Section 7.6

Section 7.6 - Differential Equations Math 308, Spring 2008...

Info iconThis preview shows pages 1–2. Sign up to view the full content.

View Full Document Right Arrow Icon

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: Differential Equations Math 308, Spring 2008 Texas A&M University c F. Dos Reis Section 7.6 Definition: The unit step function u(t) is defined by u(t) = 0 t<0 1 t>0 Exercise 1. Describe the function v(t) = M u(t - a) Find the Laplace transform of u(t - a). Theorem: L {u(t - a)} (s) = L-1 e-as s e-as s (t) = u(t - a) Exercise 2. The function g(t) is defined by 2 t<5 6 5 < t < 10 g(t) = 2 t 10 < t Express g using unit step functions. Theorem: If f is of exponential order and a is a positive real number, then L {u(t - a)f (t - a)} (s) = e-as L {f (t)} s, Equivalently, if g is of exponential order L {u(t - a)g(t)} (s) = e-as L {g(t + a)} s for s > for s > Exercise 3. Determine the Laplace transform of g(t) = sin(3t)u(t - ). h(t0 = t2 u(t - 1) 1 Differential Equations Math 308, Spring 2008 Exercise 4. Determine the inverse Laplace transform of F (s) = e-2s F (s) = e-s 3s . s2 +9 Texas A&M University c F. Dos Reis 24 . s4 Exercise 5. Solve the initial value problem y + y = u(t - 3) with y(0) = 0 and y (0) = 1. Theorem: If f has period T and is piecewise continuous on [0, T ], then L {f } (s) = T 0 e-st f (t)dt 1 - e-sT Exercise 6. Let f be a periodic function with period 2 such that f (t) = e3t for t [0, 2). Find the Laplace transform of f . 2 ...
View Full Document

Page1 / 2

Section 7.6 - Differential Equations Math 308, Spring 2008...

This preview shows document pages 1 - 2. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online