2M A 3 6 6 00F I N A L R E V I E W such that i. Each g k ( t ) is continuous on I . (There are m functions to consider.) ii. Each p ij ( t ) is continuous on I . (There are m · n functions to consider.) iii. t 0∈ I . Then there exists a unique solution on the interval I . This is known as the Existence and Uniqueness Theorem for Linear Systems . • Consider a LRC Circuit i.e., an electrical circuit which contains three objects: – An Inductor (which behaves like a mass) V inductor ∝ dI inductor dt = ⇒ V inductor = L · dI inductor dt . The constant L is called the inductance . – A Resistor (which behaves like friction): V resistor ∝ I resistor = ⇒ V resistor = R · I resistor . The constant R is called the resistance . (This is called Ohm’s Law .) – A Capacitor (which behaves like a spring): dV capacitor dt ∝ I capacitor = ⇒ dV capacitor dt = 1 C · I capacitor . The constant C is called the capacitance . Let I = I ( t ) and V = V ( t ) denote the current and the voltage. KirchhoF’s Laws of Circuits state 1. The net Fow of current I through a node is zero. 2. The net voltage
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