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Unformatted text preview: IEEE Revision Lecture for MA1505 Tutor: Hu Hengnan 16 Nov 2010 Hu Hengnan (NUS) IEEE Revision Lecture 16 Nov 2010 1 / 36 Outline In these two hour, we are going to follow this arrangement: Take about 20 minutes to demonstrate some basic concepts and useful formulas. Take about 70 minutes or so to work through all the problems in detail. The rest of time is up to you. Hu Hengnan (NUS) IEEE Revision Lecture 16 Nov 2010 2 / 36 Outline In these two hour, we are going to follow this arrangement: Take about 20 minutes to demonstrate some basic concepts and useful formulas. Take about 70 minutes or so to work through all the problems in detail. The rest of time is up to you. Hu Hengnan (NUS) IEEE Revision Lecture 16 Nov 2010 2 / 36 Outline In these two hour, we are going to follow this arrangement: Take about 20 minutes to demonstrate some basic concepts and useful formulas. Take about 70 minutes or so to work through all the problems in detail. The rest of time is up to you. Hu Hengnan (NUS) IEEE Revision Lecture 16 Nov 2010 2 / 36 Outline In these two hour, we are going to follow this arrangement: Take about 20 minutes to demonstrate some basic concepts and useful formulas. Take about 70 minutes or so to work through all the problems in detail. The rest of time is up to you. Hu Hengnan (NUS) IEEE Revision Lecture 16 Nov 2010 2 / 36 Part I Related Concepts and Formulas Hu Hengnan (NUS) IEEE Revision Lecture 16 Nov 2010 3 / 36 Statistics of the All 13 Problems Taylor Series: 3 Qns Fourier Series: 1 Qns and 3 other Qns mentioned Series sums: 4 Qns line integral: 1 Qns related Surface integral: 4 Qns Hu Hengnan (NUS) IEEE Revision Lecture 16 Nov 2010 4 / 36 Taylor Series What is Taylor Series:In brief,change function f ( x ) to the sum of Power series. For example the Taylor series of f ( x ) at x = a is the following Power series at x = a : f ( x ) = ∑ ∞ n = f ( n ) ( a ) n ! ( x a ) n . Classical results: e x = 1 + x + x 2 2 ! + ... = ∑ ∞ n = x n n ! . 1 1 + x = ∑ ∞ n = ( 1 ) n t n sin x = ∑ ∞ n = ( 1 ) n x 2 n + 1 ( 2 n + 1 )! Hu Hengnan (NUS) IEEE Revision Lecture 16 Nov 2010 5 / 36 Taylor Series What is Taylor Series:In brief,change function f ( x ) to the sum of Power series. For example the Taylor series of f ( x ) at x = a is the following Power series at x = a : f ( x ) = ∑ ∞ n = f ( n ) ( a ) n ! ( x a ) n . Classical results: e x = 1 + x + x 2 2 ! + ... = ∑ ∞ n = x n n ! . 1 1 + x = ∑ ∞ n = ( 1 ) n t n sin x = ∑ ∞ n = ( 1 ) n x 2 n + 1 ( 2 n + 1 )! Hu Hengnan (NUS) IEEE Revision Lecture 16 Nov 2010 5 / 36 Taylor Series What is Taylor Series:In brief,change function f ( x ) to the sum of Power series. For example the Taylor series of f ( x ) at x = a is the following Power series at x = a : f ( x ) = ∑ ∞ n = f ( n ) ( a ) n !...
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 Math, Factorials

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