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Unformatted text preview: Mathematics of Engineering - ME17 Final Exam Review, Spring 2008 Note: boxed formulas are so important that you should have them memorized, and should have a good idea how they can be derived or verified • Matlab – assigning a matrix; view element, row, column of matrix in Matlab – +- * .* / ./ ^ .^ ’ – plot, semilogx, semilogy, loglog, subplot, title, xlabel, ylabel – trig functions, abs, sqrt, exp, log, log10 – max, min, sum, cumsum, prod, cumprod – logical statements in Matlab: if statement, ~ & | == – functions: external, inline, anonymous – loops: for, while – you will need to write a short Matlab program on the exam! • probability – basic definitions, rules for mutually exclusive events and independent events – probability distribution functions – expected values • matrices – matrix addition, subtraction, multiplication – calculate determinant, trace, eigenvalues/eigenvectors, transpose of matrix determinant = product of eigenvalues, trace = sum of eigenvalues – inverse of matrix, including “trick” for 2 × 2 matrices: a b c d !- 1 = 1 ad- bc d- b- c a ! – calculate norms of matrix - don’t need to memorize formulas, but should know how to use – LU decomposition – proofs using indices, for example ( AB ) C = A ( BC ) trace( AB ) = trace( BA ) , ( AB ) T = B T A T • basics of complex numbers – Euler formula e ix = cos( x ) + i sin( x ) – going from Cartesian to polar coordinates and vice versa • basics of calculus –...
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This document was uploaded on 12/29/2011.
- Fall '09