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Differential equations, with applications and historical notes /
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...
| Main Authors: | , |
|---|---|
| Format: | Printed Book |
| Language: | English |
| Published: |
Chennai:
McGraw-Hill,
2003.
|
| Edition: | 2nd ed. |
| Subjects: |
| LEADER | 02787nam a22002057a 4500 | ||
|---|---|---|---|
| 008 | 200630b ||||| |||| 00| 0 eng d | ||
| 020 | |a 978007053013 | ||
| 082 | |a 515.35 | ||
| 100 | |a Simmons, George F | ||
| 245 | |a Differential equations, with applications and historical notes / |c George F Simmons and John S. Robertson -- a new chapter on numerical methods | ||
| 250 | |a 2nd ed. | ||
| 260 | |a Chennai: |b McGraw-Hill, |c 2003. | ||
| 300 | |a xxi, 629 p. |b ill. |c 24 cm. | ||
| 505 | |a 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. | ||
| 520 | |a 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 methods. | ||
| 650 | |a Differential equations. |v Équations différentielles. | ||
| 700 | |a John S. Robertson. |e Author | ||
| 942 | |c BK | ||
| 999 | |c 351262 |d 351262 | ||
| 952 | |0 0 |1 0 |2 ddc |4 0 |6 515_350000000000000_SIM_D |7 0 |9 405807 |a SDE |b SDE |c ST1 |d 2020-06-30 |g 775.00 |i 4766 |l 0 |o 515.35 SIM/D |p SDE4766 |r 2020-06-30 |y BK | ||