{"product_id":"calculus-in-context-9781421422305","title":"Calculus in Context","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003eCalculus in Context is a compelling exploration-for students and instructors alike-of a discipline that is both rich in conceptual beauty and broad in its applied relevance.\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTrade Review\u003c\/b\u003e\u003cbr\u003eThe depth of detail in each application [offered by \u003ci\u003eCalculus in Context\u003c\/i\u003e] provides an excellent structure for guiding students through the “why should we care” moments that every calculus class experiences.\u003cbr\u003e—\u003ci\u003eMathematical Association of America\u003c\/i\u003e\u003cbr\u003eRecommended.\u003cbr\u003e—\u003ci\u003eChoice\u003c\/i\u003e\u003cbr\u003eHahn's book is the perfect choice for college and university teachers who want to teach calculus with reference to its origins and applications.\u003cbr\u003e—\u003ci\u003eZentralblatt Math\u003c\/i\u003e\u003cbr\u003eVery well written in an engaging and enthusiastic style: it is very suitable for first year students, is perhaps not too demanding for students about to enter university, and it is particularly useful to those with more than a passing interest in astronomy. There is plenty to learn for the reader, and the massive text is also a good reference book on calculus. This labour of love from the author more than satisfies the high hopes for a good calculus book... and I highly recommend it.\u003cbr\u003e—Peter Shiu, \u003ci\u003eMathematical Gazette\u003c\/i\u003e\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTable of Contents\u003c\/b\u003e\u003cbr\u003e\u003cp\u003ePreface\u003cbr\u003e\u003cb\u003ePart I\u003c\/b\u003e\u003cbr\u003e1. The Astronomy and Geometry of the Greeks\u003cbr\u003e1.1. The Greeks Explain the Universe\u003cbr\u003e1.2. Achieving the Impossible?\u003cbr\u003e1.3. Greek Geometry\u003cbr\u003e1.4. The Pythagorean Theorem\u003cbr\u003e1.5. The Radian Measure of an Angle\u003cbr\u003e1.6. Greek Trigonometry\u003cbr\u003e1.7. Aristarchus Sizes Up the Universe\u003cbr\u003e1.8. Problems and Projects\u003cbr\u003e2. The Genius of Archimedes\u003cbr\u003e2.1. The Conic Sections\u003cbr\u003e2.2. The Question of Area\u003cbr\u003e2.3. Playing with Squares\u003cbr\u003e2.4. The Area of a Parabolic Section\u003cbr\u003e2.5. The Method of Archimedes\u003cbr\u003e2.6. Problems and Projects\u003cbr\u003e3. A New Astronomy\u003cbr\u003e3.1. A Fixed Sun at the Center\u003cbr\u003e3.2. Copernicus's Model of Earth's Orbit\u003cbr\u003e3.3. About the Distances of the Planets from the Sun\u003cbr\u003e3.4. Tycho Brahe and Parallax\u003cbr\u003e3.5. Kepler's Elliptical Orbits\u003cbr\u003e3.6. The Studies of Galileo\u003cbr\u003e3.7. The Size of the Solar System\u003cbr\u003e3.8. Problems and Projects\u003cbr\u003e4. The Coordinate Geometry of Descartes\u003cbr\u003e4.1. The Real Numbers\u003cbr\u003e4.2. The Coordinate Plane\u003cbr\u003e4.3. About the Parabola\u003cbr\u003e4.4. About the Ellipse\u003cbr\u003e4.5. Quadratic Equations in x and y\u003cbr\u003e4.6. Circles and Trigonometry\u003cbr\u003e4.7. Problems and Projects\u003cbr\u003e5. The Calculus of Leibniz\u003cbr\u003e5.1. Straight Lines\u003cbr\u003e5.2. Tangent Lines to Curves\u003cbr\u003e5.3. The Function Concept\u003cbr\u003e5.4. The Derivative of a Function\u003cbr\u003e5.5. Fermat, Kepler, and Wine Barrels\u003cbr\u003e5.6. The Definite Integral\u003cbr\u003e5.7. Cavalieri's Principle\u003cbr\u003e5.8. Differentials and the Fundamental Theorem\u003cbr\u003e5.9. Volumes of Revolution\u003cbr\u003e5.10. Problems and Projects\u003cbr\u003e6. The Calculus of Newton\u003cbr\u003e6.1. Simple Functions and Areas\u003cbr\u003e6.2. The Derivative of a Simple Function\u003cbr\u003e6.3. From Simple Functions to Power Series\u003cbr\u003e6.4. The Mathematics of a Moving Point\u003cbr\u003e6.5. Galileo and Acceleration\u003cbr\u003e6.6. Dealing with Forces\u003cbr\u003e6.7. The Trajectory of a Projectile\u003cbr\u003e6.8. Newton Studies the Motion of the Planets\u003cbr\u003e6.9. Connecting Force and Geometry\u003cbr\u003e6.10. The Law of Universal Gravitation\u003cbr\u003e6.11. Problems and Projects\u003cbr\u003e\u003cb\u003ePart II\u003c\/b\u003e\u003cbr\u003e7. Differential Calculus\u003cbr\u003e7.1. Mathematical Functions\u003cbr\u003e7.2. A Study of Limits\u003cbr\u003e7.3. Continuous Functions\u003cbr\u003e7.4. Differentiable Functions\u003cbr\u003e7.5. Computing Derivatives\u003cbr\u003e7.6. Some Theoretical Concerns\u003cbr\u003e7.7. Derivatives of Trigonometric Functions\u003cbr\u003e7.8. Understanding Functions\u003cbr\u003e7.9. Graphing Functions\u003cbr\u003e7.10. Exponential Functions\u003cbr\u003e7.11. Logarithm Functions\u003cbr\u003e7.12. Hyperbolic Functions\u003cbr\u003e7.13. Final Comments about Graphs\u003cbr\u003e7.14. Problems and Projects\u003cbr\u003e8. Applications of Differential Calculus\u003cbr\u003e8.1. Derivatives as Rates of Change\u003cbr\u003e8.1.1. Growth of Organisms\u003cbr\u003e8.1.2. Radioactive Decay\u003cbr\u003e8.1.3. Cost of Production\u003cbr\u003e8.2. The Pulley Problem of L'Hospital\u003cbr\u003e8.2.1. The Solution Using Calculus\u003cbr\u003e8.2.2. The Solution by Balancing Forces\u003cbr\u003e8.3. The Suspension Bridge\u003cbr\u003e8.4. An Experiment of Galileo\u003cbr\u003e8.4.1. Sliding Ice Cubes and Spinning Wheels\u003cbr\u003e8.4.2. Torque and Rotational Inertia\u003cbr\u003e8.4.3. The Mathematics behind Galileo's Experiment\u003cbr\u003e8.5. From Fermat's Principle to the Reflecting Telescope\u003cbr\u003e8.5.1. Fermat's Principle and the Reflection of Light\u003cbr\u003e8.5.2. The Refraction of Light\u003cbr\u003e8.5.3. About Lenses\u003cbr\u003e8.5.4. Refracting and Reflecting Telescopes\u003cbr\u003e8.6. Problems and Projects\u003cbr\u003e9. The Basics of Integral Calculus\u003cbr\u003e9.1. The Definite Integral of a Function\u003cbr\u003e9.2. Volume and the Definite Integral\u003cbr\u003e9.3. Lengths of Curves and the Definite Integral\u003cbr\u003e9.4. Surface Area and the Definite Integral\u003cbr\u003e9.5. The Definite Integral and the Fundamental Theorem\u003cbr\u003e9.6. Area as Antiderivative\u003cbr\u003e9.7. Finding Antiderivatives\u003cbr\u003e9.7.1. Integration by Substitution\u003cbr\u003e9.7.2. Integration by Parts\u003cbr\u003e9.7.3. Some Algebraic Moves\u003cbr\u003e9.8. Inverse Functions\u003cbr\u003e9.9. Inverse Trigonometric and Hyperbolic Functions\u003cbr\u003e9.9.1. Trigonometric Inverses\u003cbr\u003e9.9.2. Hyperbolic Inverses\u003cbr\u003e9.10. Trigonometric and Hyperbolic Substitutions\u003cbr\u003e9.11. Some Integral Formulas\u003cbr\u003e9.12. The Trapezoidal and Simpson Rules\u003cbr\u003e9.13. One Loop of the Sine Curve\u003cbr\u003e9.14. Problems and Projects\u003cbr\u003e10. Applications of Integral Calculus\u003cbr\u003e10.1. Estimating the Weight of Domes\u003cbr\u003e10.1.1. The Hagia Sophia\u003cbr\u003e10.1.2. The Roman Pantheon\u003cbr\u003e10.2. The Cables of a Suspension Bridge\u003cbr\u003e10.3. From Pocket Watch to Pseudosphere\u003cbr\u003e10.3.1. Volume and Surface Area of Revolution of the Tractrix\u003cbr\u003e10.3.2. The Pseudosphere\u003cbr\u003e10.4. Calculating the Motion of a Planet\u003cbr\u003e10.4.1. Determining Position in Terms of Time\u003cbr\u003e10.4.2. Determining Speed and Direction\u003cbr\u003e10.4.3. Earth, Jupiter, and Halley\u003cbr\u003e10.5. Integral Calculus and the Action of Forces\u003cbr\u003e10.5.1. Work and Energy, Impulse and Momentum\u003cbr\u003e10.5.2. Analysis of Springs\u003cbr\u003e10.5.3. The Force in a Gun Barrel\u003cbr\u003e10.5.4. The Springfield Rifle\u003cbr\u003e10.6. Problems and Projects\u003cbr\u003e11. Basics of Differential Equations\u003cbr\u003e11.1. First-Order Separable Differential Equations\u003cbr\u003e11.2. The Method of Integrating Factors\u003cbr\u003e11.3. Direction Fields and Euler's Method\u003cbr\u003e11.4. The Polar Coordinate System\u003cbr\u003e11.5. The Complex Plane\u003cbr\u003e11.6. Second-Order Differential Equations\u003cbr\u003e11.7. The Basics of Power Series\u003cbr\u003e11.8. Taylor and Maclaurin Series\u003cbr\u003e11.9. Solving a Second-Order Differential Equation\u003cbr\u003e11.10. Free Fall with Air Resistance\u003cbr\u003e11.10.1. Going Up\u003cbr\u003e11.10.2. Coming Down\u003cbr\u003e11.10.3. Bullets and Ping-Pong Balls\u003cbr\u003e11.11. Systems with Springs and Damping Elements\u003cbr\u003e11.11.1. The Family Sedan and the Stock Car\u003cbr\u003e11.12. More about Hanging Cables\u003cbr\u003e11.13. Problems and Projects\u003cbr\u003e12. Polar Calculus and Newton's Planetary Orbits\u003cbr\u003e12.1. Graphing Polar Equations\u003cbr\u003e12.2. The Conic Sections in Polar Coordinates\u003cbr\u003e12.3. The Derivative of a Polar Function\u003cbr\u003e12.4. The Lengths of Polar Curves\u003cbr\u003e12.5. Areas in Polar Coordinates\u003cbr\u003e12.6. Equiangular Spirals\u003cbr\u003e12.7. Centripetal Force in Cartesian Coordinates\u003cbr\u003e12.8. Going Polar\u003cbr\u003e12.9. From Conic Section to Inverse Square Law and Back Again\u003cbr\u003e12.10. Gravity and Geometry\u003cbr\u003e12.11. Spiral Galaxies\u003cbr\u003e12.12. Problems and Projects\u003cbr\u003eReferences\u003cbr\u003eImage Credits and Notes\u003cbr\u003eIndex\u003c\/p\u003e","brand":"Johns Hopkins University Press","offers":[{"title":"Default Title","offer_id":49408121766231,"sku":"9781421422305","price":80.5,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9781421422305.jpg?v=1730501664","url":"https:\/\/bookcurl.com\/products\/calculus-in-context-9781421422305","provider":"Book Curl","version":"1.0","type":"link"}