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

Subject Matter

 * Integral Calculus

Contents

 * Preface


 * Preface to the Second Edition


 * $\text {I}$: 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


 * $\text {II}$: 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 $\textit {I}$


 * $\text {III}$: MULTIPLE INTEGRALS
 * 13. Double Integrals
 * 14. Repeated Integrals
 * 15. Triple Integrals
 * 16. Change of Variable in Multiple Integrals
 * 17. Polar Coordinates
 * Examples $\textit {II}$


 * $\text {IV}$: 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 $\textit {III}$


 * $\text {V}$: THE RIEMANN INTEGRAL
 * 27. Preliminary Definitions
 * 28. Definition of the Integral
 * 29. Fundamental Theorem
 * 30. Integration of Continuous Functions
 * 31. Properties of the Integral


 * $\text {VI}$: 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 $\textit {IV}$


 * $\text {VII}$: 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



Source work progress
* : Chapter $\text I$: $\S 1$. Area of a Circle