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- Ordinary Differential Equations | SpringerLink
- Ordinary differential equation
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Special functions are introduced here. Regular and singular perturbation expansion techniques, asymptotic series solutions, dominant balance, and WKB theory are used to determine approximate solutions of linear and nonlinear differential equations. Throughout, the theory is set in the context of examples from applied mathematics and mathematical physics such as nonlinear oscillators, boundary layers and dispersive phenomena. In addition to learning specific skills that will assist students in their future careers in science, they will have the opportunity to develop generic skills that will assist them in any future career path.
These include:. Undergraduate subjects Graduate subjects Research subjects. Breadth search Breadth tracks. About this subject Overview Eligibility and requirements Assessment Dates and times Further information Timetable opens in new window Single page view for printing Contact information Please refer to the specific study period for contact information.
A chain 4 feet long starts with 1 foot hanging over the edge of a table. Neglect friction, and find the time for the chain to slide off the table.
A smooth football having the shape of a prolate spheroid 12 inches long and 6 inches thick is lying outdoors in a rainstorm. Find the paths along which the water will run down its sides. The clepsydra, or ancient water clock, was a bowl from which water was allowed to escape through a small hole in the bottom. It was often used in Greek and Roman courts to time the speeches of lawyers, in order to keep them from talking too much.
Ordinary Differential Equations | SpringerLink
Find the shape it should have if the water level is to fall at a constant rate. I wouldn't even have realized that there was such a path, and I had to ponder for a while to persuade myself that there was. The differential equations class I took as a youth was disappointing, because it seemed like little more than a bag of tricks that would work for a few equations, leaving the vast majority of interesting problems insoluble. Simmons' book fixed that.
All of these cover basic intro ODE for a first look. All have lots of problems, worked solutions, and answers to the other problems. All are easy to read. I don't think some of the other comments and suggestions were responsive to the conditions you mentioned "Ideally it should have a variety of problems with worked solutions and be easy to read.
Ordinary differential equation
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Ideally it should have a variety of problems with worked solutions and be easy to read. Al Jebr 4, 4 4 gold badges 39 39 silver badges 85 85 bronze badges.
Finance Finance 2 2 gold badges 6 6 silver badges 10 10 bronze badges. Teaches the theory; solving equations is not something taught in of itself? Largely acquired as tools - usually in physics.
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Is this the same book? Many course sites have past exams and homework with solutions.
Beats a trip to the bookstore any day. Here are some examples, all from chapter 1: Consider a bead at the highest part of a circle in a vertical plane, and let that point be joined to any lower point on the circle by a straight wire, If the bead slides down the wire without friction, show that it will reach the circle in the same time regardless of the position of the lower point.
This one might be my favorite: A destroyer is hunting a submarine in a dense fog.