Cargando…
A course of mathematics for engineers and scientists. Volume 2 /
A Course of Mathematics for Engineers and Scientists, Volume 2 continues the course of pure and applied mathematics for undergraduate science and engineering students. It contains further examples and exercises from examination papers from Oxford University, Cambridge University, and the University...
| Clasificación: | Libro Electrónico |
|---|---|
| Autores principales: | , |
| Formato: | Electrónico eBook |
| Idioma: | Inglés |
| Publicado: |
Oxford ; New York :
Pergamon Press,
1972.
|
| Edición: | Second edition. |
| Temas: | |
| Acceso en línea: | Texto completo |
Tabla de Contenidos:
- Front Cover; A Course of Mathematics for Engineers and Scientists; Copyright Page; Table of Contents; PREFACE TO THE SECOND EDITION; CHAPTER I.FIRST ORDER DIFFERENTIAL EQUATIONS; 1:1 Introduction-formation of differential equations; 1:2 Simple examples solved by direct integration; 1:3 Separable and homogeneous types; 1:4 First order linear equations-Bernoulli's equation; 1:5 Miscellaneous first order types; 1:6 Orthogonal trajectories and geometrical applications; 1:7 Application to dynamics-resisted motion; 1:8 Other applications; 1:9 Graphical methods; 1:10 Picard's method
- 1:11 The Taylor series method1:12 Step-by-step methods; 1:13 The use of difference formulae; CHAPTER II.LINEAR DIFFERENTIAL EQUATIONS; 2:1 Introduction and general principles; 2:2 Linear differential equations with constant coefficients-the operator D; 2:3 Homogeneous linear differential equations; 2:4 Simultaneous linear differential equations with constant coefficients; 2:5 Special methods for the solution of differential equations of the second order; 2:6 Separable partial differential equations; 2:7 Simple applications to particle dynamics; 2:8 Applications to electric circuits
- 2:9 Linear difference equations2:10 Step-by-step methods for second and higher order differential equations; 2:11 Predictor-corrector methods; 2:12 Build-up of error; CHAPTER III. LINEAR EQUATIONS, MATRICES AND DETERMINANTS; 3:1 Introduction; 3:2 Linear equations in two unknowns; 3:3 Matrix notation; 3:4 The determinant of a matrix; 3:5 Matrix algebra; 3:6 Some properties of determinants; 3:7 The solution of linear equations; 3:8 The use of triangular matrices; 3:9 Singular matrices; 3:10 Linear dependence; 3:11 Eigenvalues and eigenvectors
- CHAPTER IV. VECTOR ALGEBRA AND COORDINATE GEOMETRY OF THREE DIMENSIONS4:1 The concept of a vector; 4:2 Cartesian coordinates and elements; 4:3 The definitions of vectors and scalars; 4:4 The addition and subtraction of vectors; 4:5 The scalar product; 4:6 The vector product; 4:7 Triple products; 4:8 Surfaces in general; 4:9 Special characteristics of surfaces; 4:10 The sphere; 4:11 The standard equation of a quadric surface; 4:12 Curves in space; 4:13 Differentiation and integration of vectors with respect to a scalar parameter; CHAPTER V.PARTIAL DIFFERENTIATION
- 5:1 Continuity and partial derivatives5:2 Applications of the Mean Value Theorem; 5:3 Differentiation under the integral sign; 5:4 Taylor's theorem; 5:5 Tangent plane and normal to a surface; 5:6 Maxima and minima; 5:7 Conditional stationary points; 5:8 The Method of Least Squares; 5:10 Jacobian; CHAPTER VI.MULTIPLE INTEGRALS; 6:1 Area integrals; 6:2 Volume integrals; 6:3 Change in the order of integration in repeated integrals; 6:4 Change of variables in multiple integrals; 6:5 Applications of multiple integrals; 6:6 Some special integrals: Gamma and Beta Functions; ANSWERS TO THE EXERCISES