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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 | |