Differential equations, with applications and historical notes /

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A revision of a much-admired text distinguished by the exceptional prose and historical/mathematical context that have made Simmons' books classics. The Second Edition includes expanded coverage of Laplace transforms and partial differential equations as well as a new chapter on numerical me...

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Bibliographic Details
Main Authors: Simmons, George F, John S. Robertson (Author)
Format: Printed Book
Language:English
Published: Chennai: McGraw-Hill, 2003.
Edition:2nd ed.
Subjects:
Differential equations. > Équations différentielles.
Table of Contents:
  • 1. The nature of differential equations
  • Families of curves
  • Orthogonal trajectories
  • Growth, decay, chemical reactions, and mixing
  • Falling bodies and other motion problems
  • The Brachistochrone
  • Fermat and the Bernoullis
  • 2. First order equations
  • Homogeneous equations
  • Exact equations
  • Integrating factors
  • Linear equations
  • Reduction of order
  • The hanging chain
  • Pursuit curves
  • Simple electric circuits
  • 3. Second order linear equations
  • Vibrations in mechanical and electrical systems
  • Newton's Law of Gravitation and the motion of the planets
  • Coupled harmonic oscillators
  • 4. Qualitative properties of solutions
  • Oscillations and the Sturm Separation theorem
  • The Sturm Comparison theorem
  • 5. Power series solutions and special functions
  • Gauss's hypergeometric equation
  • The point at infinity
  • Hermite polynomials and quantum mechanics
  • Chebyshev polynomials and the minimax property
  • Riemann's equation
  • 6. Fourier series and orthogonal functions
  • 7. Partial differential equations and boundary value problems
  • Eigenvalues, eigenfunctions, and the vibrating string
  • The heat equation
  • The Dirichlet problem for a circle
  • Poisson's integral
  • Sturm-Liouville problems
  • 8. Some special functions of mathematical physics
  • Legendre polynomials
  • Bessel functions
  • 9. Laplace transforms
  • 10. Systems of first order equations
  • Linear systems
  • 11. Linear equations
  • Liapunov
  • Poincccaré-Bendixson theorem
  • Proof of Liénard's theorem
  • 12. The calculus of variations
  • 13. The existence and uniqueness of solutions
  • Successive approximations
  • Picard
  • 14. Numerical methods
  • Euler.

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