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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 office hours. • Modeling (Section 2.3) • Existence and uniqueness (Section 2.4 - not going test on the theory) • Second order linear equations - constant coefficients, Wronskian (3.1, 3.2)

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Office 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) • Inflow/outflow problems

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Modeling (Section 2.3) • Inflow/outflow problems • Determine what quantity(-ies) to track (e.g. mass, concentration, temperature, etc.).
Modeling (Section 2.3) • Inflow/outflow 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) • Inflow/outflow 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) • Inflow/outflow 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 flows 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 inflow. (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 ( )? 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 flows 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 inflow. (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 flows 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 inflow. (a) Write down an IVP for the mass of salt in the tank as a function of time.
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