College Algebra with Intermediate Algebra A Blended Course

Intermediate through College Algebra: A Streamlined Experience

College Algebra with Intermediate Algebra: A Blended Course is an innovative new program from the Beecher et al. author team. Designed to meet your changing needs in Intermediate Algebra and College Algebra courses, this program eliminates the repetition in topic coverage across the traditional, two-course sequence. The result is a streamlined course experience that makes better use of time and resources. The careful arrangement of topics—one building on the next without redundancy—motivates and creates a solid foundation of knowledge. This new, streamlined approach to these courses is complemented by the authors’ innovative ability to help you “see the math” through their focus on visualization, early introduction to functions and graphing, and making connections between math concepts and the real world.

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Judy Beecher has an undergraduate degree in mathematics from Indiana University and a graduate degree in mathematics from Purdue University. She has taught at both the high school and college levels with many years of developmental math and precalculus teaching experience at Indiana University—Purdue University Indianapolis (IUPUI). In addition to her career in textbook publishing, she enjoys traveling, spending time with her grandchildren, and promoting charity projects for a children's camp.

Judy Penna received her undergraduate degree in mathematics from Kansas State University and her graduate degree in mathematics from the University of Illinois. Since then, she has taught at Indiana University—Purdue University Indianapolis (IUPUI) and at Butler University, and continues to focus on writing quality textbooks for undergraduate mathematics students. In her free time she likes to travel, read, knit and spend time with her children and grandchildren.

Barbara Johnson has a BS in mathematics from Bob Jones University and a MS in mathematics from Clemson University, and she is currently pursuing a PhD in Educational Studies at Ball state University. She has taught high school and college math for 30 years, and she enjoys the challenge of helping each student grow in appreciation for and understanding of mathematics. As a Purdue Master Gardener, she also enjoys helping others learn gardening skills. Believing that the best teacher is always learning, she is also a student of karate.

Marvin Bittinger has taught math at the university level for more than thirty-eight years, and he is now professor emeritus of mathematics education at Indiana University-Purdue University. Professor Bittinger has authored numerous textbooks on topics ranging from basic mathematics to algebra and trigonometry to applied calculus. He received his BA in mathematics from Manchester College and his PhD in mathematics education from Purdue University. Special honors include Distinguished Visiting Professor at the United States Air Force Academy. His hobbies include hiking in Utah, baseball, golf, and bowling. Professor Bittinger has also had the privilege of speaking at many mathematics conventions, most recently giving a lecture entitled "Baseball and Mathematics." In addition, he also has an interest in philosophy and theology, in particular, apologetics. Professor Bittinger currently lives in Carmel, Indiana with his wife Elaine. He has two grown and married sons, Lowell and Chris, and four granddaughters.

R.1 The Set of Real Numbers

R.2 Operations with Real Numbers

R.3 Exponential Notation and Order of Operations

Part 2 Manipulations

R.4 Introduction to Algebraic Expressions

R.5 Equivalent Algebraic Expressions

R.6 Simplifying Algebraic Expressions

R.7 Properties of Exponents and Scientific Notation

1 Solving Linear Equations and Inequalities

1.1 Solving Equations

1.2 Formulas and Applications

1.3 Applications and Problem Solving

1.4 Sets, Inequalities, and Interval Notation

1.5 Intersections, Unions, and Compound Inequalities

1.6 Absolute-Value Equations and Inequalities

2 Graphs, Functions, and Applications

2.1 Graphs of Equations

2.2 Functions and Graphs

2.3 Finding Domain and Range

2.4 The Algebra of Functions

2.5 Linear Functions: Graphs and Slope

2.6 More on Graphing Linear Equations

2.7 Finding Equations of Lines; Applications

3 Systems of Equations

3.1 Systems of Equations in Two Variables

3.2 Solving by Substitution

3.3 Solving by Elimination

3.4 Solving Applied Problems: Two Equations

3.5 Systems of Equations in Three Variables

3.6 Solving Applied Problems: Three Equations

3.7 Systems of Inequalities and Linear Programming

4 Polynomials and Polynomial Functions

4.1 Introduction to Polynomials and Polynomial Functions

4.2 Multiplication of Polynomials

4.3 Introduction to Factoring

4.4 Factoring Trinomials: x2 + bx + c

4.5 Factoring Trinomials: ax2 + bx + c, a  _1

4.6 Special Factoring

4.7 Factoring: A General Strategy

4.8 Applications of Polynomial Equations and Functions

5 Rational Expressions, Equations, and Functions

5.1 Rational Expressions and Functions: Multiplying, Dividing, and Simplifying

5.2 LCMs, LCDs, Addition, and Subtraction

5.3 Division of Polynomials

5.4 Complex Rational Expressions

5.5 Solving Rational Equations

5.6 Applications and Proportions

5.7 Formulas and Applications

5.8 Variation and Applications

6 Radical Expressions, Equations, and Functions

6.1 Radical Expressions and Functions

6.2 Rational Numbers as Exponents

6.3 Simplifying Radical Expressions

6.4 Addition, Subtraction, and More Multiplication

6.5 More on Division of Radical Expressions

6.6 Solving Radical Equations

6.7 Applications Involving Powers and Roots

6.8 Increasing, Decreasing, and Piecewise Functions; Applications

7 Quadratic Functions and Equations

7.1 Symmetry

7.2 Transformations

7.3 The Complex Numbers

7.4 Quadratic Equations, Functions, Zeros, and Models

7.5 Analyzing Graphs of Quadratic Functions

8 Polynomial Functions and Rational Functions

8.1 Polynomial Functions and Models

8.2 Graphing Polynomials Functions

8.3 Polynomial Division; The Remainder Theorem and the Factor Theorem

8.4 Theorems about Zeros of Polynomial Functions

8.5 Rational Functions

8.6 Polynomial Inequalities and Rational Inequalities

9 Exponential Functions and Logarithmic Functions

9.1  The Composition of Functions

9.2 Inverse Functions

9.3 Exponential Functions and Graphs

9.4 Logarithmic Functions and Graphs

9.5 Properties of Logarithmic Functions

9.6 Solving Exponential Equations and Logarithmic Equations

9.7 Applications and Models: Growth and Decay; Compound Interest

10 Matrices

10.1 Matrices and Systems of Equations

10.2 Matrix Operations

10.3 Inverses of Matrices

10.4 Determinants and Cramer’s Rule

11 Conic Sections

11.1 The Parabola

11.2 The Circle and the Ellipse

11.3 The Hyperbola

11.4 Nonlinear Systems of Equations and Inequalities

12 Sequences, Series, and Combinatorics

12.1 Sequences and Series

12.2 Arithmetic Sequences and Series

12.3 Geometric Sequences and Series

12.4 Mathematical Induction

12.5 Combinatorics: Permutations

12.6 Combinatorics: Combinations

12.7 The Binomial Theorem

12.8 Probability

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