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Calculus AB, Assignment Seven
In this Assignment, we will be studying Ordinary Differential Equations (O.D.E.s or D.E.s) . For perhaps the first time, we will see equations whose solutions aren't numbers, but are functions instead. D.E.s state relationships between the solution (function) and any number of its derivatives (as an example y'=ky). Solutions are those functions which satisfy the equation. Many 'real life' situations give rise to D.E.s. Models of population growth/decay and the spread of disease are among the situations we will consider.
|
Day Number |
Class Topic |
Homework |
|
One |
Intro to Differential Equations: Intro to Slope Fields |
Pg 589 #1,3,5 Pg 597#1,3,9 |
|
Two |
Euler's Method |
Pg 597 #5,11a,13 |
|
Three
|
More Euler's Method, Intro to Partial Fractions |
Pg 542 #1,9,11 Pg 597#17 |
|
Four |
Solving D.E. s: the Method of Separation of Variables. |
Pg 542 #33 (let u=sin(theta)),42 Pg 589#9,11,27 |
|
Five |
Solving D. E.s: the Method of Integrating factors |
Pg 589 #7,19,21,25 Pg 597#20 |
|
Six |
PRACTICE |
Handouts? |
|
Seven |
Modeling: Exponential Growth/Decay |
Pg 609 #1,3,5,7 |
|
Eight
|
Modeling:Logistic Growth |
Pg 609 #9 (actually use an exponential model, not a logistic), 11,23,25 |