DIFFERENTIAL EQUATIONS AND THEIR APPLICATIONSPHI Learning Pvt. Ltd., 2004 M01 1 - 528 pages Primarily intended for the undergraduate students in Mathematics, Physics and Engineering, this text gives in-depth coverage of differential equations and the methods of solving them. The book begins with the basic definitions, the physical and geometric origins of differential equations, and the methods for solving first-order differential equations. Then it goes on to give the applications of these equations to such areas as biology, medical sciences, electrical engineering and economics. The text also discusses, systematically and logically, higher-order differential equations and their applications to telecom-munications, civil engineering, cardiology and detec-tion of diabetes, as also the methods of solving simultaneous differential equations and their applica-tions. Besides, the book provides a detailed discussion on Laplace transform and their applications, partial differential equations and their applications to vibration of a stretched string, heat flow, transmission lines, etc., and calculus of variations and its applications. This book, which is a happy fusion of theory and application, would also be useful to postgraduate students. |
Contents
DIFFERENTIAL EQUATIONS OF FIRST ORDER | 27 |
EQUATIONS OF THE FIRST ORDER BUT NOT | 66 |
APPLICATIONS OF FIRST ORDER DIFFERENTIAL | 78 |
HIGHER ORDER LINEAR DIFFERENTIAL EQUATIONS | 162 |
APPLICATIONS OF HIGHERORDER DIFFERENTIAL | 230 |
Exercises | 292 |
SYSTEMS OF LINEAR DIFFERENTIAL EQUATIONS | 299 |
8 | 317 |
LAPLACE TRANSFORMS AND THEIR APPLICATIONS | 353 |
Exercises | 388 |
5 | 399 |
7 | 406 |
Exercises | 439 |
| 485 | |
| 511 | |
Common terms and phrases
a₁ amplitude arbitrary constants assume b₁ boundary conditions c₁ c₁x c₂ c₂e complete solution concentration curve d²x d²y damping denote Differentiating Eq dt dt dx dx dx dy dx/dt dx² dy dx e²x equilibrium position Euler's equation Example Find force Fourier series ft/s function given differential equation given equation glucose Hence indicial equation initial conditions k₁ k₂ Laplace transform linear differential equation m₁ mass motion N₁ Newton's second law obtain ordinary differential equation orthogonal trajectories partial differential equation problem required solution respect roots Separating the variables simple harmonic motion Solution Let solution of Eq Solution The given Solve Substituting tank temperature velocity weight x-axis y₁ zero ди дл др ду дх