Book:R.P. Gillespie/Integration/Second Edition

R.P. Gillespie: Integration (2nd Edition)

Published $\text {1944}$, Oliver & Boyd

Subject Matter

• Integral Calculus

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

Next

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