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Engineering Mathematics

Complex Variables & Applications Chapter 3. Engineering Mathematics. 郑伟诗 wszheng@ieee.org, http://sist.sysu.edu.cn/~zhwshi/. Exponential Function Logarithmic Function Complex Exponents. Outline. Exponential Function. Definition :. 3. Equivalent between two complex variables.

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Engineering Mathematics

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  1. Complex Variables & Applications Chapter 3 Engineering Mathematics • 郑伟诗 • wszheng@ieee.org, • http://sist.sysu.edu.cn/~zhwshi/

  2. Exponential Function Logarithmic Function Complex Exponents Outline 1/7/2020, Page 2

  3. Exponential Function Definition: 3

  4. Equivalent between two complex variables Exponential Function 1/7/2020, Page 4

  5. Roots root Exponential Function 1/7/2020, Page 5

  6. Exponential Function The definition of exponential function is equivalent to the expression: Sum Rule: 6

  7. Exponential Function >0

  8. Exponential Function *Example 1: *Solution: 8

  9. Exponential Function 9

  10. Exponential Function Example 2: Compute the principal angles Give the principal value of argument: Solution: 10

  11. Exponential Function 11

  12. Exponential Function Example 3: Solution: 12

  13. Exponential Function Example 4: ?

  14. Logarithmic Function 1.Definition: 14

  15. Logarithmic Function

  16. Logarithmic Function

  17. Logarithmic Function

  18. Logarithmic Function Review

  19. Logarithmic Function

  20. Branch Logarithmic Function

  21. Branch Cut Logarithmic Function

  22. Logarithmic Function branch cut(including the origin) f(z) singular points F(z) branch

  23. Logarithmic Function *Example 4: *Solution: *Remark: Among Functions of Real Variable, negative numbers do not have logarithm, yet complex variable logarithmic function is the extension of real variable logarithmic function. 23

  24. Logarithmic Function *Example 5: *Solution: 24

  25. Logarithmic Function *Example 6: *Solution: 25

  26. Logarithmic Function 26

  27. Logarithmic Function Properties: 27

  28. Logarithmic Function Properties: 4) 5) 6) 28

  29. Complex Exponents any complex number Definition

  30. Complex Exponents

  31. Complex Exponents Example

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