MAT 3724 Applied Analysis I

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MAT 3724Applied Analysis I

• 3.2 Part II Theory of Orthogonal Functions

http//myhome.spu.edu/lauw
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Last HW

• Hold on to your HW, you may need it for the
  classwork.

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Quiz Contest

• Each group can prepare and submit a quiz by 10 pm
  tomorrow night.
• If your quiz is adopted for Thursday, you will
  get 8 points for the quiz.
• As usual, the quiz should have 6 answers with
  majority of them fill in the blanks.

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Recall 3.1
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Generalizations

• Given a set of orthogonal functions
• in . For , we want to find
  such that

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Generalizations

• Given a set of orthogonal functions
• in . For , we want to find
  such that

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Convergence

• Skip It!

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How to find the Fourier Coeff.?
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Comparisons

• Taylor Series at x0
• Basis

• Fourier Series on -?,?
• Basis

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Comparisons

• Taylor Series at x0
• Conditions

• Fourier Series on -?,?
• Conditions

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Comparisons

• Taylor Series at x0
• Nature of the
• Approximation

• Fourier Series on -?,?
• Nature of the
• Approximation

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Local Approximation

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Local Approximation
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Local Approximation
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Comparisons

• Taylor Series at x0
• Nature of the
• Approximation

• Fourier Series on -?,?
• Nature of the
• Approximation

QWhich one is better?