Kirk Trigsted teaches mathematics at the University of Idaho and has been Director of the Polya Mathematics Center since its inception in 2001. Kirk is the author of a successful precalculus and developmental eText series. Kirk has also been actively involved with the National Center for Academic Transformation (NCAT) for several years.

Kirk has been married for 20 years and has four children. He is an avid fly fisherman and golfer.

BRIEF TABLE OF CONTENTS:

Review Chapter

1. Equations, Inequalities, and Applications

2. The Rectangular Coordinate System, Lines, and Circles

3.  Functions

4.  Polynomial and Rational Functions

5. Exponential and Logarithmic Functions and Equations

6. An Introduction to Trigonometric Functions

7. The Graphs of Trigonometric Functions

8. Trigonometric Identities, Formulas, and Equations

9. Applications of Trigonometry

10. Polar Equations, Complex Numbers, and Vectors

11. Conic Sections and Parametric Equations

12. Systems of Equations and Inequalities

13.  Matrices

14.  Sequences and Series; Counting and Probability

Appendix A: Degree, Minute, Second Form and Degree Decimal Form
Appendix B: Conic Section Proofs

COMPREHENSIVE TABLE OF CONTENTS:

Review Chapter

R.1 Real Numbers

R.2 The Order of Operations and Algebraic Expressions

R.3 The Laws of Exponents; Radicals

R.4 Polynomials

R.5 Operations with Radicals (New Section)

R.6 Factoring Polynomials

R.7 Rational Expressions

1. Equations, Inequalities, and Applications

1.1 Linear and Rational Equations  

1.2 Applications of Linear Equations and Rational Equation

1.3 Complex Numbers

1.4 Quadratic Equations

1.5 Applications of Quadratic Equations

1.6 Other Types of Equations

1.7 Linear Inequalities in One Variable

1.8 Absolute Value Equations and Inequalities

1.9 Polynomial and Rational Inequalities

2.  The Rectangular Coordinate System, Lines, and Circles

2.1 The Rectangular Coordinate System

2.2 Circles

2.3 Lines

2.4 Parallel and Perpendicular Lines

3.  Functions

3.1 Relations and Functions

3.2 Properties of a Function's Graph

3.3 Graphs of Basic Functions; Piecewise Functions

3.4 Transformations of Functions

3.5 The Algebra of Functions; Composite Functions

3.6 One-to-One Functions; Inverse Functions

4.  Polynomial and Rational Functions

4.1 Quadratic Functions

4.2 Applications and Modeling of Quadratic Functions

4.3 The Graphs of Polynomial Functions

4.4 Synthetic Division; The Remainder and Factor Theorems

4.5 The Zeros of Polynomial Functions; The Fundamental Theorem of Algebra  

4.6 Rational Functions and Their Graphs

4.7 Variation

5. Exponential and Logarithmic Functions and Equations

5.1  Exponential Functions  

5.2  Logarithmic Functions

5.3  Properties of Logarithms

5.4  Exponential and Logarithmic Equations

5.5  Applications of Exponential and Logarithmic Functions

6.1  An Introduction to Angles: Degree and Radian Measure
6.2  Applications of Radian Measure

6.3  Triangles
6.4  Right Triangle Trigonometry
6.5  Trigonometric Functions of General Angles

6.6  The Unit Circle

7.1  The Graphs of Sine and Cosine
7.2  More on Graphs of Sine and Cosine; Phase Shift
7.3  The Graphs of the Tangent, Cotangent , Cosecant, and Secant Functions
7.4  Inverse Trigonometric Functions I
7.5   Inverse Trigonometric Functions II

8. Trigonometric Identities, Formulas, and Equations
8.1  Trigonometric Identities
8.2  The Sum and Difference Formulas
8.3  The Double-Angle and Half-Angle Formulas
8.4  The Product-to-Sum and Sum-to-Product Formulas
8.5  Trigonometric Equations

9. Applications of Trigonometry
9.1  Right Triangle Applications

9.2 The Law of Sines

9.3 The Law of Cosines
9.4 Area of Triangles

10. Polar Equations, Complex Numbers, and Vectors

10.1  Polar Coordinates and Polar Equations
10.2  Graphing Polar Equations
10.3  Complex Numbers in Polar Form; DeMoivre’s Theorem
10.4  Vectors

10.5  The Dot Product

11. Conic Sections and Parametric Equations

11.1 Introduction to Conic Sections

11.2 The Parabola

11.3 The Ellipse
11.4 The Hyperbola

11.5 Conic Sections in Polar Form
11.6 Parametric Equations

12.1 Solving Systems of Linear Equations in Two Variables

12.2 Solving Systems of Linear Equations in Three Variables Using the Elimination Method

12.3 Solving Systems of Linear Equations in Three Variables Using Gaussian Elimination and Gauss-Jordan Elimination

12.4 Partial Fraction Decomposition

12.5 Systems of Nonlinear Equations

12.6 Systems of Inequalities

13.  Matrices

13.1 Matrix Operations

13.2 Inverses of Matrices and Matrix Equations

13.3 Determinants and Cramer's Rule

14.  Sequences and Series; Counting and Probability

14.1 Introduction to Sequences and Series

14.2 Arithmetic Sequences and Series

14.3 Geometric Sequences and Series

14.4 The Binomial Theorem

14.5 Mathematical Induction

14.6 The Theory of Counting

14.7 An Introduction to Probability

Appendix A: Degree, Minute, Second Form and Degree Decimal Form
Appendix B: Conic Section Proofs

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