Missed final exam Dont miss the final Contact the instructor ASAP or a grade of

Missed final exam dont miss the final contact the

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Missed final exam: Don’t miss the final! Contact the instructor ASAP or a grade of incomplete or F will be assigned. Academic honesty : Submit your own work. Any cheating will be reported to University authorities and a ZERO will be given for that HW assignment or Exam. Joseph M. Mahaffy, h [email protected] i Lecture Notes – Introduction to Differential Equa — (10/47) The Class — Overview The Class... Introduction Applications of Differential Equations MatLab Formal Prerequisites MatLab Students can obtain MatLab from EDORAS Academic Computing. Google SDSU MatLab or access download/matlab.html . MatLab and Maple can also be accessed in the Computer Labs GMCS 421 , 422 , and 425 . A discounted student version of Maple is available. Joseph M. Mahaffy, h [email protected] i Lecture Notes – Introduction to Differential Equations — (11/47) The Class — Overview The Class... Introduction Applications of Differential Equations MatLab Formal Prerequisites Math 337: Formal Prerequisites Math 254 or Math 342A or AE 280 These courses all require Calculus 151 . Assume good knowledge of differentiation and integration . Understand series techniques (especially Taylor’s Theorem ) Recall Partial Fractions Decomposition . These courses all have sections on basic Linear Algebra . Joseph M. Mahaffy, h [email protected] i Lecture Notes – Introduction to Differential Equa — (12/47)
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The Class — Overview The Class... Introduction Applications of Differential Equations Malthusian Growth Example Definitions - What is a Differential Equation? Classification Introduction Introduction Differential equations frequently arise in modeling situations They describe population growth, chemical reactions, heat exchange, motion, and many other applications Differential equations are continuous analogs of discrete dynamical systems Joseph M. Mahaffy, h [email protected] i Lecture Notes – Introduction to Differential Equations — (13/47) The Class — Overview The Class... Introduction Applications of Differential Equations Malthusian Growth Example Definitions - What is a Differential Equation? Classification Malthusian Growth 1 Discrete Malthusian Growth Model : Let the initial population, P ( t 0 ) = P 0 Define t n = t 0 + n Δ t and P n = P ( t n ) Let r be the per capita growth rate per unit time The Discrete Malthusian Growth Model satisfies: P n +1 = P n + r Δ tP n = (1 + r Δ t ) P n New population = Old population + per capita growth rate × length of time × Old population Joseph M. Mahaffy, h [email protected] i Lecture Notes – Introduction to Differential Equa — (14/47) The Class — Overview The Class... Introduction Applications of Differential Equations Malthusian Growth Example Definitions - What is a Differential Equation? Classification Malthusian Growth 2 Discrete Malthusian Growth : P n +1 = (1 + r Δ t ) P n , so P 1 = (1 + r Δ t ) P 0 P 2 = (1 + r Δ t ) P 1 = (1 + r Δ t ) 2 P 0 P 3 = (1 + r Δ t ) P 2 = (1 + r Δ t ) 3 P 0 .
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