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Unformatted text preview: MA366 Sathaye Final Thoughts First, some general advice. Review notes (class and on line), quizzes and old exams. You will be allowed three sheets of notes to be used during the exam. Be sure to have these hand written or typed, but not Xerox copies of printed material. Make sure that your notes are accurate and understandable. No calculators are allowed. Be sure to review your integration skills and algebraic manipulations. If you tend to forget some of the formulas, write them down in your notes. Verify the time an place of the exam carefully. We now describe how to prepare for the final exam. 1. Basic Theory. • Review the basic definitions of linear/ nonlinear equations, order of equations and concept of a solution. • Review the fundamental theorems of existence and uniqueness for linear as well as nonlinear equations of order 1. Also review how the theorems are modified for higher order equations and linear systems. 2. Equations of order 1. • Study the precise method to solve a first order linear equation. Review necessary integration skills. • Learn how to recognize a separable equation and how to solve it. Note that in general, it is difficult to solve in terms of y , but you should be able to solve for y if needed. • A special case of separable equations is the case of autonomous equation y = f ( y ). Review how the phase line is constructed and how to sketch sample solution curves to illustrate the nature of solutions. Be sure to review the concepts of critical points (equilibrium solutions).nature of solutions....
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- Fall '09
- Quadratic equation, Elementary algebra, Nonlinear system