Nonlinear differential equations
This report is the text of a graduate course on nonlinear differential equations given by the author at the University of Wisconsin-Madison during the summer of 1987. The topics covered are: direction fields of first-order differential equations; the Lie (group) theory of ordinary differential equations; similarity solutions of second-order partial differential equations; maximum principles and differential inequalities; monotone operators and iteration; complementary variational principles; and stability of numerical methods. The report should be of interest to graduate students, faculty, and practicing scientists and engineers. No prior knowledge is required beyond a good working knowledge of the calculus. The emphasis is on practical results. Most of the illustrative examples are taken from the fields of nonlinear diffusion, heat and mass transfer, applied superconductivity, and helium cryogenics.
- Research Organization:
- Oak Ridge National Lab. (ORNL), Oak Ridge, TN (United States)
- DOE Contract Number:
- AC05-84OR21400
- OSTI ID:
- 5495671
- Report Number(s):
- ORNL/TM-10655; ON: DE88006047; TRN: 88-011016
- Resource Relation:
- Other Information: Portions of this document are illegible in microfiche products. Original copy available until stock is exhausted
- Country of Publication:
- United States
- Language:
- English
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Related Subjects
MATHEMATICS
NONLINEAR PROBLEMS
DIFFERENTIAL EQUATIONS
CRYOGENICS
MASS TRANSFER
NUMERICAL SOLUTION
PARTIAL DIFFERENTIAL EQUATIONS
REVIEWS
STABILITY
SUPERCONDUCTIVITY
VARIATIONAL METHODS
DOCUMENT TYPES
ELECTRIC CONDUCTIVITY
ELECTRICAL PROPERTIES
EQUATIONS
PHYSICAL PROPERTIES
990230* - Mathematics & Mathematical Models- (1987-1989)