Book:E.L. Ince/Integration of Ordinary Differential Equations/Seventh Edition
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E.L. Ince: Integration of Ordinary Differential Equations (7th Edition)
Published $\text {1956}$, Oliver and Boyd Ltd
Subject Matter
Contents
- Preface (May 1939)
- Preface to the Second Edition (April 1943) (A.C. Aitken and D.E. Rutherford)
- CHAPTER $\text {I}$: EQUATIONS OF THE FIRST ORDER AND DEGREE
- 1. Definitions
- 2. Integration
- 3. Separation of Variables
- 4. The Homogeneous Type
- 5. The Equation with Linear Coefficients
- 6. Exact Equations
- 7. Integrating Factors
- 8. The Quotient of Two Integrating Factors
- 9. Special Types of Integrating Factor
- 10. The Linear Equation
- 11. The Bernoulli Equation
- 12. The Riccati Equation
- 13. Change of Variable
- CHAPTER $\text {II}$: INTEGRAL CURVES
- 14. Families of Plane Curves
- 15. Trajectories
- 16. Level Lines and Lines of Slope on a Surface
- 17. Singular Points
- CHAPTER $\text {III}$: EQUATIONS OF HIGHER DEGREE
- 18. The General Integral
- 19. The Clairaut Equation
- 20. Generalisation - the d'Alembert Equation
- 21. Further Generalisation
- 22. Equations with One Variable Missing
- 23. Homogeneous Equations
- 24. Geometrical Interpretation of a Differential Equation
- 25. Cusp on the Integral Curve
- 26. Envelope of Integral Curves
- 27. Equation of the Second Degree
- CHAPTER $\text {IV}$: EQUATIONS OF THE SECOND AND HIGHER ORDERS
- 28. Reduction of the Order of an Equation
- 29. Equations that do not Involve $y$
- 30. Equations that do not Involve $x$
- 31. First Homogeneous Type
- 32. Second Homogeneous Type
- 33. Third Homogeneous Type
- 34. A Special Case of Homogeneity
- 35. First Integral
- 36. Problems Involving Curvature
- CHAPTER $\text {V}$: LINEAR EQUATIONS
- 37. Form of the General Integral
- 38. Depression of the Order
- 39. Reduced Equation with Constant Coefficients
- 40. Properties of the Operator $\map F D$
- 41. Pairs of Conjugate Factors
- 42. Repeated Real Factors
- 43. Repeated Complex Factors
- 44. Inverse Operators
- 45. Inverse Operators Relative to a Periodic Function
- 46. Development of an Inverse Operator
- 47. General Integral by Quadratures
- 48. The Euler Linear Equation
- 49. The Laplace Linear Equation
- 50. Variation of Parameters
- 51. Linear Systems with Constant Coefficients
- CHAPTER $\text {VI}$: SOLUTION IN SERIES
- 52. Solution Developed as a Taylor Series
- 53. Regular Singularity
- 54. The Hypergeometric Equation
- 55. The Legendre Equation and the Function $\map {P_n} x$
- 56. Solution for Large Values of $\size x$
- 57. The Bessel Equation and the Function $\map {J_n} x$
- 58. The Function $\map {Y_n} x$
- EXAMPLES
- SOLUTIONS
- INDEX
Further Editions
- 1939: E.L. Ince: Integration of Ordinary Differential Equations
- 1943: E.L. Ince: Integration of Ordinary Differential Equations (2nd ed.)
- 1944: E.L. Ince: Integration of Ordinary Differential Equations (3rd ed.)
- 1946: E.L. Ince: Integration of Ordinary Differential Equations (4th ed.)
- 1949: E.L. Ince: Integration of Ordinary Differential Equations (5th ed.)
- 1952: E.L. Ince: Integration of Ordinary Differential Equations (6th ed.)
Source work progress
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