Book contents
- Frontmatter
- Contents
- Preface
- 1 Introduction
- 2 Proof of Fejér's theorem
- 3 Weyl's equidistribution theorem
- 4 The Weierstrass polynomial approximation theorem
- 5 A second proof of Weierstrass's theorem
- 6 Hausdorff's moment problem
- 7 The importance of linearity
- 8 Compass and tides
- 9 The simplest convergence theorem
- 10 The rate of convergence
- 11 A nowhere differentiable function
- 12 Reactions
- 13 Monte Carlo methods
- 15 Pointwise convergence
- 16 Behaviour at points of discontinuity I
- 17 Behaviour at points of discontinuity II
- 18 A Fourier series divergent at a point
- 19 Pointwise convergence, the answer
- 20 The undisturbed damped oscillator does not explode
- 21 The disturbed damped linear oscillator does not explode
- 23 The linear damped oscillator with periodic input
- 27 Poisson summation
- 28 Dirichlet's problem
- 29 Potential theory with smoothness assumptions
- 30 An example of Hadamard
- 31 Potential theory without smoothness assumptions
- 32 Mean square approximation I
- 33 Mean square approximation II
- 34 Mean square convergence
- 35 The isoperimetric problem I
- 36 The isoperimetric problem II
- 37 The Sturm–Liouville equation I
- 38 Liouville
- 39 The Sturm–Liouville equation II
- 40 Orthogonal polynomials
- 41 Gaussian quadrature
- 43 Tchebychev and uniform approximation I
- 44 The existence of the best approximation
- 45 Tchebychev and uniform approximation II
- 46 Introduction to Fourier transforms
- 47 Change in the order of integration I
- 48 Change in the order of integration II
- 49 Fejér's theorem for Fourier transforms
- 50 Sums of independent random variables
- 51 Convolution
- 52 Convolution on T
- 53 Differentiation under the integral
- 54 Lord Kelvin
- 55 The heat equation
- 57 The age of the earth II
- 59 Weierstrass's proof of Weierstrass's theorem
- 60 The inversion formula
- 63 A second approach
- 64 The wave equation
- 71 The central limit theorem II
- 72 Stability and control
- 73 Instability
- 74 The Laplace transform
- 75 Deeper properties
- 76 Poles and stability
- 77 A simple time delay equation
- 79 Many dimensions
- 80 Sums of random vectors
- 81 A chi squared test
- 82 Haldane on fraud
- 86 Will a random walk return?
- 87 Will a Brownian motion return?
- 89 Will a Brownian motion tangle?
- 94 Why do we compute?
- 95 The diameter of stars
- 97 Fourier analysis on the roots of unity
- 99 How fast can we multiply?
- 102 A good code?
- 103 A little more group theory
- 104 Fourier analysis on finite Abelian groups
- 105 A formula of Euler
- 107 Primes in some arithmetical progressions
- 108 Extension from real to complex variable
- 109 Primes in general arithmetical progressions
- Appendixes A, B, G
- References
- Index
21 - The disturbed damped linear oscillator does not explode
Published online by Cambridge University Press: 05 August 2012
- Frontmatter
- Contents
- Preface
- 1 Introduction
- 2 Proof of Fejér's theorem
- 3 Weyl's equidistribution theorem
- 4 The Weierstrass polynomial approximation theorem
- 5 A second proof of Weierstrass's theorem
- 6 Hausdorff's moment problem
- 7 The importance of linearity
- 8 Compass and tides
- 9 The simplest convergence theorem
- 10 The rate of convergence
- 11 A nowhere differentiable function
- 12 Reactions
- 13 Monte Carlo methods
- 15 Pointwise convergence
- 16 Behaviour at points of discontinuity I
- 17 Behaviour at points of discontinuity II
- 18 A Fourier series divergent at a point
- 19 Pointwise convergence, the answer
- 20 The undisturbed damped oscillator does not explode
- 21 The disturbed damped linear oscillator does not explode
- 23 The linear damped oscillator with periodic input
- 27 Poisson summation
- 28 Dirichlet's problem
- 29 Potential theory with smoothness assumptions
- 30 An example of Hadamard
- 31 Potential theory without smoothness assumptions
- 32 Mean square approximation I
- 33 Mean square approximation II
- 34 Mean square convergence
- 35 The isoperimetric problem I
- 36 The isoperimetric problem II
- 37 The Sturm–Liouville equation I
- 38 Liouville
- 39 The Sturm–Liouville equation II
- 40 Orthogonal polynomials
- 41 Gaussian quadrature
- 43 Tchebychev and uniform approximation I
- 44 The existence of the best approximation
- 45 Tchebychev and uniform approximation II
- 46 Introduction to Fourier transforms
- 47 Change in the order of integration I
- 48 Change in the order of integration II
- 49 Fejér's theorem for Fourier transforms
- 50 Sums of independent random variables
- 51 Convolution
- 52 Convolution on T
- 53 Differentiation under the integral
- 54 Lord Kelvin
- 55 The heat equation
- 57 The age of the earth II
- 59 Weierstrass's proof of Weierstrass's theorem
- 60 The inversion formula
- 63 A second approach
- 64 The wave equation
- 71 The central limit theorem II
- 72 Stability and control
- 73 Instability
- 74 The Laplace transform
- 75 Deeper properties
- 76 Poles and stability
- 77 A simple time delay equation
- 79 Many dimensions
- 80 Sums of random vectors
- 81 A chi squared test
- 82 Haldane on fraud
- 86 Will a random walk return?
- 87 Will a Brownian motion return?
- 89 Will a Brownian motion tangle?
- 94 Why do we compute?
- 95 The diameter of stars
- 97 Fourier analysis on the roots of unity
- 99 How fast can we multiply?
- 102 A good code?
- 103 A little more group theory
- 104 Fourier analysis on finite Abelian groups
- 105 A formula of Euler
- 107 Primes in some arithmetical progressions
- 108 Extension from real to complex variable
- 109 Primes in general arithmetical progressions
- Appendixes A, B, G
- References
- Index
Summary
- Type
- Chapter
- Information
- Exercises in Fourier Analysis , pp. 95 - 96Publisher: Cambridge University PressPrint publication year: 1993