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Algebra 2 Details
Thinkwell's Algebra 2 with Edward Burger lays the foundation for success because, unlike a traditional textbook, students actually like using it. Thinkwell works with the learning styles of students who have found that traditional textbooks are not effective. Watch one Thinkwell video lecture and you'll understand why Thinkwell works better.
Comprehensive Video Tutorials
We've built Algebra 2 around hundreds of multimedia tutorials that provide dozens of hours of instructional material. Thinkwell offers a more engaging, more effective way for you to learn.
Instead of reading dense chunks of text from a printed book, you can watch video lectures filled with illustrations, examples, and even humor. Students report learning more easily with Thinkwell than with traditional textbooks.
Interactive Exercises with Feedback
There are hundreds of exercise items with fully worked-out solutions and explanations. Each video topic has corresponding exercises to test your understanding.
Test your understanding with hundreds of exercises that are automatically graded. Your results are available immediately, including fully worked-out solutions and explanations for each exercise. You can work on the exercises at the computer or print them out to work on later. Access your cumulative results anytime.
Review Notes and More
While the video lectures are the heart of Thinkwell products, we also offer concise, illustrated review notes, a glossary, transcripts of the video lectures, and links to relevant websites. All of these materials may be viewed online, and the notes and transcripts may be printed and kept for reference.
Table of Contents
(Expand All - Close All)1. Foundations for Functions
- 1.1 Properties and Operations
- 1.1.1 Sets of Numbers
- 1.1.2 Properties of Real Numbers
- 1.1.3 Square Roots
- 1.1.4 Simplifying Algebraic Expressions
- 1.1.5 Properties of Exponents and Scientific Notation
- 1.2 Introduction to Functions
- 1.2.1 Relations and Functions
- 1.2.2 Function Notation
- 1.2.3 Exploring Transformations
- 1.2.4 Introduction to Parent Functions
2. Linear Functions
- 2.1 Linear Equations and Inequalities
- 2.1.1 Solving Linear Equations and Inequalities
- 2.1.2 Proportional Reasoning
- 2.1.3 Graphing Linear Functions
- 2.1.4 Writing Linear Functions
- 2.1.5 Linear Inequalities in Two Variables
- 2.2 Applying Linear Functions
- 2.2.1 Transforming Linear Functions
- 2.2.2 Curve Fitting With Linear Models
- 2.2.3 Solving Absolute-Value Equations and Inequalities
- 2.2.4 Absolute-Value Functions
3. Linear Systems
- 3.1 Linear Systems in Two Dimensions
- 3.1.1 Using Graphs and Tables to Solve Linear Systems
- 3.1.2 Using Algebraic Methods to Solve Linear Systems
- 3.1.3 Solving Systems of Linear Inequalities
- 3.1.4 Linear Programming
- 3.2 Linear Systems in Three Dimensions
- 3.2.1 Linear Equations in Three Dimensions
- 3.2.2 Solving Linear Systems in Three Variables
4. Matrices
- 4.1 Matrix Operations
- 4.1.1 Matrices and Data
- 4.1.2 Multiplying Matrices
- 4.1.3 Using Matrices to Transform Geometric Figures
- 4.2 Using Matrices to Solve Systems
- 4.2.1 Determinants and Cramer's Rule
- 4.2.2 Matrix Inverses and Solving Systems
- 4.2.3 Row Operations and Augmented Matrices
5. Quadratic Functions
- 5.1 Quadratic Functions and Complex Numbers
- 5.1.1 Using Transformations to Graph Quadratic Functions
- 5.1.2 Properties of Quadratic Functions in Standard Form
- 5.1.3 Solving Quadratic Equations by Graphing and Factoring
- 5.1.4 Completing the Square
- 5.1.5 Complex Numbers and Roots
- 5.1.6 The Quadratic Formula
- 5.2 Applying Quadratic Functions
- 5.2.1 Solving Quadratic Inequalities
- 5.2.2 Curve Fitting with Quadratic Models
- 5.2.3 Operations with Complex Numbers
6. Polynomial Functions
- 6.1 Operations with Polynomials
- 6.1.1 Polynomials
- 6.1.2 Adding and Subtracting Polynomials
- 6.1.3 Multiplying Polynomials
- 6.1.4 Factoring Polynomials
- 6.1.5 Dividing Polynomials
- 6.1.6 Synthetic Division and the Remainder and Factor Theorems
- 6.2 Roots and Graphs of Polynomial Functions
- 6.2.1 Finding Real Roots of Polynomial Equations
- 6.2.2 Fundamental Theorem of Algebra
- 6.2.3 Investigating Graphs of Polynomial Functions
- 6.2.4 Transforming Polynomial Functions
- 6.2.5 Curve Fitting with Polynomial Models
7. Exponential and Logarithmic Functions
- 7.1 Exponential Functions and Logarithms
- 7.1.1 Exponential Functions, Growth, and Decay
- 7.1.2 Inverses of Relations and Functions
- 7.1.3 Logarithmic Functions
- 7.1.4 Properties of Logarithms
- 7.2 Applying Exponential and Logarithmic Functions
- 7.2.1 Exponential and Logarithmic Equations and Inequalities
- 7.2.2 The Natural Base, e
- 7.2.3 Transforming Exponential and Logarithmic Functions
- 7.2.4 Curve Fitting With Exponential and Logarithmic Models
8. Rational and Radical Functions
- 8.1 Rational Functions
- 8.1.1 Variation Functions
- 8.1.2 Multiplying and Dividing Rational Expressions
- 8.1.3 Adding and Subtracting Rational Expressions
- 8.1.4 Rational Functions
- 8.1.5 Solving Rational Equations and Inequalities
- 8.2 Radical Functions
- 8.2.1 Radical Expressions and Rational Exponents
- 8.2.2 Radical Functions
- 8.2.3 Solving Radical Equations and Inequalities
9. Properties and Attributes of Functions
- 9.1 Functions and Their Graphs
- 9.1.1 Multiple Representations of Functions
- 9.1.2 Piecewise Functions
- 9.1.3 Transforming Functions
- 9.2 Functional Relationships
- 9.2.1 Operations with Functions
- 9.2.2 Functions and Their Inverses
- 9.2.3 Modeling Real-World Data
10. Conic Sections
- 10.1 Understanding Conic Sections
- 10.1.1 Introduction to Conic Sections
- 10.1.2 Circles
- 10.1.3 Ellipses
- 10.1.4 Hyperbolas
- 10.1.5 Parabolas
- 10.2 Applying Conic Sections
- 10.2.1 Identifying Conic Sections
- 10.2.2 Solving Nonlinear Systems
11. Probability and Statistics
- 11.1 Probability
- 11.1.1 Permutations and Combinations
- 11.1.2 Theoretical and Experimental Probability
- 11.1.3 Independent and Dependent Events
- 11.1.4 Compound Events
- 11.2 Data Analysis and Statistics
- 11.2.1 Measures of Central Tendency and Variation
- 11.2.2 Binomial Distributions
12. Sequences and Series
- 12.1 Exploring Arithmetic Sequences and Series
- 12.1.1 Introduction to Sequences
- 12.1.2 Series and Summation Notation
- 12.1.3 Arithmetic Sequences and Series
- 12.2 Exploring Geometric Sequences and Series
- 12.2.1 Geometric Sequences and Series
- 12.2.2 Mathematical Induction and Infinite Geometric Series
13. Trigonometric Functions
- 13.1 Introduction to Trigonometric Functions
- 13.1.1 Right-Angle Trigonometry
- 13.1.2 Angles of Rotation
- 13.1.3 The Unit Circle
- 13.1.4 Inverses of Trigonometric Functions
- 13.2 Applying Trigonometric Functions
- 13.2.1 The Law of Sines
- 13.2.2 The Law of Cosines
14. Trigonometric Graphs and Identities
- 14.1 Exploring Trigonometric Graphs
- 14.1.1 Graphs of Sine and Cosine
- 14.1.2 Graphs of Other Trigonometric Functions
- 14.2 Trigonometric Identities
- 14.2.1 Fundamental Trigonometric Identities
- 14.2.2 Sum and Difference Identities
- 14.2.3 Double-Angle and Half-Angle Identities
- 14.2.4 Solving Trigonometric Equations
About the Author
Edward Burger
Williams College
Edward Burger, Professor of Mathematics at Williams College, earned his Ph.D. at the University of Texas at Austin, having graduated summa cum laude with distinction in mathematics from Connecticut College.
He has also taught at UT-Austin and the University of Colorado at Boulder, and he served as a fellow at the University of Waterloo in Canada and at Macquarie University in Australia. Prof. Burger has won many awards, including the 2001 Haimo Award for Distinguished Teaching of Mathematics, the 2004 Chauvenet Prize, and the 2006 Lester R. Ford Award, all from the Mathematical Association of America. In 2006, Reader's Digest listed him in the "100 Best of America". After completing his tenure as Gaudino Scholar at Williams, he was named Lissack Professor for Social Responsibility and Personal Ethics.
Prof. Burger is the author of over 50 articles, videos, and books, including the trade book, Coincidences, Chaos, and All That Math Jazz: Making Light of Weighty Ideas and of the textbook The Heart of Mathematics: An Invitation to Effective Thinking. He also speaks frequently to professional and public audiences, referees professional journals, and publishes articles in leading math journals, including The Journal of Number Theory and American Mathematical Monthly. His areas of specialty include number theory, Diophantine approximation, p-adic analysis, the geometry of numbers, and the theory of continued fractions.
Prof. Burger's unique sense of humor and his teaching expertise combine to make him the ideal presenter of Thinkwell's entertaining and informative video lectures.
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