However the result will be mathematically equivalent While this is acceptable

However the result will be mathematically equivalent

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look exactly like those calculated by hand. However, the result will be mathematically equivalent. While this is acceptable for actual calculations, it can be a hindrance when using the software to check your work. In these cases, you can at least check your intermediate partial fraction decomposition, as well. For example, if we use the from the Case 4 example, one will notice that the result is the same as our own expansion: > convert( (10*s*(s-3))/((s+5)*(s^2+4*s+5)^2), parfrac, s, complex ); Once again, it is strongly recommended that you acquire and become familiar with Maple; not only is it an immense time-saver when doing real circuits work, but it can also be used to save time by checking your work. 48 e ( ) 6 t 72 e ( ) 8 t 120 5.000000000 7.500000000 I ( ) s 2.000000000 1.000000000 I 2 2.000000000 11.00000000 I s 2. 1. I 4.000000000 s 5. 5.000000000 7.500000000 I ( ) s 2. 1. I 2 2.000000000 11.00000000 I s 2.000000000 1.000000000 I Tip: Maple and Inverse Laplace

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42 Lecture Slides : None Current Topics : Inverse Laplace Transform, Circuit Elements, and Initial Conditions Problems Next Topics : Final Value Problems, Introduction to Op-Amps and Filters Laplace Transform and Differential Equations The original (historical) application of the Laplace Transform was to provide a simpler method of solving differential equations. Circuits can be represented and solved using differential equations. Example 1 Find the Laplace Transform of the following time-domain function: Find a simple Laplace transform from the table, such as : (1) Using the Differentiation property of the Laplace transform: (2) Class Notes (and Review)
43 Example 2 Find the Laplace Transform of the following differential equation: ̈ ̇ ̇ Relevant Laplace Transform properties: (1) Final transform after applying the above properties: (2) Inverse Laplace Transform Partial Fractions General procedure for finding Inverse Laplace Transform: Use table of common transforms and properties to reverse Laplace process Apply Linearity in particular to reduce complex problems to simple ones

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44 Often we need to make use of partial fraction expansion to determine the inverse Laplace transform of a particular function. The procedure depends on the type and nature of poles. Cases are as follows: (A) All real poles, no repeated poles (B) All real poles, with one or more repeated poles (C) At least one pair of complex poles, but no repeated pairs (D) At least one pair of complex poles, with one or more repeated pairs Example 1 Case A Step 1 Write partial fraction terms. (1) Step 2 For each pole, evaluate the unknown coefficients. (2)