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mat293f_assignment_2008

# mat293f_assignment_2008 - MAT293F Vector Calculus Problem...

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1 MAT293F Vector Calculus Problem Assignments, September 2008 1. Multiple Integrals: 1.1 Integrals as a Function of a parameter: Stewart6 Section 16.2 # 3, 9, 17, 19, 29 Section 16.3 # 5, 11, 27, 43, 45, 49, 59 1.2 Differentiability of an Integral with respect to its Parameter: 1) Find the derivatives, dF ( x )/ dx , for the following functions in two ways: (a) integrating first and (b) differentiating first: 2) Find the derivatives, dF ( t )/ dt , for the following functions: 3) Find the derivatives, dF ( x )/ dx , for the following functions: 4) Solve the following integral equations; that is, find the functions f ( x ) which satisfy the following relationships: 5) Given the integral where b is a constant and t is a parameter, show that

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2 6) Evaluate and use the result to help you evaluate: dt xt x () 22 0 + and dt x 2 0 + dt x 3 0 + 7) a) Given that for x > 0 (which can be shown by et d t x xt = + sin 1 1 2 0 integration by parts), evaluate: te tdt t e tdt xt xt −− sin sin and 2 0 0 b) Referring to part a), for x > 0 evaluate: Fx e t t dt xt sin = 0 Use this result to evaluate the integral: sin t t dt 0 1.3 Formal Definition of Double Integrals: Stewart6 Section 16.1 # 4, 5, 9, 15 1.4 Polar Coordinates: Stewart6 Section 16.4 # 7, 11, 17, 25, 27, 31, 36 1.5 Applications of Double Integrals: Stewart6 Section 16.5 # 1, 7, 9, 15, 17, 19
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mat293f_assignment_2008 - MAT293F Vector Calculus Problem...

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