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 Bruce K. Driver - Springer
These are lecture notes from Real analysis and PDE: Basic Topological, Metric and Banach Space Notions; Riemann Integral and ODE; Lebesbgue Integration; Hilbert Spaces and Spectral Theory of Compact Operators; Complex Variable Theory; etc.
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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'.
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Introductory notes on ordinary and partial differential equations for engineers. The text covers only the most important ideas. Assumed background is calculus and a little physics. Linear algebra is introduced in four of the lectures.
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Trench includes a thorough treatment of boundary-value problems and partial differential equations and has organized the book to allow instructors to select the level of technology desired. This has been simplified by using symbols, C and L ...