Solving Initial Value Problems with Laplace Transforms · seed 1 · A4, ink-friendly. The answer key prints on its own page for grown-ups.

Trade calculus for algebra

Mathematics · Differential Equations · ages 21-22
Name ______________________   Date ____________

  1. The transform of e to the two t is one over (s minus two). Evaluated at s equal three, what value results?

    Answer: ______________

  2. y(0) is 4. What is the Laplace transform of y prime?

    • s times Y
    • Y divided by s
    • s times Y minus 4
    • s squared times Y

  3. What does the method turn calculus into?

    • Algebra for Y
    • A longer differential equation
    • A drawing of the answer

  4. Starting values enter at the end of this method.

    Circle one:   True   False

  5. Splitting four divided by (s times (s plus two)) gives A over s plus B over (s plus two). Covering s, A is four divided by two. What is A?

    Answer: ______________

  6. A shifted quadratic chunk inverts to what family?

    • Sines, cosines, and damped cousins
    • Only whole numbers
    • Logarithms of s

  7. Y(s) is three divided by (s minus two) plus one divided by (s plus one). What is y(t)?

    • Three e to the two t plus e to minus t
    • Three e to minus two t plus e to the t
    • Three t squared plus one
    • Three cosine plus sine

  8. A student transforms u of (t minus two) times sin(t minus two) to e to minus two s divided by (s squared plus one). True or false?

    Circle one:   True   False

  9. Forcing of sine of t minus three meets u of t minus three. What factor appears?

    • e to plus three s
    • No factor at all
    • e to minus three s

  10. Y(s) is two divided by (s squared plus four) plus one divided by (s minus one). What is y(t)?

    • Cosine of two t plus e to the t
    • Sine of two t plus e to minus t
    • Two t plus e to the t
    • Sine of two t plus e to the t
LightMySky · lightmysky.comW1-mt_0BhjPVNUwl-s1

Answer key

For grown-ups. Fold this page away before handing over the rest.

Trade calculus for algebra W1-mt_0BhjPVNUwl-s1

  1. 1 · One over (three minus two) is one.
  2. s times Y minus 4 · Differentiation gives s times Y minus the initial value 4.
  3. Algebra for Y · Derivatives become s multiples, leaving plain algebra for Y.
  4. False · Starts peel off up front, which suits the method to switching forces.
  5. 2 · Four divided by two is two.
  6. Sines, cosines, and damped cousins · Shifted quadratics are the sine and cosine lines of the table.
  7. Three e to the two t plus e to minus t · Each chunk inverts by sight to its exponential.
  8. True · True. The shift matches, so the second shift theorem applies directly.
  9. e to minus three s · A matched delay of three shifts the transform by e to minus three s.
  10. Sine of two t plus e to the t · Two over (s squared plus four) is sine of two t, and one over (s minus one) is e to the t.
Worksheet · LightMySky