Cargando…
A primer of infinitesimal analysis /
One of the most remarkable recent occurrences in mathematics is the refounding, on a rigorous basis, of the idea of infinitesimal quantity, a notion which played an important role in the early development of the calculus and mathematical analysis. In this new edition basic calculus, together with so...
| Clasificación: | Libro Electrónico |
|---|---|
| Autor principal: | |
| Formato: | Electrónico eBook |
| Idioma: | Inglés |
| Publicado: |
Cambridge ; New York :
Cambridge University Press,
©2008.
|
| Edición: | 2nd ed. |
| Temas: | |
| Acceso en línea: | Texto completo |
Tabla de Contenidos:
- Basic features of smooth worlds
- Basic differential calculus
- The derivative of a function
- Stationary points of functions
- Areas under curves and the constancy principle
- The special functions
- First applications of the differential calculus
- Areas and volumes
- Volumes of revolution
- Arc length; surfaces of revolution; curvature
- Application to physics
- Moments of inertia
- Centres of mass
- Pappus' theorems
- Centres of pressure
- Stretching a spring
- Flexure of beams
- The catenary, the loaded chain, and the bollard-rope
- The Kepler-Newton areal law of motion under a central force
- Multivariable calculus and applications
- Partial derivatives
- Stationary values of functions
- Theory of surfaces. Spacetime metrics
- The heat equation
- The basic equations of hydrodynamics
- The wave equation
- The Cauchy-Riemann equations for complex functions
- The definite integral. Higher-order infinitesimals
- The definite integral
- Higher-order infinitesimals and Taylor's theorem
- The three natural microneighbourhoods of zero
- Synthetic differential geometry
- Tangent vectors and tangent spaces
- Vector fields
- Differentials and directional derivatives
- Smooth infinitesimal analysis as an axiomatic system
- Natural numbers in smooth worlds
- Nonstandard analysis.