Topics in dynamics I: Flows
by Edward Nelson
Publisher: Princeton University Press 1969
Number of pages: 122
These are the lecture notes for the first term of a course on differential equations, given in Fine Hall the autumn of 1968. The text covers differential calculus, Picard's method, the local structure of vector fields, sums and Lie products of vector fields, self-adjoint operators on Hilbert space, commutative multiplicity theory, extensions of Hermitean operators, sums and Lie products of self-adjoint operators.
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by M. Kuranishi - Tata Institute of Fundamental Research
Contents: Parametrization of sets of integral submanifolds (Regular linear maps, Germs of submanifolds of a manifold); Exterior differential systems (Differential systems with independent variables); Prolongation of Exterior Differential Systems.
by H.T.H. Piaggio - G. Bell
The object of this book is to give an account of the central parts of the subject in as simple a form as possible, suitable for those with no previous knowledge of it, and to point out the different directions in which it may be developed.
by Paul Dawkins - Lamar University
Contents: Basic Concepts; First Order Differential Equations; Second Order DE; Laplace Transforms; Systems of Differential Equations; Series Solutions; Higher Order DE; Boundary Value Problems and Fourier Series; Partial Differential Equations.
by Andrew Fowler - University of Oxford
This course develops mathematical techniques which are useful in solving 'real-world' problems involving differential equations. The course embraces the ethos of mathematical modelling, and aims to show in a practical way how equations 'work'.