252 Mid2_info.pdf - Math 252 Midterm 2 info Date April 15 Monday Location Normal classroom Time In-class(10:20-11:40am Note Calculators and other

252 Mid2_info.pdf - Math 252 Midterm 2 info Date April 15...

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Math 252 - Midterm 2 info Date: April 15, Monday Location: Normal classroom Time: In-class (10:20-11:40am) Note: Calculators and other electronic devices are prohibited . All calculations will be able to be completed by hand. Suggestions: 1. Read over covered sections in the textbook, as well as notes from class. 2. Understand all assigned homework questions. 3. Do the review problems posted on the course site. 4. Solve other (unassigned) homework questions from the same section of the textbook. Material: Sections 2.2 and 2.3 , all sections in Chapter 3 and the material Matrix Exponential uploaded on Sakai. Some key topics to review are given below. But be aware: this list is not exhaustive, and anything covered could appear on the exam. (a) Know definitions and theorems. (b) Able to calculate eigenvalues and corresponding eigenvectors, and to form the characteristic polynomial.
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Unformatted text preview: (c) Know behavior of solutions depending on eigenvalues, and phase portrait. (d) Know the classification of the equilibrium point which is the origin (e) Tell how the solution behaves as t → ∞ (f) Able to solve second-order linear equations. (g) Know harmonic oscillator - converting from a second order DE to a linear system, vice versa; classification of it. (h) Understand the trace-determinant plane. (i) Able to analyze one-parameter or two-parameter family of linear systems. 1 (j) Know how to calculate determinant of a 3 × 3 matrix. (k) Able to solve a linear system in three dimentsions. (l) Know how the system decouples. (m) Know how to calculate matrix exponential e At where A is a n × n matrix. (n) Able to get a solution of an initial value problem by using matrix exponential and matrix similarity. 2...
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