Applications of Lie's Theory of Ordinary and Partial by L Dresner

By L Dresner

Lie's staff idea of differential equations unifies the various advert hoc tools recognized for fixing differential equations and gives strong new how one can locate ideas. the idea has functions to either traditional and partial differential equations and isn't limited to linear equations. functions of Lie's thought of normal and Partial Differential Equations presents a concise, uncomplicated creation to the appliance of Lie's thought to the answer of differential equations. the writer emphasizes readability and immediacy of figuring out instead of encyclopedic completeness, rigor, and generality. this permits readers to fast take hold of the necessities and begin utilizing the the way to locate options. The publication contains labored examples and difficulties from a variety of medical and engineering fields.

Show description

Read or Download Applications of Lie's Theory of Ordinary and Partial Differential Equations PDF

Best mathematical physics books

An Introduction to Chaos in Nonequilibrium Statistical Mechanics

This ebook is an creation to the purposes in nonequilibrium statistical mechanics of chaotic dynamics, and in addition to using innovations in statistical mechanics very important for an realizing of the chaotic behaviour of fluid platforms. the basic thoughts of dynamical structures thought are reviewed and easy examples are given.

Labyrinth of Thought: A History of Set Theory and Its Role in Modern Mathematics

"José Ferreirós has written a magisterial account of the heritage of set conception that's panoramic, balanced, and fascinating. not just does this ebook synthesize a lot prior paintings and supply clean insights and issues of view, however it additionally contains a significant innovation, a full-fledged therapy of the emergence of the set-theoretic method in arithmetic from the early 19th century.

Computational Physics: Problem Solving with Python

Using computation and simulation has develop into an important a part of the medical strategy. having the ability to remodel a concept into an set of rules calls for major theoretical perception, designated actual and mathematical knowing, and a operating point of competency in programming. This upper-division textual content presents an strangely large survey of the themes of contemporary computational physics from a multidisciplinary, computational technology viewpoint.

Additional resources for Applications of Lie's Theory of Ordinary and Partial Differential Equations

Sample text

10 A curve C2 is said to be parallel to a curve CI if the distance from C I along its normal to the curve C2 is the same for all points of C l . (a) Prove that any normal to the curve CI is also normal to the curve C2. (b) Imagine the (x, y)-plane filled with the one-parameter family F of curves parallel to Cl . Denote by Cs the curve parallel to C1 at a distance 6 from C1. Define the set of transformations T, of points P: (x, y) into images P': (x', y') in the following way. Through the point P passes a curve C, of the family F.

2 Find a group which leaves the differential equation y = xy(1 In y x2) invariant, and using Lie's integrating factor find the general solution. 3 The linear, first-order, inhomogeneous differential equation y P(x) y = Q(x) has the well-known integrating factor exp(l," P ( 2 ) dz). (Here z is a dummy variable of integration. 2) to find the transformation equations of two different groups to which this differential equation is invariant. 4 Find a group under which the differential equation Y = ax + by c is invariant, calculate Lie's integrating factor and find the integral curves of the differential equation.

Now since xt3y'= x'y and ~ ' ~ j=l x4jl, y'(xt) of p(x) determines the same locus in the (p, 9)-plane as the curve y(x) itself. 1. The curves on which dqldp = 0 or dqldp = koo divide the plane into regions in which the algebraic sign of dq/dp is constant. The locus of zero slope Co is the curve 44 p2/*= 0 and the locus of infinite slope C, is the line 3 p q = 0. The intersections of these loci are the singular points of the differential equation. 1. 14~). Co is the locus of zero slope and C, is the locus of infinite slope.

Download PDF sample

Rated 4.38 of 5 – based on 11 votes