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Lecture 3 Notes

Lecture 3 Notes - Today Reminders WeBWorK assignment 1 due...

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Today • Reminders: • WeBWorK assignment 1 due Thursday 1 pm. • Quiz 2 on Monday in tutorial sections. • If you have questions, post them on Piazza (don’t email me) and/or come to ofFce hours. • Modeling (Section 2.3) • Existence and uniqueness (Section 2.4 - not going test on the theory) • Second order linear equations - constant coefFcients, Wronskian (3.1, 3.2)

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OfFce hours • Eric - MATX 1219 (might change to MATX 1215 during the term) • Tues 11 am -12:30 pm • Wed 1 pm - 2 pm • Ye - location TBA in tutorial • Fri 1 pm - 2 pm • Mengdi - location TBA in tutorial • Mon 1 pm - 2 pm
Modeling (Section 2.3) • Infow/outfow problems

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Modeling (Section 2.3) • Infow/outfow problems • Determine what quantity(-ies) to track (e.g. mass, concentration, temperature, etc.).
Modeling (Section 2.3) • Infow/outfow problems • Determine what quantity(-ies) to track (e.g. mass, concentration, temperature, etc.). • Choose a small interval oF time, , and add up all the changes. t

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Modeling (Section 2.3) • Infow/outfow problems • Determine what quantity(-ies) to track (e.g. mass, concentration, temperature, etc.). • Choose a small interval oF time, , and add up all the changes. • Note that change during intervening . t t q ( t + t )= q ( t )+
Modeling (Section 2.3) • Infow/outfow problems • Determine what quantity(-ies) to track (e.g. mass, concentration, temperature, etc.). • Choose a small interval oF time, , and add up all the changes. • Note that change during intervening . • Take limit as to get an equation For q(t). t t 0 t q ( t + t )= q ( t )+

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Modeling (Section 2.3) - Example • Freshwater fows into a tank at a rate 2 L/min. The tank starts with a concentration o± 100 g / L o± salt in it and holds 10 L. The tank is well mixed and the mixed water drains out at the same rate as the infow. (a) Write down an IVP ±or the mass o± salt in the tank as a ±unction o± time. (b) What is the limiting mass o± salt in the tank ( )? lim t →∞ m ( t )
(a) What is the change in the mass of salt in any short interval of time ? Modeling (Section 2.3) - Example • Freshwater ±ows into a tank at a rate 2 L/min. The tank starts with a concentration of 100 g / L of salt in it and holds 10 L. The tank is well mixed and the mixed water drains out at the same rate as the in±ow. (a) Write down an IVP for the mass of salt in the tank as a function of time. (b) What is the limiting mass of salt in the tank ( )? t lim t →∞ m ( t )

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(a) What is the change in the mass of salt in any short interval of time ? (A) (B) (C) (D) Modeling (Section 2.3) - Example • Freshwater ±ows into a tank at a rate 2 L/min. The tank starts with a concentration of 100 g / L of salt in it and holds 10 L. The tank is well mixed and the mixed water drains out at the same rate as the in±ow. (a) Write down an IVP for the mass of salt in the tank as a function of time.
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Lecture 3 Notes - Today Reminders WeBWorK assignment 1 due...

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