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Outline course of pure mathematics /
Outline Course of Pure Mathematics presents a unified treatment of the algebra, geometry, and calculus that are considered fundamental for the foundation of undergraduate mathematics. This book discusses several topics, including elementary treatments of the real number system, simple harmonic motio...
| Clasificación: | Libro Electrónico |
|---|---|
| Autor principal: | |
| Formato: | Electrónico eBook |
| Idioma: | Inglés |
| Publicado: |
Oxford ; New York :
Pergamon Press,
[1968]
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| Edición: | First edition]. |
| Temas: | |
| Acceso en línea: | Texto completo |
Tabla de Contenidos:
- Front Cover; Outline Course of Pure Mathematics; Copyright Page; Table of Contents; PREFACE; GREEK ALPHABET; SELECT BIBLIOGRAPHY; CHAPTER 1. DIFFERENTIAL CALCULUS; 1. DIFFERENTIATION (REVISION); 2. DIFFERENTIALS; 3. MAXIMA AND MINIMA (REVISION); EXERCISES 1; Chapter 2. INVERSE TRIGONOMETRICAL FUNCTIONS; 4. NATURE OF INVERSE FUNCTIONS; 5. SPECIAL PROPERTIES OF INVERSE TRIGONOMETRICAL FUNCTIONS; EXERCISES 2; CHAPTER 3. ELEMENTARY ANALYSIS; 6. LIMITS (REVISION). THE SYMBOL ; 7. CONCEPT OF THE LIMIT OF A FUNCTION; 8. CONCEPT OF CONTINUITY.
- 9. THE MEAN VALUE THEOREM. ROLLE'S THEOREM 10. L' H O S P I TA L' S RULE (1694) (L' Ho spital, 1661-1704, French; EXERCISES 3; CHAPTER 4. EXPONENTIAL AND LOGARITHMIC FUNCTIONS; 11. EXPONENTIAL FUNCTION. EXPONENTIALNUMBER; 12. GRAPHS OF THE EXPONENTIAL AND LOGARITHMIC FUNCTIONS; 13. DIFFERENTIATION OF THE EXPONENTIAL AND LOGARITHMIC FUNCTIONS; EXERCISES 4; CHAPTER 5. HYPERBOLIC FUNCTIONS; 14. THE HYPERBOLIC FUNCTIONS; 15. DIFFERENTIATION OF THE HYPERBOLIC FUNCTIONS; 1 6. GRAPHS OF THE HYPERBOLIC FUNCTIONS; 17. INVERSE HYPERBOLIC FUNCTIONS.
- 18. THE GUDERMANNIAN AND INVERSE GUDERMANNIANEXERCISES 5; CHAPTER 6. PARTIAL DIFFERENTIATION; 19. n-DIMENSIONAL GEOMETRY; 20. POLAR COORDINATES; 21. PARTIAL DIFFERENTIATION; 22. TOTAL DIFFERENTIALS; EXERCISES 6; CHAPTER 7. INDEFINITE INTEGRALS; 23. THE INDEFINITE INTEGRAL; 24. STANDARD INTEGRALS; 25. TECHNIQUES OF INTEGRATION: CHANGE OF VARIABLE (SUBSTITUTION, TRANSFORMATION); 26. TECHNIQUES OF INTEGRATION: TRIGONOMETRIC DENOMINATOR; 27. TECHNIQUES OF INTEGRATION: INTEGRATION BY PARTS; 28. TECHNIQUES OF INTEGRATION: PARTIAL FRACTIONS.
- 29. TECHNIQUES OF INTEGRATION: QUADRATIC DENOMINATOREXERCISES 7; CHAPTER 8. DEFINITE INTEGRALS; 30. ELEMENTARY FIRST-ORDER DIFFERENTIAL EQUATIONS (METHOD OF SEPARATION OF VARIABLES); 31. THE DEFINITE INTEGRAL; 3 2. IMPROPER INTEGRALS; 33. THE DEFINITE INTEGRAL AS AN AREA AND AS THE LIMIT OF A SUM; 34. PROPERTIES OF f(x) dx; 35. REDUCTION FORMULAE; 36. AN INTEGRAL APPROACH TO THE THEORY OF LOGARITHMIC FUNCTIONS; EXERCISES 8; CHAPTER 9. INFINITE SERIES AND SEQUENCES; 37. SEQUENCES; 38. CONVERGENCE AND DIVERGENCE OF INFINITE SERIES; 39. TESTS FOR CONVERGENCE.
- 40. alternating series. absolute and conditional convergence 41. maclaurin's series; 42. leibniz's formula; exercises 9; chapter 10. complex numbers; 43. the real number system; 44. number rings and fields; 45. intuitive approach to complex numbers; 46. formal development of complex numbers; 47. geometrical representation of complex numbers. the argand diagram; 48. euler's theorem (1742); 49. complex numbers and polynomial equations; 50. elementary symmetric functions; 51. so me typical problems involving complex numbers; 52. hypercomplex numbers (quaternions).