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| Review of Numerical Computation | |
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| The Real Numbers | |
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| Addition and Subtraction | |
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| Multiplication | |
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| Division | |
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| Powers and Roots | |
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| Combined Operations | |
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| Scientific Notation and Engineering Notation | |
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| Units of Measurement | |
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| Percentage | |
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| Chapter 1 Review Problems | |
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| Introduction to Algebra | |
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| Algebraic Expressions | |
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| Adding and Subtracting Polynomials | |
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| Laws of Exponents | |
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| Product of Two Monomials | |
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| Product of a Multinomial and a Monomial | |
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| Product of Two Binomials | |
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| Product of Two Multinomials | |
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| Powers of Multinomials | |
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| Removing Symbols of Grouping | |
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| Quotient of Two Monomials | |
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| Dividing a Polynomial by a Monomial | |
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| Quotient of Two Polynomials | |
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| Chapter 2 Review Problems | |
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| Simple Equations and Word Problems | |
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| Solving First-Degree Equations | |
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| Solving Word Problems | |
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| Uniform Motion | |
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| Financial | |
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| Mixtures | |
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| Statics | |
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| Work, Fluid Flow, and Energy Flow | |
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| Chapter 3 Review Problems | |
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| Functions and Graphs | |
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| Functions | |
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| Graphing a Function | |
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| Graphing a Function by Calculator | |
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| Solving Equations Graphically | |
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| More on Functions | |
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| Chapter 4 Review Problems | |
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| Geometry | |
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| Straight Lines and Angles | |
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| Triangles | |
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| Quadrilaterals | |
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| The Circle | |
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| Volumes and Areas of Solids | |
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| Chapter 5 Review Problems | |
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| Right Triangles and Vectors | |
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| The Trigonometric Functions | |
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| Solution of Right Triangles | |
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| Applications of the Right Triangle | |
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| Introduction to Vectors | |
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| Applications of Vectors | |
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| Chapter 6 Review Problems | |
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| Oblique Triangles and Vectors | |
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| Trigonometric Functions of Any Angle | |
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| Finding the Angle When the Trigonometric Function Is Known | |
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| Law of Sines | |
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| Law of Cosines | |
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| Applications | |
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| Resultants of Nonperpendicular Vectors | |
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| Chapter 7 Review Problems | |
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| Systems of Linear Equations | |
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| Systems of Two Linear Equations | |
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| Other Systems of Equations | |
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| Applications | |
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| Systems of Three Linear Equations | |
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| Chapter 8 Review Problems | |
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| Matrices and Determinants | |
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| Introduction to Matrices | |
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| Solving Systems of Equations by the Unit Matrix Method | |
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| Second-Order Determinants | |
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| Higher-Order Determinants | |
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| Chapter 9 Review Problems | |
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| Factoring and Fractions | |
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| Common Factors | |
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| Difference of Two Squares | |
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| Factoring Trinomials | |
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| Other Factorable Expressions | |
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| Simplification of Fractions | |
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| Multiplication and Division of Fractions | |
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| Addition and Subtraction of Fractions | |
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| Complex Fractions | |
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| Fractional Equations | |
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| Literal Equations and Formulas | |
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| Chapter 10 Review Problems | |
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| Quadratic Equations | |
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| Solving a Quadratic Equation by Calculator | |
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| Solving a Quadratic by Formula | |
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| Applications | |
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| Chapter 11 Review Problems | |
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| Exponents and Radicals | |
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| Integral Exponents | |
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| Simplification of Radicals | |
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| Operations with Radicals | |
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| Radical Equations | |
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| Chapter 12 Review Problems | |
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| Radian Measure, Arc Length, and Rotation | |
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| Radian Measure | |
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| Arc Length | |
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| Uniform Circular Motion | |
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| Chapter 13 Review Problems | |
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| Trigonometric, Parametric, and Polar Graphs | |
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| Graphing the Sine Wave by Calculator | |
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| Manual Graphing of the Sine Wave | |
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| The Sine Wave as a Function of Time | |
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| Graphs of the Other Trigonometric Functions | |
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| Graphing Parametric Equations | |
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| Graphing in Polar Coordinates | |
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| Chapter 14 Review Problems | |
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| Trigonometric Identities and Equations | |
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| Fundamental Identities | |
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| Sum or Difference of Two Angles | |
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| Functions of Double Angles and Half-Angles | |
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| Evaluating Trigonometric Expressions | |
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| Solving Trigonometric Equations | |
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| Chapter 15 Review Problems | |
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| Ratio, Proportion, and Variation | |
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| Ratio and Proportion | |
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| Similar Figures | |
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| Direct Variation | |
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| The Power Function | |
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| Inverse Variation | |
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| Functions of More Than One Variable | |
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| Chapter 16 Review Problems | |
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| Exponential and Logarithmic Functions | |
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| The Exponential Function | |
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| Logarithms | |
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| Properties of Logarithms | |
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| Exponential Equations | |
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| Solving Logarithmic Equations | |
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| Chapter 17 Review Problems | |
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| Complex Numbers | |
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| Complex Numbers in Rectangular Form | |
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| Complex Numbers in Polar Form | |
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| Complex Numbers on the Calculator | |
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| Vector Operations Using Complex Numbers | |
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| Alternating Current Applications | |
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| Chapter 18 Review Problems | |
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| Sequences, Series, and the Binomial Theorem | |
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| Sequences and Series | |
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| Arithmetic and Harmonic Progressions | |
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| Geometric Progressions | |
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| Infinite Geometric Progressions | |
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| The Binomial Theorem | |
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| Chapter 19 Review Problems | |
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| Analytic Geometry | |
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| The Straight Line | |
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| Equation of a Straight Line | |
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| The Circle | |
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| The Parabola | |
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| The Ellipse | |
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| The Hyperbola | |
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| Chapter 20 Review Problems | |
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| Derivatives of Algebraic Functions | |
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| Limits | |
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| Rate of Change and the Tangent | |
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| The Derivative | |
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| Rules for Derivatives | |
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| Derivative of a Function Raised to a Power | |
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| Derivatives of Products and Quotients | |
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| Other Variables, Implicit Relations, and Differentials | |
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| Higher-Order Derivatives | |
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| Chapter 21 Review Problems | |
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| Graphical Applications of the Derivative | |
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| Equations of Tangents and Normals | |
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| Maximum, Minimum, and Inflection Points | |
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| Sketching, Verifying, and Interpreting Graphs | |
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| Chapter 22 Review Problems | |
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| More Applications of the Derivative | |
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| Rate of Change | |
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| Motion of a Point | |
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| Related Rates | |
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| Optimization | |
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| Chapter 23 Review Problems | |
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| Integration | |
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| The Indefinite Integral | |
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| Rules for Finding Integrals | |
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| Simple Differential Equations | |
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| The Definite Integral | |
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| Approximate Area under a Curve | |
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| Exact Area under a Curve | |
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| Chapter 24 Review Problems | |
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| Applications of the Integral | |
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| Applications to Motion | |
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| Applications to Eletric Circuits | |
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| Finding Areas by Integration | |
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| Volumes by Integration | |
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| Chapter 25 Review Problems | |
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| More Applications of the Integral | |
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| Length of Arc | |
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| Area of Surface of Revolution | |
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| Centroids | |
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| Fluid Pressure | |
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| Work | |
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| Moment of Inertia | |
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| Chapter 26 Review Problems | |
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| Trigonometric, Logarithmic, and Exponential Functions | |
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| Derivatives of the Sine and Cosine Functions | |
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| Derivatives of the Other Trigonometric Functions | |
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| Derivatives of the Inverse Trigonometric Functions | |
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| Derivatives of Logarithmic Functions | |
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| Derivatives of the Exponential Functions | |
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| Integrals of the Exponential and Logarithmic Functions | |
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| Integrals of the Trigonometric Functions | |
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| Average and Root Mean Square Values | |
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| Chapter 27 Review Problems | |
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| First-Order Differential Equations | |
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| Definitions | |
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| Solving a DE by Calculator, Graphically, and Numerically | |
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| First-Order DE: Variables Separable | |
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| Exact First-Order DE | |
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| First-Order Homogeneous DE | |
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| First-Order Linear DE | |
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| Geometric Applications of First-Order DE | |
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| Exponential Growth and Decay | |
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| Series RL and RC Circuits | |
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| Chapter 28 Review Problems | |
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| Second-Order DE | |
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| Second-Order DE | |
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| Constant Coefficients and Right Side Zero | |
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| Right Side Not Zero | |
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| Mechanical Vibrations | |
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| RLC Circuits | |
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| Chapter 29 Review Problems | |
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| Appendices | |
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| Summary of Facts and Formulas | |
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| Conversion Factors | |
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| Table of Integrals | |
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| Answers to Selected Problems | |
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| Indexes | |
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| Index to Applications | |
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| Index to Writing Questions | |
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| Index to Projects | |
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| General Index | |