: January 1, 1973
- Imprint: Academic Press
- No. of pages: 486
- Language: English
- eBook ISBN: 9781483262956
HF
Harley Flanders
Affiliations and expertise
Purdue University Lafayette, IndianaRead Introductory College Mathematics on ScienceDirect