final_review

final_review - Mathematics of Engineering ME17 Final Exam...

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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
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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 Derivatives * definition *
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