Preface Introduction Part I: Ordinary differential equations 19. Equations of the form y'=f(x. y) 20. Linear differential equations: general properties 21. The linear differential equation with constant coefficients 22. The linear differential equation with constant coefficients: alternative method Part II: The definition of functions by infinite series and integrals 23. The convergence of series 24. The definition of functions by series 25. Power series 26. The definition of functions by integrals 27. The solution of differential equations in terms of infinite series 28. Fourier series Part III: Laplace's equation and related equations 29. The transformation of Laplace's equation 30. 'Laplace' equations 31. Spherical harmonics Answers to examples Index.
Preface Introduction Part I: Ordinary differential equations 19. Equations of the form y'=f(x. y) 20. Linear differential equations: general properties 21. The linear differential equation with constant coefficients 22. The linear differential equation with constant coefficients: alternative method Part II: The definition of functions by infinite series and integrals 23. The convergence of series 24. The definition of functions by series 25. Power series 26. The definition of functions by integrals 27. The solution of differential equations in terms of infinite series 28. Fourier series Part III: Laplace's equation and related equations 29. The transformation of Laplace's equation 30. 'Laplace' equations 31. Spherical harmonics Answers to examples Index.
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