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Diagnostic Tests | |
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Integrals | |
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Areas and Distances | |
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The Definite Integral | |
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Discovery Project: Area Functions | |
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The Fundamental Theorem of Calculus | |
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Indefinite Integrals and the Net Change Theorem | |
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Writing Project: Newton, Leibniz, and the Invention of Calculus | |
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The Substitution Rule | |
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Review | |
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Problems Plus | |
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Applications Of Integration | |
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Areas between Curves | |
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Volume | |
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Volumes by Cylindrical Shells | |
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Work | |
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Average Value of a Function | |
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Applied Project: Where to Sit at the Movies | |
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Review | |
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Techniques Of Integration | |
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Integration by Parts | |
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Trigonometric Integrals | |
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Trigonometric Substitution | |
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Integration of Rational Functions by Partial Fractions | |
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Strategy for Integration | |
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Integration Using Tables and Computer Algebra Systems | |
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Discovery Project: Patterns in Integrals | |
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Approximate Integration | |
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Improper Integrals | |
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Review | |
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Problems Plus | |
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Further Applications Of Integration | |
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Arc Length | |
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Discovery Project: Arc Length ConteSt. Area of a Surface of Revolution | |
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Discovery Project: Rotating on a Slant | |
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Applications to Physics and Engineering | |
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Discovery Project: Complementary Coffee Cups | |
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Applications to Economics and Biology | |
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Probability | |
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Review | |
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Problems Plus | |
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Differential Equations | |
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Modeling with Differential Equations | |
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Direction Fields and Euler's Method | |
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Separable Equations | |
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Applied Project: Which is Faster, Going Up or Coming Down? | |
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Models for Population Growth | |
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Applied Project: Calculus and Baseball | |
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Linear Equations | |
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Predator-Prey Systems | |
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Review | |
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Problems Plus | |
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Parametric Equations And Polar Coordinates | |
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Curves Defined by Parametric Equations | |
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Laboratory Project: Families of Hypocycloids | |
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Calculus with Parametric Curves | |
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Laboratory Project: Bezier Curves | |
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Polar Coordinates | |
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Areas and Lengths in Polar Coordinates | |
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Conic Sections | |
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Conic Sections in Polar Coordinates | |
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Review | |
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Problems Plus | |
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Infinite Sequences And Series | |
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Sequences | |
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Laboratory Project: Logistic Sequences | |
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Series | |
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The Integral Test and Estimates of Sums | |
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The Comparison Tests | |
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Alternating Series | |
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Absolute Convergence and the Ratio and Root Tests | |
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Strategy for Testing Series | |
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Power Series | |
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Representations of Functions as Power Series | |
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Taylor and Maclaurin Series | |
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Laboratory Project: An Elusive Limit | |
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Writing Project: How Newton Discovered the | |
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Binomial Series | |
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Applications of Taylor Polynomials | |
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Applied Project: Radiation from the Stars | |
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Review | |
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Problems Plus | |
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Appendixes | |
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Numbers, Inequalities, and Absolute Values | |
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Coordinate Geometry and Lines | |
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Graphs of Second-Degree Equations | |
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Trigonometry | |
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Sigma Notation | |
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Proofs of Theorems | |
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The Logarithm Defined as an Integral | |
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Complex Numbers | |
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Answers to Odd-Numbered Exercises | |