springer new york springer us jul 1985 (2 Ergebnisse)

Taschenbuch. Zustand: Neu. Neuware -The purpose of this book is to isolate and draw attention to the most important problem-solving techniques typically encountered in undergradu ate mathematics and to illustrate their use by interesting examples and problems not easily found in other sources. Each section features a single idea, the power and versatility of which is demonstrated in the examples and reinforced in the problems. The book serves as an introduction and guide to the problems literature (e.g., as found in the problems sections of undergraduate mathematics journals) and as an easily accessed reference of essential knowledge for students and teachers of mathematics. The book is both an anthology of problems and a manual of instruction. It contains over 700 problems, over one-third of which are worked in detail. Each problem is chosen for its natural appeal and beauty, but primarily to provide the context for illustrating a given problem-solving method. The aim throughout is to show how a basic set of simple techniques can be applied in diverse ways to solve an enormous variety of problems. Whenever possible, problems within sections are chosen to cut across expected course boundaries and to thereby strengthen the evidence that a single intuition is capable of broad application. Each section concludes with 'Additional Examples' that point to other contexts where the technique is appropriate.Springer Verlag GmbH, Tiergartenstr. 17, 69121 Heidelberg 352 pp. Englisch.

Taschenbuch. Zustand: Neu. Neuware -I. Graphing.- Solved Problems.- Supplementary Problems.- II. Geometry.- Solved Problems.- Supplementary Problems.- III. Physics and Engineering.- Solved Problems.- Supplementary Problems.- >Chapter IV. Business and Economics.- Solved Problems.- Supplementary Problems.- V. Biology and Chemistry.- Solved Problems.- Supplementary Problems.- VI. Numerical Methods.- Solved Problems.- Supplementary Problems.- VII. Theory.- Solved Problems.- Supplementary Problems.- VIII. Techniques.- Solved Problems.- 1. Precalculus (absolute value, inequalities, analytic geometry, trigonometry, logarithms, functions, inverse functions).- 2. Differentiation (chain rule, implicit differentiation, differentiation of integrals).- 3. Applications of Differentiation (tangent lines, normal lines, maxima and minima).- 4. Methods of integration (indefinite integrals).- 5. Methods of integration (definite integrals).- 6. Improper integrals.- 7. Applications of definite integrals (area, volumes, arc length, area of a surface of revolution).- 8. Parametric curves.- 9. Polar coordinates.- 10. Sequences and infinite series, Taylor¿s formula, Taylor series.- 11. Indeterminate forms.- 12. Differential equations.- Supplementary Problems.- 1. Precalculus.- 2. Differentiation.- 3. Applications of differentiation.- 4. Indefinite integrals.- 5. Definite integrals.- 6. Improper integrals.- 7. Applications of definite integrals.- 8. Parametric curves.- 9. Polar coordinates.- 10. Sequences and infinite series, Taylor¿s formula, Taylor series.- 11. Indeterminate forms.- 12. Differential equations.- 13. Miscellaneous.- >Chapter IX. Answers to Supplementary Problems.- I. Graphing.- II. Geometry.- III. Physics and Engineering.- IV. Business and Economics345 V. Biology and Chemistry.- VI. Numerical Methods.- VII. Theory.- VIII. Techniques.- Problem Sources.- Index of Symbols.Springer Verlag GmbH, Tiergartenstr. 17, 69121 Heidelberg 404 pp. Englisch.