Complx Variables MATH 4337
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This 3 page Class Notes was uploaded by Ms. Ismael Spinka on Sunday October 11, 2015. The Class Notes belongs to MATH 4337 at East Tennessee State University taught by Staff in Fall. Since its upload, it has received 39 views. For similar materials see /class/221403/math-4337-east-tennessee-state-university in Mathematics (M) at East Tennessee State University.
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Date Created: 10/11/15
73 Partial Fractions 1 Chapter 7 Integration Techniques l Hopital s Rule and Improper Integrals 73 Partial Fractions Note Consider 1 m We can see that we have the algebraic identity 1 12 12 1 2T1 1 3639 1 f 12 12 712d 7 1d1d 1 1 ln1 ln1 Then we have 13 1 ZC 13 1 ZC tanhilajif lt1 ln In if lt1 Dgt Dgt D What simpli ed this computation was breaking up the denominator and undoing the common denominator process This will be the idea of the method of this section which is called the method of partial fractions 73 Partial Fractions 2 Note A polynomial with real coef cients can be factored into linear factors 33 n and irreducible quadratics 2 pja qj To show this we need to know some complex variables this result is presented in our Complex Variables class MATH 43375337 Note Method of Partial actions If f and g are polynomials to integrate fg 1 lf the degree of f is greater than or equal to the degree of g perform long division 2 Factor 9 into linear factors 33 7quot and irreducible quadratics 2 pa q 3 For each linear factor 33 7quot of g of order m that is 33 7quot divides g m times take the partial fractions A1 ii as r as r as r 4 For each irreducible quadratic factor 362 p36 q of g of order 71 take the partial fractions Blas 01 Egg 02 B7133 On 2pq 2pq2 2pq 39 5 Set fg equal to the sum of all partial fractions 7 3 Partial Fractions 3 6 Evaluate the As 37s and 07s and integrate With the methods you already know Examples Page 563 number 16 page 564 numbers 20 26 and 48 Note The following is the Heaviside Cover Up Method77 Example Page 560 Example 7
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