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Kirk Trigsted teaches mathematics at the University of Idaho and has been Director of the Polya Mathematics Center since its inception in 2001. Kirk has taught with MyMathLab for many years, and has contributed to the videos for several Pearson books. Kirk is also actively involved with the National Center for Academic Transformation (NCAT).
1. The Rectangular Coordinate System, Lines, and Circles
1.1 The Rectangular Coordinate System
1.2 Circles
1.3 Lines
1.4 Parallel and Perpendicular Lines
2. Functions
2.1 Relations and Functions
2.2 Properties of a Function's Graph
2.3 Graphs of Basic Functions; Piecewise Functions
2.4 Transformations of Functions
2.5 The Algebra of Functions; Composite Functions
2.6 One-to-One Functions; Inverse Functions
3. Polynomial and Rational Functions
3.1 Quadratic Functions
3.2 Applications and Modeling of Quadratic Functions
3.3 The Graphs of Polynomial Functions
3.4 Synthetic Division; The Remainder and Factor Theorems
3.5 The Zeros of Polynomial Functions; The Fundamental Theorem of Algebra
3.6 Rational Functions and Their Graphs
3.7 Variation
4. Exponential and Logarithmic Functions and Equations
4.1 Exponential Functions
4.2 The Natural Exponential Function
4.3 Logarithmic Functions
4.4 Properties of Logarithms
4.5 Exponential and Logarithmic Equations
4.6 Applications of Exponential and Logarithmic Functions
5. An Introduction to Trigonometric Functions
5.1 Angles: Degree and Radian Measure
5.2 Applications of Radian Measure
5.3 The Unit Circle
5.4 Trigonometric Functions of General Angles
5.5 Right Triangle Trigonometry
6. The Graphs of Trigonometric Functions
6.1 The Graphs of Sine and Cosine
6.2 More on Graphs of Sine and Cosine; Phase Shift
6.3 The Graphs of the Tangent, Cosecant, Secant, and Cotangent Functions
6.4 Inverse Trigonometric Functions I
6.5 Inverse Trigonometric Functions II
7. Trigonometric Identities, Formulas, and Equations
7.1 Trigonometric Identities
7.2 The Sum and Difference Formulas
7.3 The Double-Angle and Half-Angle Formulas
7.4 The Product-to-Sum and Sum-to-Product Formulas
7.5 Trigonometric Equations
8. Applications of Trigonometry
8.1 The Law of Sines
8.2 The Law of Cosines
8.3 Area of Triangles
9. Polar Equations, Complex Numbers, and Vectors
9.1 Polar Coordinates and Polar Equations
9.2 The Graphs of Polar Equations
9.3 Complex Numbers; DeMoivre's Theorem
9.4 Vectors
9.5 The Dot Product
10. Conic Sections
10.1 The Parabola
10.2 The Ellipse
10.3 The Hyperbola
11. Systems of Equations and Inequalities
11.1 Systems of Linear Equations in Two Variables
11.2 Systems of Linear Equations in Three Variables
11.3 Inconsistent and Dependent Linear Systems in Three Variables
11.4 Partial Fraction Decomposition
11.5 Systems of Nonlinear Equations
11.6 Systems of Inequalities
12. Matrices
12.1 Matrix Operations
12.2 Inverses of Matrices and Matrix Equations
12.3 Determinants and Cramer's Rule
13. Sequences and Series; Counting and Probability
13.1 Introduction to Sequences and Series
13.2 Arithmetic Sequences and Series
13.3 Geometric Sequences and Series
13.4 The Binomial Theorem
13.5 Mathematical Inductions
13.6 The Theory of Counting
13.7 An Introduction to Probability
Appendix A
A.1 Real Numbers
A.2 The Order of Operations and Algebraic Expressions
A.3 The Laws of Exponents; Radicals
A.4 Polynomials
A.5 Factoring Polynomials
A.6 Rational Expressions
Appendix B
B.1 Linear Equations
B.2 Applications of Linear Equations
B.3 Complex Numbers
B.4 Quadratic Equations
B.5 Applications of Quadratic Equations
B.6 Other Types of Equations
B.7 Linear Inequalities
B.8 Absolute Value Equations and Inequalities
B.9 Polynomial and Rational Inequalities
Appendix C
C.1 Degree, Minute, Second Form and Degree Decimal Form
C.2 Triangles
Appendix D. Conic Section Proofs