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MAT 4725 Numerical Analysis Section 1.4 Loops with “do” statements http://myhome.spu.edu/lauw
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Homework Download homework from the web Read 2.1.4 while-do loop 1.6.1 documentations 1.6.2 format printing Quiz on 1.6.2, we will not lecture on that section
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Preview Monotonic Sequence Theorem (Stewart, section 12.1) Introduce the first type of repetition statements – the for loop Allow a specific section of code to be executed a number of times Introduces simple arrays
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Definition A sequence {a n } is bounded above if M such that a n M n A sequence {a n } is bounded below if m such that a n m n
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Monotonic Sequence Theorem The following sequences are convergent Increasing and bounded above Decreasing and bounded below
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Example Show that the sequence defined by is convergent and find its limit.
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Example From homework 01, we know
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Zeng Section 1.4 Please listen to the explanations before you type in the program. It takes one minute to explain.
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Example 1 Print the square of the first 10 positive integers What is the task being repeated?
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Example 1
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1210 14100
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Example 1 > sq(); 1 4 9
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Structure of the for loop
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Example 2 Print the square of the first 10 positive odd integers
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Example 2
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> sq2(); 1 9 25
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Example 3 Print the square of the first n positive integers
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Example 3 Print the square of the first n positive integers Introduces array and seq Note that these commands are not necessary here
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Example 3
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> sq3(2); 1, 4 > sq3(5); 1, 4, 9, 16, 25
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Example 4 Fibonacci sequence is defined by
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Example 4 Write a program that generate the first n+1 terms of the Fibonacci sequence F 0,F 1,…,F n
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Example 4
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What happen if we do not initialize F?
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Example 4 Why there is no print statement?
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Example 4
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Example 5 Write a program, for the input of x and n, to approximate the value of sin(x) by the first sum of the first n+1 terms in the Taylor series.
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Example 5
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