1. The Beverton-Holt Dynamic Equation
12/1/2018
The Beverton-Holt Dynamic Equation
Martin Bohner
April 25, 2008
UNL Colloquium

2. This is joint work with Howard Warth
April 25, 2008
UNL Colloquium

3. Beverton-Holt Equation
April 25, 2008
UNL Colloquium

4. Jim Cushing and Shandelle Henson
April 25, 2008
UNL Colloquium

5. Rational Difference Equation
Logistic
April 25, 2008
UNL Colloquium

6. Unifying Continuous and Discrete Analysis
12/1/2018
“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
April 25, 2008
UNL Colloquium

7. Time Scales Calculus
April 25, 2008
UNL Colloquium

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
April 25, 2008
UNL Colloquium

9. Jump Operators and Graininess
April 25, 2008
UNL Colloquium

10. Delta Derivative
SUF
April 25, 2008
UNL Colloquium

11. Product Rule and Quotient Rule
April 25, 2008
UNL Colloquium

12. Quantum Calculus
April 25, 2008
UNL Colloquium

13. April 25, 2008
UNL Colloquium

14. Logistic Dynamic Equation
April 25, 2008
UNL Colloquium

15. Logistic Substitution
April 25, 2008
UNL Colloquium

16. The Regressive Group
April 25, 2008
UNL Colloquium

17. The Exponential Function
April 25, 2008
UNL Colloquium

18. Variation of Parameters
April 25, 2008
UNL Colloquium

19. Solution of the Linear Equation
April 25, 2008
UNL Colloquium

20. Periodicity
April 25, 2008
UNL Colloquium

21. Periodic Solution
April 25, 2008
UNL Colloquium

22. Proof of Cushing-Henson Conjecture
April 25, 2008
UNL Colloquium

23. Harvesting with constant effort
April 25, 2008
UNL Colloquium

24. Harvesting with variable effort
April 25, 2008
UNL Colloquium

25. Kneser’s Theorem
April 25, 2008
UNL Colloquium