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1. webster.math.umbc.edu › firstthreeTABLE OF INVERSE LAPLACE TRANSFORMS - University of Maryland,...

   webster.math.umbc.edu › firstthree

   first- and second-order equations, followed by Chapter 5 (the Laplace transform), Chapter 6 (systems), Chapter 8 (nonlinear equations), and part of Chapter 9 (partial differential equations).

2. www.math.purdue.edu › ~caiz › MA527-caiHome - Department of Mathematics - Purdue University

   www.math.purdue.edu › ~caiz › MA527-cai

   What are the steps of solving an ODE by the Laplace transform? In what cases of solving ODEs is the present method preferable to that in Chap. 2? What property of the Laplace transform is crucial in solving ODEs? = Explain.

3. www.math.unl.edu › ~bdeng1 › TeachingTable of Laplace Transforms and Inverse Transforms

   www.math.unl.edu › ~bdeng1 › Teaching

   Table of Laplace Transforms and Inverse Transforms f(t) = L¡1fF(s)g(t) F(s) = Lff(t)g(s) tneat n! (s¡a)n+1; s > a eat sinbt b (s¡a)2 +b2; s > a eat cosbt s¡a (s¡a)2 +b2; s > a eatf(t) F(s) fl fl s!s¡a u(t¡a)f(t) e¡asLff(t+a)g(s), alternatively, u(t¡a) f(t) fl fl t!t¡a ⁄ e¡asF(s) –(t¡a)f(t) f(a)e¡as f(n)(t) snF(s)¡sn¡1f(0)¡¢¢¢¡ f(n¡1)(0) tnf(t) (¡1)n dn dsn

4. math.stanford.edu › ~ralph › math53Laplace transforms table - Stanford University

   math.stanford.edu › ~ralph › math53

   Laplace transforms table Function Laplace transform eat 1 s−a tn n! sn+1 sin(at) a s 2+a cos(at) s s2 +a2

5. math.mit.edu › ~hrm › 1818.031 Laplace Transform Table - MIT Mathematics

   math.mit.edu › ~hrm › 18

   e asL(f(t + a)) (s) G(s)F (s)s(t-translation)(integration. but not included in this course.f(t)1. ( ) d. s. (The function table is on the next page.) 1. Laplace Table, 18.031.

6. web.stanford.edu › ~boyd › ee102Lecture 3 The Laplace transform - Stanford University

   web.stanford.edu › ~boyd › ee102

   The Laplace transform. we'll be interested in signals de ̄ned for t ̧ 0 L(f = ) the Laplace transform of a signal (function) de ̄ned by Z f is the function F. (s) = f (t)e¡st dt. 0. for those s 2 C for which the integral makes sense. 2 F is a complex-valued function of complex numbers.

7. wliao60.math.gatech.edu › 18Fall_Math2552 › LectureNotes5.3 The Inverse Laplace Transform 313 - wliao60.math.gatech.edu

   wliao60.math.gatech.edu › 18Fall_Math2552 › LectureNotes

   5.3 The Inverse Laplace Transform 313 TABLE 5.3.1 Elementary Laplace transforms. f(t) = −1{F(s)} F(s) = {f(t)} Notes 1. 1 1 s, s > 0 Sec. 5.1; Ex. 4 2. eat 1 s−a, s > a Sec. 5.1; Ex. 5 3. tn, n = positive integer n! sn+1, s > 0 Sec. 5.2; Cor. 5.2.5 4. tp, p > −1 Γ(p+1)sp+1, s > 0Sec.5.1;Prob.37 5. sinat a s2 +a2, s > 0Sec.5.1;Ex.7 6. cosat s s2 +a2, s > 0Sec.5.1;Prob.22 7. sinhat