A primer of infinitesimal analysis/
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| Format: | Book |
| Language: | English |
| Published: |
Cambridge:
Cambridge University Press,
2008
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| Edition: | 2nd ed. |
| Subjects: |
Table of Contents:
- 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.