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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
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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
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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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