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Complx Variables

by: Ms. Ismael Spinka

Complx Variables MATH 4337

Ms. Ismael Spinka
GPA 3.5


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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 27 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
83 Integration of Rational Functions by Partial Piractions 1 Chapter 8 Techniques of Integration 83 Integration of Rational Functions by Partial Fractions Note Consider 1 A We can see that we have the algebraic identity 1 f 12 12 1 962T1 1 33 Then we have 1 12 12 712d d d ln1 ln1 C 1x 1 96 1x 1 96 tanh71Cif lt1 0 1n Ciflt1 1 2 1 1n 2 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 section7 which is called the method of partial fractions 83 Integration of Rational Functions by Partial Piractions 2 Note A polynomial with real coef cients can be factored into linear factors a 7quot and irreducible quadratics 32 77376 qj To show this7 we need to know some complex variables this result is presented in our Complex Variables class7 MATH 4337 5337 Note Method of Partial actions If f and g are polynomials7 to integrate fg 1 If the degree of f is greater than or equal to the degree of 97 perform long division 2 Factor 9 into linear factors a 7quot and irreducible quadratics 32 7376 q 3 For each linear factor a 7quot of g of order m that is7 a 7quot divides g m times7 take the partial fractions A1 ii ac 7quot ac 7quot2 ac 7quot 4 For each irreducible quadratic factor 732 177 q of g of order 717 take the partial fractions 3176 01 3276 02 B713 On ltQPQgt ltQPCD2 ltQpxQgt 39 5 Set fg equal to the sum of all partial fractions 83 Integration of Rational Functions by Partial Piractions 3 6 Evaluate the 147s7 B7s7 and 07s and integrate with the methods you already know Examples Page 579 number 167 207 267 page 580 number 42 Note The following is the Heaviside Cover Up Method77 Example Page 577 Example 7


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