The Essential Calculus Workbook: Limits and Derivatives - Paperback
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Master Calculus Through Problem-Solving
This calculus workbook takes a different approach to learning limits and derivatives. Instead of repetitive drills and timed tests, author Tim Hill focuses on building genuine mathematical understanding through carefully structured problems that develop your number sense and problem-solving intuition.
How This Workbook Works
The Essential Calculus Workbook treats calculus as a problem-solving art requiring insight and intuitive understanding. Problems build gradually in difficulty with minimal repetition, allowing you to work at your own pace without speed pressure or anxiety. If you encounter a challenge, flip back a few pages for hints or memory refreshers.
- Solutions to basic problems are steeped in the fundamentals, including notation, terminology, definitions, theories, proofs, physical laws, and related concepts.
- Advanced problems explore variations, tricks, subtleties, and real-world applications.
- Problems build gradually in difficulty with little repetition. If you get stuck, then flip back a few pages for a hint or to jog your memory.
- Numerous pictures depicting mathematical facts help you connect visual and symbolic representations of numbers and concepts.
- Treats calculus as a problem-solving art requiring insight and intuitive understanding, not as a branch of logic requiring careful deductive reasoning.
- Discards the common and damaging misconception that fast students are strong students. Good students aren't particularly fast with numbers because they think deeply and carefully about mathematics.
- Detailed solutions and capsule reviews greatly reduce the need to cross reference a comprehensive calculus textbook.
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.
Prerequisites and Contents
Prerequisite mathematics: Elementary algebra. Real numbers. Functions. Graphs. Trigonometry.
Contents
1. The Slope of the Tangent Line
2. The Definition of the Derivative
3. Velocity and Rates of Change
4. Limits
5. Continuous Functions
Tim 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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Master Calculus Through Problem-Solving
This calculus workbook takes a different approach to learning limits and derivatives. Instead of repetitive drills and timed tests, author Tim Hill focuses on building genuine mathematical understanding through carefully structured problems that develop your number sense and problem-solving intuition.
How This Workbook Works
The Essential Calculus Workbook treats calculus as a problem-solving art requiring insight and intuitive understanding. Problems build gradually in difficulty with minimal repetition, allowing you to work at your own pace without speed pressure or anxiety. If you encounter a challenge, flip back a few pages for hints or memory refreshers.
- Solutions to basic problems are steeped in the fundamentals, including notation, terminology, definitions, theories, proofs, physical laws, and related concepts.
- Advanced problems explore variations, tricks, subtleties, and real-world applications.
- Problems build gradually in difficulty with little repetition. If you get stuck, then flip back a few pages for a hint or to jog your memory.
- Numerous pictures depicting mathematical facts help you connect visual and symbolic representations of numbers and concepts.
- Treats calculus as a problem-solving art requiring insight and intuitive understanding, not as a branch of logic requiring careful deductive reasoning.
- Discards the common and damaging misconception that fast students are strong students. Good students aren't particularly fast with numbers because they think deeply and carefully about mathematics.
- Detailed solutions and capsule reviews greatly reduce the need to cross reference a comprehensive calculus textbook.
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.
Prerequisites and Contents
Prerequisite mathematics: Elementary algebra. Real numbers. Functions. Graphs. Trigonometry.
Contents
1. The Slope of the Tangent Line
2. The Definition of the Derivative
3. Velocity and Rates of Change
4. Limits
5. Continuous Functions
Tim 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.