mt_review

mt_review - • loops for while • probability – basic...

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Mathematics of Engineering - ME17 Midterm Review, Spring 2008 basic manipulations of matrices with Matlab and by hand assigning a matrix in Matlab view element, row, column of matrix in Matlab + - * .* / ./ ^ .^ ’ matrix addition, subtraction, multiplication inverse of matrix, trick for 2 × 2 matrices ± a b c d ! - 1 = 1 ad - bc ± d - b - c a ! calculate rank, determinant, trace, eigenvalues/eigenvectors of matrix plotting commands in Matlab plot, semilogx, semilogy, loglog, subplot, title, xlabel, ylabel curve ﬁtting plots using logarithmic axes * y = Ax b plotting log 10 ( y ) vs. log 10 ( x ) gives straight line * y = A × 10 λx plotting log 10 ( y ) vs. x gives straight line * x = A × 10 λy plotting y vs. log 10 ( x ) gives straight line Matlab functions trig functions, abs, sqrt, exp, log, log10 max, min, sum, cumsum, prod, cumprod logical statements in Matlab if statement ~ | == external, inline, anonymous functions

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Unformatted text preview: • loops: for, while • probability – basic deﬁnitions – rules for mutually exclusive events and independent events – probability distribution functions – expected values • Limits – deﬁnition – calculation using Taylor series, using L’Hospital • Derivatives – deﬁnition – product rule, chain rule, quotient rule • Integrals – deﬁnition as area under a function – fundamental theorems of calculus – solving using substitution, integration by parts • Taylor series f ( x ) = f ( c ) + f ( c )( x-c ) + f 00 ( c ) 2! ( x-c ) 2 + ··· • basics of complex numbers – Euler formula e ix = cos( x ) + i sin( x ) – going from Cartesian to polar coordinates • you will need to write a short Matlab program on the exam!...
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mt_review - • loops for while • probability – basic...

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