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Numerical Methods Introduction to Fourier Series Part: Introduction to Fourier Series http://numericalmethods.eng.usf.ed

Numerical Methods Introduction to Fourier Series Part: Introduction to Fourier Series http://numericalmethods.eng.usf.edu. For more details on this topic Go to http://numericalmethods.eng.usf.edu Click on Keyword Click on Introduction to Fourier Series. You are free.

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Numerical Methods Introduction to Fourier Series Part: Introduction to Fourier Series http://numericalmethods.eng.usf.ed

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  1. Numerical MethodsIntroduction to Fourier SeriesPart: Introduction to Fourier Serieshttp://numericalmethods.eng.usf.edu

  2. For more details on this topic • Go to http://numericalmethods.eng.usf.edu • Click on Keyword • Click on Introduction to Fourier Series

  3. You are free • to Share – to copy, distribute, display and perform the work • to Remix – to make derivative works

  4. Under the following conditions • Attribution — You must attribute the work in the manner specified by the author or licensor (but not in any way that suggests that they endorse you or your use of the work). • Noncommercial — You may not use this work for commercial purposes. • Share Alike — If you alter, transform, or build upon this work, you may distribute the resulting work only under the same or similar license to this one.

  5. Chapter 11.01: Introduction to Fourier Series Lecture # 1 Major: All Engineering Majors Authors: Duc Nguyen http://numericalmethods.eng.usf.edu Numerical Methods for STEM undergraduates 4/2/2014 http://numericalmethods.eng.usf.edu 5

  6. Background The following relationships can be readily established (1) (2) 1 6 http://numericalmethods.eng.usf.edu

  7. Background cont. (3) (4) (5) http://numericalmethods.eng.usf.edu

  8. Background cont. (6) (7) Where and represents the frequency in (cycles/time) and period (in seconds) respectively. A periodic function with a period should satisfy the following equation: (8) 8 http://numericalmethods.eng.usf.edu

  9. Background cont. Example 1 Let (9) http://numericalmethods.eng.usf.edu

  10. Background cont. (10) http://numericalmethods.eng.usf.edu

  11. Background cont. Example 2 Let (11) Recall (12) (13) http://numericalmethods.eng.usf.edu

  12. Background cont. (14) http://numericalmethods.eng.usf.edu

  13. Background cont. Example 3 Let (15) http://numericalmethods.eng.usf.edu

  14. Background cont. Recall that (16) (17) http://numericalmethods.eng.usf.edu

  15. Background cont. (18) (19) Adding Equations (15), (19), (20) http://numericalmethods.eng.usf.edu

  16. Background cont. since the right side of the above equation is zero Thus, (21) http://numericalmethods.eng.usf.edu

  17. The End http://numericalmethods.eng.usf.edu

  18. Acknowledgement This instructional power point brought to you by Numerical Methods for STEM undergraduate http://numericalmethods.eng.usf.edu Committed to bringing numerical methods to the undergraduate

  19. For instructional videos on other topics, go to http://numericalmethods.eng.usf.edu/videos/ This material is based upon work supported by the National Science Foundation under Grant # 0717624. Any opinions, findings, and conclusions or recommendations expressed in this material are those of the author(s) and do not necessarily reflect the views of the National Science Foundation.

  20. The End - Really

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