Across
- 3. what solutions to some differential equations tend toward in the long run
- 4. in a growth model, the maximum population that the environment can sustain is the ___ capacity
- 5. when a linear system has two real roots that are both below zero, it behaves like a ___ around the origin
- 7. this type of differential equation is time independent
- 10. 1/recovery parameter
- 12. the sum of the elements on the main diagonal of a matrix is equal to this
- 15. if forcing frequency and natural frequency are the same, the oscillator is in this state
- 17. this is a special kind of solution when the differential equation is equal to zero
- 18. this occurs when the forced response and natural response are approximately the same
- 22. when a linear system sits on the parabola in the trace-determinant plane, it has this kind of roots
- 23. a line diagram that shows the qualitative behavior of an autonomous ordinary differential equation in a single variable
- 24. one of the eigenvalues of the system y’’ - 3y’ + 2y = 0
- 25. the particular solution to y’’ + y = 2cost (no parentheses in answer)
- 27. the bifurcation value for the differential equation dy/dt = y² - 2y + 𝜇
- 28. a classification of equilibrium solutions on a phase line in which the curve goes away from the equilibrium in both directions
- 29. when a harmonic oscillator has no friction on it
- 30. this kind of matrix has all first-order partial derivatives of several variables
Down
- 1. the basic reproduction number is equal to this multiplied by the average contact rate and the duration of the infection
- 2. a method of solving differential equations involving the product rule
- 6. these types of eigenvalues require Euler’s Formula to find a general solution
- 8. in an equation for an oscillator, when the coefficient for the first differential term equals zero, it is called a ___ harmonic oscillator
- 9. quantities that do not change with the independent variable
- 11. this type of linear differential equation has a constant term b that is not equal to zero
- 13. this is a principle stating that the sum of two solutions to a linear equation added together is also a solution
- 14. the values of a parameter that change the number of roots there are
- 16. this percentage of the population needs to be vaccinated given a basic reproduction number equal to 5 (give the answer as the written form of the number)
- 19. equilibrium behavior when both eigenvalues are real and distinct and one is positive and one is negative
- 20. a system in which both differential equations are autonomous
- 21. another name for a sink is a ___ fixed point
- 26. the first compartment of an SIR Model that the population starts in