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Tim HillThe Essential Calculus Workbook: Limits and Derivatives, Paperback
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Ready to step up your game in calculus? This workbook isn't the usual parade of repetitive questions and answers. Author Tim Hill's approach lets you work on problems you enjoy, rather than through exercises and drills you fear, without the speed pressure, timed testing, and rote memorization that damage your experience of mathematics. Working through varied problems in this anxiety-free way helps you develop an understanding of numerical relations apart from the catalog of mathematical facts that's often stressed in classrooms and households. This number sense, common in high-achieving students, lets you apply and combine concepts, methods, and numbers flexibly, without relying on distant memories.
Topics covered: The tangent line. Delta notation. The derivative of a function. Differentiable functions. Leibniz notation. Average and instantaneous velocity. Speed. Projectile paths. Rates of change. Acceleration. Marginal cost. Limits. Epsilon-delta definition. Limit laws. Trigonometric limits. Continuity. Continuous functions. The Mean Value Theorem. The Extreme Value Theorem. The Intermediate Value Theorem. Fermat's theorem.
Prerequisite mathematics: Elementary algebra. Real numbers. Functions. Graphs. Trigonometry.
Contents1. The Slope of the Tangent Line2. The Definition of the Derivative3. Velocity and Rates of Change4. Limits5. Continuous Functions
About the AuthorTim Hill is a statistician living in Boulder, Colorado. He holds degrees in mathematics and statistics from Stanford University and the University of Colorado. Tim has written guides for calculus, trigonometry, algebra, geometry, precalculus, permutations and combinations, and Excel pivot tables. When he's not crunching numbers, Tim climbs rocks, hikes canyons, and avoids malls.
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