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Algebra and Trigonometry: Graphs & Models and Graphing Calculator Manual Package 4th edition [Kietas viršelis]

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  • Formatas: Hardback, 1052 pages, weight: 2336 g, Contains 1 Hardback and 1 Paperback / softback
  • Išleidimo metai: 19-Feb-2008
  • Leidėjas: Pearson
  • ISBN-10: 0321501519
  • ISBN-13: 9780321501516
Kitos knygos pagal šią temą:
  • Formatas: Hardback, 1052 pages, weight: 2336 g, Contains 1 Hardback and 1 Paperback / softback
  • Išleidimo metai: 19-Feb-2008
  • Leidėjas: Pearson
  • ISBN-10: 0321501519
  • ISBN-13: 9780321501516
Kitos knygos pagal šią temą:
The authors help students "see the math" through their focus on functions; visual emphasis; side-by-side algebraic and graphical solutions; real-data applications; and examples and exercises. By remaining focused on today's students and their needs, the authors lead students to mathematical understanding and, ultimately, success in class.

Daugiau informacijos

The authors help students "see the math" through their focus on functions; visual emphasis; side-by-side algebraic and graphical solutions; real-data applications; and examples and exercises. By remaining focused on today's students and their needs, the authors lead students to mathematical understanding and, ultimately, success in class.
Preface xiii
Basic Concepts of Algebra
1(970)
The Real-Number System
2(7)
Real Numbers
Interval Notation
Properties of the Real Numbers
Absolute Value
Integer Exponents, Scientific Notation, and Order of Operations
9(9)
Integers as Exponents
Scientific Notation
Order of Operations
Addition, Subtraction, and Multiplication of Polynomials
18(5)
Polynomials
Addition and Subtraction
Multiplication
Factoring
23(9)
Terms with Common Factors
Factoring by Grouping
Trinomials of the Type x2 + bx + c
Trinomials of the Type ax2 + bx + c, a ≠ 1
Special Factorizations
The Basics of Equation Solving
32(4)
Linear and Quadratic Equations
Rational Expressions
36(9)
The Domain of a Rational Expression
Simplifying, Multiplying, and Dividing Rational Expressions
Adding and Subtracting Rational Expressions
Complex Rational Expressions
Radical Notation and Rational Exponents
45(16)
Simplifying Radical Expressions
An Application
Rationalizing Denominators or Numerators
Rational Exponents
Summary and Review
55(4)
Test
59(2)
Graphs, Functions, and Models
61(104)
Introduction to Graphing
62(18)
Graphs
Solutions of Equations
Graphs of Equations
The Distance Formula
Midpoints of Segments
Circles
Visualizing the Graph
74(6)
Functions and Graphs
80(17)
Functions
Notation for Functions
Graphs of Functions
Finding Domains of Functions
Visualizing Domain and Range
Applications of Functions
Linear Functions, Slope, and Applications
97(18)
Linear Functions
The Linear Function f(x) = mx + b and Slope
Applications of Slope
Slope-Intercept Equations of Lines
Graphing f(x) = mx + b Using m and b
Applications of Linear Functions
Visualizing the Graph
109(6)
Equations of Lines and Modeling
115(14)
Slope-Intercept Equations of Lines
Point-Slope Equations of Lines
Parallel Lines
Perpendicular Lines
Mathematical Models
Curve Fitting
Linear Regression
Linear Equations, Functions, Zeros, and Applications
129(21)
Linear Equations
Applications Using Linear Models
Zeros of Linear Functions
Formulas
Solving Linear Inequalities
150(6)
Linear Inequalities
Compound Inequalities
An Application
Summary and Review
156(5)
Test
161(4)
More on Functions
165(70)
Increasing, Decreasing, and Piecewise Functions; Applications
166(15)
Increasing, Decreasing, and Constant Functions
Relative Maximum and Minimum Values
Applications of Functions
Functions Defined Piecewise
The Algebra of Functions
181(8)
The Algebra of Functions: Sums, Differences, Products, and Quotients
Difference Quotients
The Composition of Functions
189(9)
The Composition of Functions
Decomposing a Function as a Composition
Symmetry and Transformations
198(21)
Symmetry
Even and Odd Functions
Transformations of Functions
Vertical and Horizontal Translations
Reflections
Vertical and Horizontal Stretchings and Shrinkings
Visualizing the Graph
213(6)
Variation and Applications
219(16)
Direct Variation
Inverse Variation
Combined Variation
Summary and Review
228(4)
Test
232(3)
Quadratic Functions and Equations; Inequalities
235(60)
The Complex Numbers
236(8)
The Complex-Number System
Addition and Subtraction
Multiplication
Conjugates and Division
Quadratic Equations, Functions, Zeros, and Models
244(17)
Quadratic Equations and Quadratic Functions
Completing the Square
Using the Quadratic Formula
The Discriminant
Equations Reducible to Quadratic
Applications
Analyzing Graphs of Quadratic Functions
261(15)
Graphing Quadratic Functions of the Type f(x) = a(x -- h)2 + k
Graphing Quadratic Functions of the Type f(x) = ax2 + bx + c, ≠ 0
Applications
Visualizing the Graph
271(5)
Solving Rational Equations and Radical Equations
276(8)
Rational Equations
Radical Equations
Solving Equations and Inequalities with Absolute Value
284(11)
Equations with Absolute Value
Inequalities with Absolute Value
Summary and Review
289(4)
Test
293(2)
Polynomial and Rational Functions
295(84)
Polynomial Functions and Modeling
296(17)
The Leading-Term Test
Finding Zeros of Factored Polynomial Functions
Finding Real Zeros on a Calculator
Polynomial Models
Graphing Polynomial Functions
313(10)
Graphing Polynomial Functions
The Intermediate Value Theorem
Visualizing the Graph
320(3)
Polynomial Division; The Remainder and Factor Theorems
323(9)
Division and Factors
The Remainder Theorem and Synthetic Division
Finding Factors of Polynomials
Theorems about Zeros of Polynomial Functions
332(10)
The Fundamental Theorem of Algebra
Finding Polynomials with Given Zeros
Zeros of Polynomial Functions with Real Coefficients
Rational Coefficients
Integer Coefficients and the Rational Zeros Theorem
Descartes' Rule of Signs
Rational Functions
342(18)
The Domain of a Rational Function
Asymptotes
Applications
Visualizing the Graph
356(4)
Polynomial and Rational Inequalities
360(19)
Polynomial Inequalities
Rational Inequalities
Summary and Review
372(5)
Test
377(2)
Exponential and Logarithmic Functions
379(92)
Inverse Functions
380(14)
Inverses
Inverses and One-to-One Functions
Finding Formulas for Inverses
Inverse Functions and Composition
Restricting a Domain
Exponential Functions and Graphs
394(14)
Graphing Exponential Functions
Applications
The Number e
Graphs of Exponential Functions, Base e
Logarithmic Functions and Graphs
408(18)
Logarithmic Functions
Finding Certain Logarithms
Converting Between Exponential Equations and Logarithmic Equations
Finding Logarithms on a Calculator
Natural Logarithms
Changing Logarithmic Bases
Graphs of Logarithmic Functions
Applications
Visualizing the Graph
422(4)
Properties of Logarithmic Functions
426(9)
Logarithms of Products
Logarithms of Powers
Logarithms of Quotients
Applying the Properties
Simplifying Expressions of the Type loga ax and alogax
Solving Exponential and Logarithmic Equations
435(11)
Solving Exponential Equations
Solving Logarithmic Equations
Applications and Models: Growth and Decay; Compound Interest
446(25)
Population Growth
Interest Compounded Continuously
Models of Limited Growth
Exponential Decay
Exponential and Logarithmic Curve Fitting
Summary and Review
464(5)
Test
469(2)
The Trigonometric Functions
471(102)
Trigonometric Functions of Acute Angles
472(13)
The Trigonometric Ratios
The Six Functions Related
Function Values of 30°, 45°, and 60°
Function Values of Any Acute Angle
Cofunctions and Complements
Applications of Right Triangles
485(13)
Solving Right Triangles
Applications
Trigonometric Functions of Any Angle
498(16)
Angles, Rotations, and Degree Measure
Trigonometric Functions of Angles or Rotations
The Six Functions Related
Terminal Side on an Axis
Reference Angles: 30°, 45°, and 60°
Function Values for Any Angle
Radians, Arc Length, and Angular Speed
514(16)
Distances on the Unit Circle
Radian Measure
Arc Length and Central Angles
Linear Speed and Angular Speed
Circular Functions: Graphs and Properties
530(17)
Reflections on the Unit Circle
Finding Function Values
Graphs of the Sine and Cosine Functions
Graphs of the Tangent, Cotangent, Cosecant, and Secant Functions
Graphs of Transformed Sine and Cosine Functions
547(26)
Variations of Basic Graphs
Graphs of Sums: Addition of Ordinates
Damped Oscillation: Multiplication of Ordinates
Visualizing the Graph
561(5)
Summary and Review
566(5)
Test
571(2)
Trigonometric Identities, Inverse Functions, and Equations
573(66)
Identities: Pythagorean and Sum and Difference
574(14)
Pythagorean Identities
Simplifying Trigonometric Expressions
Sum and Difference Identities
Identities: Cofunction, Double-Angle, and Half-Angle
588(10)
Cofunction Identities
Double-Angle Identities
Half-Angle Identities
Proving Trigonometric Identities
598(8)
The Logic of Proving Identities
Proving Identities
Product-to-Sum and Sum-to-Product Identities
Inverses of the Trigonometric Functions
606(12)
Restricting Ranges to Define Inverse Functions
Composition of Trigonometric Functions and Their Inverses
Solving Trigonometric Equations
618(21)
Visualizing the Graph
629(4)
Summary and Review
633(5)
Test
638(1)
Applications of Trigonometry
639(80)
The Law of Sines
640(14)
Solving Oblique Triangles
The Law of Sines
Solving Triangles (AAS and ASA)
Solving Triangles (SSA)
The Area of a Triangle
The Law of Cosines
654(10)
The Law of Cosines
Solving Triangles (SAS)
Solving Triangles (SSS)
Complex Numbers: Trigonometric Form
664(12)
Graphical Representation
Trigonometric Notation for Complex Numbers
Multiplication and Division with Trigonometric Notation
Powers of Complex Numbers
Roots of Complex Numbers
Polar Coordinates and Graphs
676(12)
Polar Coordinates
Polar and Rectangular Equations
Graphing Polar Equations
Visualizing the Graph
685(3)
Vectors and Applications
688(9)
Vectors
Vector Addition
Applications
Components
Vector Operations
697(22)
Position Vectors
Operations on Vectors
Unit Vectors
Direction Angles
Angle Between Vectors
Forces in Equilibrium
Summary and Review
712(5)
Test
717(2)
Systems of Equations and Matrices
719(94)
Systems of Equations in Two Variables
720(16)
Solving Systems of Equations Graphically
The Substitution Method
The Elimination Method
Applications
Visualizing the Graph
730(6)
Systems of Equations in Three Variables
736(12)
Solving Systems of Equations in Three Variables
Applications
Mathematical Models and Applications
Matrices and Systems of Equations
748(8)
Matrices and Row-Equivalent Operations
Gaussian Elimination with Matrices
Gauss-Jordan Elimination
Matrix Operations
756(12)
Matrix Addition and Subtraction
Scalar Multiplication
Products of Matrices
Matrix Equations
Inverses of Matrices
768(8)
The Identity Matrix
The Inverse of a Matrix
Solving Systems of Equations
Determinants and Cramer's Rule
776(8)
Determinants of Square Matrices
Evaluating Determinants Using Cofactors
Cramer's Rule
Systems of Inequalities and Linear Programming
784(14)
Graphs of Linear Inequalities
Systems of Linear Inequalities
Applications: Linear Programming
Partial Fractions
798(15)
Partial Fraction Decompositions
Summary and Review
805(6)
Test
811(2)
Analytic Geometry Topics
813(76)
The Parabola
814(8)
Parabolas
Finding Standard Form by Completing the Square
Applications
The Circle and the Ellipse
822(11)
Circles
Ellipses
Applications
The Hyperbola
833(10)
Standard Equations of Hyperbolas
Applications
Nonlinear Systems of Equations and Inequalities
843(12)
Nonlinear Systems of Equations
Modeling and Problem Solving
Nonlinear Systems of Inequalities
Visualizing the Graph
850(5)
Rotation of Axes
855(10)
Rotation of Axes
The Discriminant
Polar Equations of Conics
865(7)
Polar Equations of Conics
Converting from Polar Equations to Rectangular Equations
Finding Polar Equations of Conics
Parametric Equations
872(17)
Graphing Parametric Equations
Determining a Rectangular Equation for Given Parametric Equations
Determining Parametric Equations for a Given Rectangular Equation
Applications
Summary and Review
881(5)
Test
886(3)
Sequences, Series, and Combinatorics
889(82)
Sequences and Series
890(10)
Sequences
Finding the General Term
Sums and Series
Sigma Notation
Recursive Definitions
Arithmetic Sequences and Series
900(10)
Arithmetic Sequences
Sum of the First n Terms of an Arithmetic Sequence
Applications
Geometric Sequences and Series
910(12)
Geometric Sequences
Sum of the First n Terms of a Geometric Sequence
Infinite Geometric Series
Applications
Visualizing the Graph
918(4)
Mathematical Induction
922(6)
Sequences of Statements
Proving Infinite Sequences of Statements
Combinatorics: Permutations
928(10)
Permutations
Factorial Notation
Permutations of n Objects Taken k at a Time
Permutations of Sets with Nondistinguishable Objects
Combinatorics: Combinations
938(8)
Combinations
The Binomial Theorem
946(8)
Binomial Expansions Using Pascal's Triangle
Binomial Expansion Using Factorial Notation
Finding a Specific Term
Total Number of Subsets
Probability
954(17)
Experimental and Theoretical Probability
Computing Experimental Probabilities
Theoretical Probability
Summary and Review
965(4)
Test
969(2)
Appendix: Basic Concepts from Geometry 971(22)
Photo Credits 993
Answers 1(1)
Index 1(14)
Index of Applications 15
The TI-83 Plus and TI-84 Plus Graphing Calculators
1(76)
The TI-89 Graphing Calculator
77
TI-83 Plus and TI-84 Plus Index 1(6)
TI-89 Index 7
Marvin Bittinger For over thirty-eight years, Professor Marvin L. Bittinger has been teaching math at the university level. Since 1968, he has been employed  at Indiana University - Purdue University Indianapolis, and is now professor emeritus of mathematics education. Professor Bittinger has authored over 190 publications 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 and his election to the Manchester College Board of Trustees from 1992 to 1999. 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.

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. In addition to her career in textbook publishing, she spends time traveling, enjoying her grandchildren, and promoting charity projects for a children's camp.

David Ellenbogen    David Ellenbogen has taught math at the college level for twenty-two years, spending most of that time in the Massachusetts and Vermont community college systems, where he has served on both curriculum and developmental math committees.  He has also taught at St. Michael's College and The University of Vermont. Professor Ellenbogen has been active in the Mathematical Association of Two Year Colleges since 1985, having served on its Developmental Mathematics Committee and as a delegate, and has been a member of the Mathematical Association of America since 1979.  He has authored dozens of publications on topics ranging from prealgebra to calculus and has delivered lectures at numerous conferences on the use of language in mathematics.  Professor Ellenbogen received his BA in mathematics from Bates College and his MA in community college mathematics education from The University of Massachusetts at Amherst. A co-founder of the Colchester Vermont Recycling Program, Professor Ellenbogen has a deep love for the environment and the outdoors, especially in his home state of Vermont.  In his spare time, he enjoys playing keyboard in the band Soularium, volunteering as a community mentor, hiking, biking, and skiing.  He has two sons, Monroe and Zack.

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 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.