| ASSIGNED TEXTBOOK PROBLEMS |
| Here is the list of assigned book problems for the year. Some of you have lost/misplaced yours so here it is on-line! ;) No excuse, and no more need to do ALL of them! |
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| Notes 9-11-08 |
| Today we developed the idea of the derivative. As is the case with most big calculus ideas, the LIMIT is essential to this development.
Tomorrow there is a short quiz on limits, continuity, and beginning derivatives. |
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| In Class work 9/15/08 |
| We worked with the derivative at all points x, thus discovering the derivative FUNCTION, by first drawing tangent lines at various points, and for corresponding values of x, plotted the value of the slope of the tangent line. We physically built the derivative function point by point. Then, by changing the limit to as a -->x, we discovered the algebraic rule for the derivative function of x*x and x*x*x. |
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| Homework on 9/15/08 for Tuesday 9/16/08 |
| The homework for Tuesday is to do the listed exrecises for section 2.4. Please remember to bring your textbook to class and be ready to present problems with a partner. |
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| Homework on 9-16 for Wed 9-17 |
| Lab 8 is an intense graphical lok at differentiation. There are several items within the problems which will be noted in class when discussed. This is an important assignment! |
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| Notesheet handed out on FRiday, Sept 26, 2008 |
| We discussed the idea that most curves look like lines when viewed close up. Using this idea, we can extrapolate from a data table by writing the equation of a line using some of the last points in the table, or interpolate using some of the internal points of the table. We can use the line to estimate, and then ask if our estimate is high or low. Knowing the concavity of the function will help answer that question. |
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| Class notes 10-02 |
| Today we developed the idea of the definite integral using the Jeff-Arthur v vs t example where we estimated the total distance Arthur ran. We discussed left hand vs right hand rectangles, inscribed vs. circumscribed rectangles and which (LH or RH) rectangles led to ins or cir based on increasing or decreasing function. The notation for the integral was introduced and discussed carefully. |
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| Class notes 10-03 The Definite Integral |
| Today we discussed the notation for the definite integral, and how to approximate it using left and right hand rectangles. We also found this approximation using the sum(seq( command on our TI-89s. The actual value can also be found (for now) using the integral command on our TI-89s. |
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| Calculus Ch 5 Review Homework |
| Here is a set of problems from chapter 5.
It is due in completion by Friday. There is a test next week Tuesday (part 1) and Thursday (part 2). |
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| Wed and Thursday's class |
| We are working on presenting in groups the problems from sections 5.1 through 5.4. I handed out a sheet on instructions for group presentations. Here it is. |
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| Derivatives of Trig Functions |
| Today we proved the derivatives of sin(x) and cos(x) and also derived the derivatives of the remaining six trig functions. We also practiced with the chain rule. The quiz was moved to Monday, Nov 3. |
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| Implicit DIfferentiation |
| Today, Election Day, we worked with more implicitly-defined functions, practicing finding their derivatives. We also did some related rate problems which implement implicit differentiation. |
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| First and Second Derivative Tests |
| Today we discovered how to use calculus to test for local extrema. The ideas behind the tests are not new, but the write-up must be extremely clear.
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| Optimization Intro Notes |
| Optimization problems can be very tricky, but ironically, it's not due to the calculus which simply involves the application of the first and second derivative tests. Here is the model, and a few example problems shown. For most problems, the model is applicable and should be used (Find ____which max/minimizes___subject to_____). |
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| Related Rates notes |
| Today we gave a structure to these important problems which are found nearly everywhere in our natural world, economy, industrial world and more.
Tomorrow we'll be going through optimization problems and the assignment on related rates (handout) so be ready with these. |
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