Chapter 5 APPLICATIONS OF ODE.

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Presentation transcript:

Chapter 5 APPLICATIONS OF ODE

OVERVIEW LAW of GROWTH or DECAY LAW of COOLING CHEMICAL REACTIONS ELECTRIC CIRCUITS

Rate of change of a quantity proportional to the quantity present Law of Growth or Decay Rate of change of a quantity proportional to the quantity present

Law of Growth or Decay The number of bacteria in a culture grows at a rate proportional to the number of bacteria present. The number triples in 1 hour. If the initial number is 10, find: The number of bacteria after 5 hours. 2) After how long the number was exactly 270. 1) 2430 2) 3

Law of Cooling Temperature of the hot substance Temperature of the surrounding

Law of Cooling A cup of Coffee at 90⁰C is placed in a room at 25⁰C. In 5 minutes, it cools to 70⁰C. Find 1) The temperature of the cup after another 5 minutes. 2) After how long the cup will be exactly at 27⁰C. 1) 56.15 2) 47.33

Chemical reactions - Solutions Amount of salt in the tank Volume tank Concentration of incoming mixture rate of incoming mixture rate of outgoing mixture

Chemical reactions - Solutions A tank contains 100 liters of brine (solution of salt) in which 500g of salt is dissolved. If brine containing 20 g of salt per liter runs into the tank at the rate of 3 liters per minute and the mixture, which is kept uniform, runs out of the tank at the rate of 2 liters per minute, find the amount of salt in the tank after exactly 30 minutes. 1712.42

Electric circuits L-R-C circuit, where R (resistance), L (inductance), and C (capacitance) are in series, and acted on by an electromotive force E. The current satisfies: The current is the rate of flow of the positive charge : 

Electric circuits A voltage is applied at at a circuit containing an inductance L and a resistance R. Assuming , show that the current in the circuit is: