# 3 - Last day. Suppose the battery is replaced with a...

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Math 2860 Summer 2010: Lecture 3 Page 1 of 22 Last day…. Suppose the battery is replaced with a generator that produces a variable voltage of E ( t ) = 60 sin 30 t volts. Find I ( t ).

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Math 2860 Summer 2010: Lecture 3 Page 2 of 22 Example 6 This circuit contains a battery, a capacitor with a capacitance of C farads ( F ), and a resistor of R ohms ( Ω ). Kirchhoff’s Second Law E
Math 2860 Summer 2010: Lecture 3 Page 3 of 22 Find Q ( t ). E

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Math 2860 Summer 2010: Lecture 3 Page 4 of 22 Modelling with Systems Example 1
Math 2860 Summer 2010: Lecture 3 Page 5 of 22

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Math 2860 Summer 2010: Lecture 3 Page 6 of 22 Example 2 Kirchhoff’s First Law: Kirchhoff’s Second Law: E R E R
Math 2860 Summer 2010: Lecture 3 Page 7 of 22 System of Equations: We’ve worked with first-order linear equations…. E R E R

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Math 2860 Summer 2010: Lecture 3 Page 8 of 22 What are n th-Order Linear Equations? They have this form: a n ( x ) y ( n ) + a n 1 ( x ) y ( n 1) + ... + a 1 ( x ) y + a 0 ( x ) y = g ( x ) When are they n th-Order IVPs? When they are also subject to n initial conditions: y ( x 0 ) = y 0 , y ( x 0 ) = y 1 , ..., y ( n 1) ( x 0 ) = y n 1 When do solutions exist? Let x 0 I (an interval). If
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## This note was uploaded on 11/10/2010 for the course DEFFERENTI 2080 taught by Professor Kidnan during the Spring '10 term at UOIT.

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3 - Last day. Suppose the battery is replaced with a...

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