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Clase1-handouts

# Clase1-handouts - Differential Equations and Linear Algebra...

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Differential Equations and Linear Algebra Maria Isabel Bueno Cachadina South Hall 6524 [email protected] Office hours : Mondays and Thursdays from 4:00-5:30 pm Differential Equations and Linear Algebra

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Syllabus Textbook: “Differential Equations and Linear Algebra”, Farlow, Hall, McDill, West. Ed. Pearson, 2nd edition. We will cover Chapters 1-3. Weekly homework. Webwork. Due Thursdays at 8:00 am. 10% Two midterms and the final exam. 20% each. Mandatory problem sessions. TA’s. 30%. Office hours. M-R from 4:00 to 5:30 or by appointment. Differential Equations and Linear Algebra
Differential equations as mathematical models Mathematical model : a mathematical description of a system or a phenomenon. Example : We have a glass of milk with chocolate for breakfast and we want to explain, through a mathematical model, how quickly it will get cold. Differential Equations and Linear Algebra

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To construct a mathematical model of a system: 1. Identify the variables that are responsible for changing the system. The temperature of the chocolate Time The ambient temperature The temperature of the cup Differential Equations and Linear Algebra
To construct a mathematical model of a system: 2. Specify the level of resolution of the model by deciding which of these variables to incorporate into the model. The temperature of the chocolate, T Time, t The ambient temperature, A The temperature of the cup Differential Equations and Linear Algebra

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To construct a mathematical model of a system: 3. Formulate a mathematical model. The rate of change of the temperature T of the chocolate is proportional to the difference between the temperature A of the ambient and the temperature of the chocolate.
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