Calculus Volume 3 · free preview

Nonhomogeneous Linear Equations

Nonhomogeneous equations add a particular solution to the homogeneous's general solution, the undetermined coefficients and variation of parameters the two methods, resonance when the forcing matches a natural frequency.

1. The general solution's structure

The general solution's structure

2. Undetermined coefficients

Undetermined coefficients

3. Variation of parameters

Variation of parameters

4. Resonance and the forced oscillation

Resonance and the forced oscillation

5. General solution structure

The general solution of the nonhomogeneous equation is which sum?

6. Undetermined coefficients guess

For the forcing g = e^(kt), the undetermined coefficients method guesses which form?

7. Resonance signature

When the forcing's frequency matches the natural frequency, the resonance's signature in the solution is what?

8. Variation of parameters scope

The variation of parameters method handles which forcings?

9. Transient and steady state

In the forced damped oscillation, the homogeneous's decaying part and the persistent particular are called what?

10. Resonant guess multiplier

At resonance the guess gains a factor of which variable? Answer with one lowercase letter.

11. Beat frequency

Near resonance the alternating amplitude has which two-word name? Answer like answer key.

12. Wronskian denominator

The variation of parameters divides by which determinant? Answer with one word.

13. Damping's effect on resonance

Including damping, the resonant response becomes which instead of unbounded?

14. Complementary solution

The homogeneous's general solution is also called which two-word name? Answer like answer keys.

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