Calculus for the ambitious
Machine generated contents note: 1. Preliminary ideas -- 1.1. Why is calculus hard? -- 1.2. A simple trick -- 1.3. The art of prophecy -- 1.4. Better prophecy -- 1.5.T angents -- 2. The integral -- 2.1. Area -- 2.2. Integration -- 2.3. The fundamental theorem -- 2.4. Growth -- 2.5. Maxima and minima...
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| Format: | UnknownFormat |
| Sprache: | eng |
| Veröffentlicht: |
Cambridge
Cambridge University Press
2014
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| Schlagworte: | |
| Online Zugang: | Autorenbiografie Verlagsangaben |
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Tag hinzufügen | Zusammenfassung: | Machine generated contents note: 1. Preliminary ideas -- 1.1. Why is calculus hard? -- 1.2. A simple trick -- 1.3. The art of prophecy -- 1.4. Better prophecy -- 1.5.T angents -- 2. The integral -- 2.1. Area -- 2.2. Integration -- 2.3. The fundamental theorem -- 2.4. Growth -- 2.5. Maxima and minima -- 2.6. Snell's law -- 3. Functions, old and new -- 3.1. The logarithm -- 3.2. The exponential function -- 3.3. Trigonometric functions -- 4. Falling bodies -- 4.1. Galileo -- 4.2. Air resistance -- 4.3. A dose of reality -- 5. Compound interest and horse kicks -- 5.1. Compound interest -- 5.2. Digging tunnels -- 5.3. Horse kicks -- 5.4. Gremlins -- 6. Taylor's theorem -- 6.1. Do the higher derivatives exist? -- 6.2. Taylor's theorem -- 6.3. Calculation with Taylor's theorem -- 7. Approximations, good and bad -- 7.1. Find the root -- 7.2. The Newton--Raphson method -- 7.3. There are lots of numbers -- 8. Hills and dales -- 8.1. More than one variable -- 8.2. Taylor's theorem in two variables -- 8.3. On the persistence of passes -- 9. Differential equations via computers -- 9.1. Firing tables -- 9.2. Euler's method -- 9.3. A good idea badly implemented -- 10. Paradise lost -- 10.1. The snake enters the garden -- 10.2. Too beautiful to lose -- 11. Paradise regained -- 11.1. A short pep talk -- 11.2. The Euclidean method -- 11.3. Are there enough numbers? -- 11.4. Can we guarantee a maximum? -- 11.5. A glass wall problem -- 11.6. What next? -- 11.7. The second turtle -- Further reading From the author of The Pleasures of Counting and Naïve Decision Making comes a calculus book perfect for self-study. It will open up the ideas of the calculus for any 16 to 18 year old about to begin studies in mathematics, and will be useful for anyone who would like to see a different account of the calculus from that given in the standard texts. In a lively and easy-to-read style, Professor Körner uses approximation and estimates in a way that will easily merge into the standard development of analysis. By using Taylor's theorem with error bounds he is able to discuss topics that are rarely covered at this introductory level. This book describes important and interesting ideas in a way that will enthuse a new generation of mathematicians |
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| Beschreibung: | Includes bibliographical references (page 163) and index |
| Beschreibung: | XII, 165 S. Ill., graph. Darst. 24 cm |
| ISBN: | 1107063922 1-107-06392-2 9781107063921 978-1-107-06392-1 9781107686748 978-1-107-68674-8 1107686741 1-107-68674-1 |