Science:Math Exam Resources/Courses/MATH307/December 2012/Question 04 (b)
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Question 04 (b) 

Consider the Fourier series for . (b) The coefficient c_{n} can be written as an inner product . What are ƒ and g? 
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Hint 

Science:Math Exam Resources/Courses/MATH307/December 2012/Question 04 (b)/Hint 1 
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Solution 

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Please rate my easiness! It's quick and helps everyone guide their studies. To compute the coefficient, start with where and . Also, we have L=10=1. Take the inner product of ƒ(t) with . The only term in the infinite sum that remains is the one with , and in this case . Thus and we get the formula Since we have , and so we overall find that 