Calculus: Graphical, Numerical, Algebraic

Chapter P Prerequisites P.1 Real Numbers P.2 Cartesian Coordinate System P.3 Linear Equations and Inequalities P.4 Lines in the Plane P.5 Solving Equations Graphically, Numerically, and Algebraically P.6 Complex Numbers P. 7 Solving Inequalities Algebraically and Graphically Chapter 1 Functions and Graphs 1.1 Modeling and Equation Solving 1.2 Functions and Their Properties 1.3 Twelve Basic Functions 1.4 Building Functions from Functions 1.5 Parametric Relations and Inverses 1.6 Graphical Transformations 1.7 Modeling With Functions Chapter 2 Polynomial, Power, and Rational Functions 2.1 Linear and Quadratic Functions with Modeling 2.2 Power Functions with Modeling 2.3 Polynomial Functions of Higher Degree with Modeling 2.4 Real Zeros of Polynomial Functions 2.5 Complex Zeros and the Fundamental Theorem of Algebra 2.6 Graphs of Rational Functions 2.7 Solving Equations in One Variable 2.8 Solving Inequalities in One Variable Chapter 3 Exponential, Logistic, and Logarithmic Functions 3.1 Exponential and Logistic Functions 3.2 Exponential and Logistic Modeling 3.3 Logarithmic Functions and Their Graphs 3.4 Properties of Logarithmic Functions 3.5 Equation Solving and Modeling 3.6 Mathematics of Finance Chapter 4 Trigonometric Functions 4.1 Angles and Their Measures 4.2 Trigonometric Functions of Acute Angles 4.3 Trigonometry Extended: The Circular Functions 4.4 Graphs of Sine and Cosine: Sinusoids 4.5 Graphs of Tangent, Cotangent, Secant, and Cosecant 4.6 Graphs of Composite Trigonometric Functions 4.7 Inverse Trigonometric Functions 4.8 Solving Problems with Trigonometry Chapter 5 Analytic Trigonometry 5.1 Fundamental Identities 5.2 Proving Trigonometric Identities 5.3 Sum and Difference Identities 5.4 Multiple-Angle Identities 5.5 The Law of Sines 5.6 The Law of Cosines Chapter 6 Applications of Trigonometry 6.1 Vectors in the Plane 6.2 Dot Product of Vectors 6.3 Parametric Equations and Motion 6.4 Polar Coordinates 6.5 Graphs of Polar Equations 6.6 De Moivre's Theorem and nth Roots Chapter 7 Systems and Matrices 7.1 Solving Systems of Two Equations 7.2 Matrix Algebra 7.3 Multivariate Linear Systems and Row Operations 7.4 Partial Fractions 7.5 Systems of Inequalities in Two Variables Chapter 8 Analytic Geometry in Two and Three Dimensions 8.1 Conic Sections and Parabolas 8.2 Ellipses 8.3 Hyperbolas 8.4 Translation and Rotation of Axes 8.5 Polar Equations of Conics 8.6 Three-Dimensional Cartesian Coordinate System Chapter 9 Discrete Mathematics 9.1 Basic Combinatorics 9.2 The Binomial Theorem 9.3 Probability 9.4 Sequences 9.5 Series 9.6 Mathematical Induction 9.7 Statistics and Data (Graphical) 9.8 Statistics and Data (Algebraic) Chapter 10 An Introduction to Calculus: Limits, Derivatives, and Integrals 10.1 Limits and Motion: The Tangent Problem 10.2 Limits and Motion: The Area Problem 10.3 More on Limits 10.4 Numerical Derivatives and Integrals Appendix A Algebra Review Appendix B Key Formulas Appendix C Logic