Chapter 1: Functions and Mathematical ModelsSection 1:
Functions: Graphically, Algebraically, Numerically, and Verbally
Section 2:
Types of Functions
Section 3:
Dilation and Translation of Function Graphs
Section 4:
Composition of Functions
Section 5:
Inverse of a Function
Section 6:
Reflections, Absolute Values, and Other Transformations
Section 8:
Chapter Review and Test
Chapter 2: Periodic Functions and Right Triangle ProblemsSection 1:
Introduction to Periodic Functions
Section 2:
Measurement of Rotation
Section 3:
Sine and cosine Functions
Section 4:
Values of the Six Trigonometric Functions
Section 5:
Inverse Trigonometric Functions and Triangle Problems
Section 6:
Chapter Review and Test
Chapter 3: Applications of Trigonometric and Circular FunctionsSection 1:
Sinusoids: Amplitude, Period, and Cycles
Section 2:
General Sinusoidal Graphs
Section 3:
Graphs of Tangent, Cotangent, Secant, and Cosecant Functions
Section 4:
Radian Measure of Angles
Section 5:
circular Functions
Section 6:
Inverse Circular Relations: Given y, Find x
Section 7:
Sinusoidal Functions as Mathematical Models
Section 8:
Rotary Motion
Section 9:
Chapter Review and Test
Chapter 4: Trigonometric Function Properties, Identities, and Parametric FunctionsSection 1:
Introduction to the Pythagorean Property
Section 2:
Pythagorean, Reciprocal, and Quotient Properties
Section 3:
Identities and Algebraic Transformation of Expressions
Section 4:
Arcsine, Arctangent, Arccosine, and Trigonometric Equations
Section 5:
Parametric Functions
Section 6:
Inverse Trigonometric Relations Graphs
Section 7:
Chapter Review and Test
Chapter 5: Properties of Combined SinusoidsSection 1:
Introduction to Combinations of Sinusoids
Section 2:
Composite Argument and Linear Combination Properties
Section 3:
Other Composite Argument Properties
Section 4:
Composition of Ordinates and Harmonic Analysis
Section 5:
The Sum and Product Properties
Section 6:
Double and Half Argument Properties
Section 7:
Chapter Review and Test
Chapter 6: Triangle TrigonometrySection 1:
Introduction to Oblique Triangles
Section 2:
Oblique Triangles: Law of Cosines
Section 3:
Area of a Triangle
Section 4:
Oblique Triangles: Law of Sines
Section 5:
The Ambiguous Case
Section 6:
Vector Addition
Section 7:
Real-World Triangle Problems
Section 8:
Chapter Review and Test
Section 9:
Cumulative Review, Chapter 1-6
Chapter 7: Properties of Elementary FunctionsSection 1:
Shapes of Function Graphs
Section 2:
Identifying Functions from Graphical Patterns
Section 3:
Identifying Functions from Numerical Patterns
Section 4:
Properties of Logarithms
Section 5:
Logarithms: Equations and Other Bases
Section 6:
Logarithmic Functions
Section 7:
Logistic Functions for Restrained Growth
Section 8:
Chapter Review and Test
Chapter 8: Fitting Functions to DataSection 1:
Introduction to Regression for Linear Data
Section 2:
Deviations, Residuals, and the Correlation Coefficient
Section 3:
Regression for Nonlinear DataSection 4:
Linearizing Data and Logarithmic Graph Paper
Section 5:
Residual Plots and Mathematical ModelsSection 6:
Chapter Review and Test
Chapter 9: Probability, and Functions of Random VariableSection 1:
Introduction to Probability
Section 2:
Words Associated with Probability
Section 3:
Two Counting Principles
Section 4:
Probabilities of Various Permutations
Section 5:
Probabilities of Various Combinations
Section 6:
Properties of Probability
Section 7:
Functions of a Random Variable
Section 8:
Mathematical Expectation
Section 9:
Chapter Review and Test
Section 10:
Cumulative Review, Chapters 7-9
Chapter 10: Three-Dimensional VectorsSection 1:
Review of Two-Dimensional Vectors
Section 2:
Two-Dimensional Vector Practice
Section 3:
Vectors in Space
Section 4:
Scalar Products and Projections of Vectors
Section 5:
Planes in Space
Section 6:
Vector Product of Two Vectors
Section 7:
Directional Angles and direction Cosines
Section 8:
Chapter Review and Test
Chapter 11: Matrix Transformations and Fractal FiguresSection 1:
Introduction to Iterated Transformations
Section 2:
Matrix Operations and Solutions of Linear Systems
Section 3:
Rotation and Dilation Matrices
Section 4:
Translation with Rotation and Dilation Matrices
Section 5:
Strange Attractors for Several Iterated Transformations
Section 6:
Fractal DimensionsSection 7:
Chapter Review and Test
Chapter 12: Analytic Geometry of Conic Sections and Quadric SurfacesSection 1:
Introduction to Conic Sections
Section 2:
Parametric and Cartesian Equations fo the Conic Sections
Section 3:
Quadric Surfaces and Inscribed FiguresSection 4:
Analytic Geometry of the Conic Sections
Section 5:
Parametric and Cartesian Equations of Rotated ConicsSection 6:
Applications of Conic SectionsSection 7:
Chapter Review and Test
Chapter 13: Polar Coordinates, Complex Numbers, and Moving ObjectsSection 7:
Chapter Review and Test
Section 1:
Introduction to Polar Coordinates
Section 2:
Intersections of Polar Coordinates
Section 3:
Intersections of Polar CurvesSection 4:
Complex Numbers in Polar Form
Section 5:
Parametric Equations of Moving Objects
Page 594:
Concept Problems
Page 631:
Review Problems
Page 633:
Concept ProblemsPage 635:
Chapter Test
Exercise 1d
Exercise 1e
Exercise 1f
Exercise 1g
Exercise 2a
Exercise 2b
Exercise 2c
Exercise 2d
Exercise 2e
Exercise 2f
Exercise 2g
Exercise 2h
Chapter 14: Sequences and SeriesSection 1:
Introduction to Sequences and Series
Section 2:
Arithmetic, Geometric, and Other Sequences
Section 3:
Series and Partial Sums
Section 4:
Chapter Review and Test
Chapter 15: Polynomial and Rational Functions, Limits, and DerivativesSection 1:
Review of Polynomial Functions
Section 2:
Graphs and Zeros of Polynomial Functions
Section 3:
Fitting Polynomial Functions to Data
Section 4:
Rational Functions: Discontinuities, Limits, and Partial Fractions
Section 5:
Instantaneous Rate of Change of a Functions: The Derivative
Section 6:
Chapter Review and Test
Section 7:
Cumulative Review, Chapters 10-15
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