Simmons, George Finlay, 1925-

Differential equations, with applications and historical notes / George F. Simmons, with a new chapter on numerical methods by John S. Robertson. - 2nd ed. - New York : McGraw-Hill, c1991[reprint 2003] - xxi, 629 p. : ill. ; 24 cm. - International series in pure and applied mathematics .

Includes bibliographical references and index.

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. Table of contents



0070575401 : 9780070575400

90033686


Differential equations.

QA372 / .S49 1991

515.35 / SID 1991

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