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: Basic trigonometry. Limits, derivatives, integrals, and graphs of basic and inverse trigonometric functions. Solids of revolution. Buffon’s needle problem. The corridor problem. Simple harmonic motion. Newton’s second law of motion. The hyperbolic functions sinh, cosh, and tanh. Catenaries.
Prerequisite mathematics: Tangent lines. Curve sketching. Limits. Continuity. Basic derivatives. Basic integrals. Inverse functions. Maxima and minima. Inflection points.
1. Review of Trigonometry
2. Elementary Trigonometry
3. Derivatives of Sine and Cosine
4. Integrals of Sine and Cosine
5. Derivatives of Other Trigonometric Functions
6. Inverse Trigonometric Functions
7. Harmonic Motion
8. Hyperbolic Functions
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