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Review

# Review - back of the Huges-Hallett text on this test as...

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Math 254 Review test Thursday January 24 th There will be a 30 minute review test at the start of class on Thursday January 24th. The reason we have this review test is to make sure that you are all fully up to speed on the prerequisite material. Success in this course requires that you are able to quickly and correctly apply your knowledge from Calculus (and algebra). The test will cover diﬀerentiation, integration, (very) basic power series, and a little bit of complex arithmetic. The material on diﬀerentiation will be taken from the review problems 1-66 at the end of chapter 3 in “Calculus of a Single Variable” by Hughes-Hallett et al. This is the text we use in math 124, 125 and 129. The integration will be taken from problems 1-120 in the review problems at the end of chapter 7. For your convenience, the problems and the solutions for the odd numbers are posted on D2L (under content- handouts). You will be given the table of integrals (also posted) as in the
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Unformatted text preview: back of the Huges-Hallett text on this test as well as on all of our exams. You will also be tested on your knowledge of the basic power series ex-pansions for: e x , sin( x ) , cos( x ) , 1 1-x (geometric series) , and (1 + x ) α (binomial expansion) Note that the value of α can be any number, not just positive integers. The ﬁnal topic that is included on the review test is the basics of complex arithmetic. You should know how to add, subtract, multiply and divide using complex numbers, and you should be able to convert between Cartesian and polar form using: x + iy = re iθ = r (cos θ + i sin θ ) where r = q x 2 + y 2 , θ = arctan( y/x ) x = r cos θ, y = r sin θ Please do bear in mind that the formula for θ above only determines θ up to a multiple π radians. To determine whether you need to add π , you look at which quadrant in the complex plane you are in. 1...
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