1. Time Scales Martin Bohner Missouri S&T Universidade de Brasília
7/29/2018
Time Scales
Martin Bohner
Missouri S&T
Universidade de Brasília
May 25, 2017
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2. Differential Calculus
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3. Difference Calculus
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4. Quantum Calculus
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5. Unifying Continuous and Discrete Analysis
7/29/2018
“A major task of mathematics
today is to harmonize the continuous
and the discrete, to include them in
one comprehensive mathematics,
and to eliminate obscurity from both.”
E.T. Bell, 1937
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6. Time Scales Calculus
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7. Time Scales Cover Story in New Scientist
Time Scales Cover Story in New Scientist
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8. The Time Scales Calculus
If the time scale is
The set of all real numbers, the (delta) derivative is the usual derivative
The set of all integers, the (delta) derivative is the usual forward difference
The set of all nonnegative integer powers of a number q>1, the (delta) derivative is the usual Jackson derivative
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9. Some Time Scales
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10. Jump Operators and Graininess
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11. Insect Populations
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12. Delta Derivative
SUF
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13. Product Rule and Quotient Rule
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14. Taylor’s Formula
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15. Chain Rule
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16. May 25, 2017
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17. The Regressive Group
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18. The Exponential Function
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19. Circle Dot
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20. Regressive Vector Space
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21. Variation of Parameters
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22. The Laplace Transform
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23. Table of Laplace Transforms
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24. Example
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25. Example
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26. Convolution Theorem
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27. 7/29/2018
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