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Unformatted text preview: Math 5A - Final Exam Review Problems Winter 2009 The exam will be cumulative, but focus more on topics covered since the second midterm: Sections 6.1 - 6.4, 6.7 and 7.1-7.2. Below is an outline of the key topics (from the new material only) and sample problems of the type you may be asked on the test. Many are similar to homework problems you have done–just remember that you will be required to show your work and/or justify your answers on the exam. Solving 2x2 Homogeneous, Linear Systems of DEs. A homogeneous, linear 2 × 2 system has the form x = ax + by y = cx + dy for real numbers a, b, c, d . Writing ~x for the vector x y , and A = a b c d , we have the matrix form of the system ~x = A~x . To find the general solution of the system, you will need to find the eigenvalues and eigenvectors of A first. You should also be able to solve initial value problems. • 6.2: Real Eigenvalues. There are two different formulas you need to know: one (p. 358) for the case where A has distinct eigenvalues, and the other (p. 365) for the case where A has a single repeated eigenvalue....
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- Winter '07
- Math, Eigenvalue, eigenvector and eigenspace, Fundamental physics concepts, Equilibrium point, Nonlinear system, Stability theory