Book:R.P. Gillespie/Integration/Second Edition
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R.P. Gillespie: Integration (2nd Edition)
Published $\text {1944}$, Oliver & Boyd
Subject Matter
Contents
- Preface
- Preface to the Second Edition
- chapter $\text {I}$: INTRODUCTION
- 1. Area of a Circle
- 2. Areas
- 3. The Integral as the Limit of a Sum
- 4. Volume of Revolution
- 5. Properties of the Integral
- chapter $\text {II}$: INTEGRATION OF ELEMENTARY FUNCTIONS
- 6. Methods of Integration
- 7. Standard Integrals
- 8. Change of Variable
- 9. Integration by Parts
- 10. Integration of Rational Functions
- 11. Integration of Trigonometric Functions
- 12. Integration of Irrational Functions
- Examples $\textit {I}$
- chapter $\text {III}$: MULTIPLE INTEGRALS
- 13. Double Integrals
- 14. Repeated Integrals
- 15. Triple Integrals
- 16. Change of Variable in Multiple Integrals
- 17. Polar Coordinates
- Examples $\textit {II}$
- chapter $\text {IV}$: CURVILINEAR AND SURFACE INTEGRALS
- 18. Length of a Curve
- 19. Curvilinear or Line Integrals
- 20. Theorem
- 21. Surface of Revolution
- 22. The Element of Surface
- 23. Freedom Equations of a Surface
- 24. Surface Integrals
- 25. Gauss's Theorem
- Examples $\textit {III}$
- chapter $\text {V}$: THE RIEMANN INTEGRAL
- 27. Preliminary Definitions
- 28. Definition of the Integral
- 29. Fundamental Theorem
- 30. Integration of Continuous Functions
- 31. Properties of the Integral
- chapter $\text {VI}$: INFINITE INTEGRALS
- 32. Definition
- 33. Fundamental Theorem
- 34. Absolute Convergence
- 35. Infinite Integrand
- 36. Two Important Integrals
- 37. Gamma and Beta Functions
- 38. Relation between Gamma and Beta Functions
- 39. Uniform Convergence of an Integral
- 40. Theorem on Repeated Integrals
- 41. Differentiation under the Integral Sign
- Examples $\textit {IV}$
- chapter $\text {VII}$: THE RIEMANN DOUBLE INTEGRAL
- 43. Change of Variable
- 44. Integration by Parts
- 45. Theorems of Mean Value
- 46. Integration of Series
- 47. Orthogonal Systems of Functions
- 48. Differentiation under the Integral Sign
- 49. Double Integral over a Rectangle
- 50. Rectifiable Curves
- 51. Theorem on Rectifiable Curves
- 52. Double Integrals
- 53. Repeated Integrals
- 54. The Generalised Element of Area
- Examples $\textit {V}$
- Index
Cited by
- 1961: I.N. Sneddon: Fourier Series
Source work progress
- 1944: R.P. Gillespie: Integration (2nd ed.) ... (previous) ... (next): Chapter $\text I$: $\S 1$. Area of a Circle
- Starting on : Chapter $\text {II}$: Integration of Elementary Functions: $\S 7$ with Next:
- 1944: R.P. Gillespie: Integration (2nd ed.) ... (previous) ... (next): Chapter $\text {II}$: Integration of Elementary Functions: $\S 8$. Change of Variable