Lecture Notes
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Notes
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Video
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| 8/23/22: We did some algebra
warmups and starting learning about limits and sagemath.
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Go here for the 8/23 video.
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| 8/25/22: More limits and algebra.
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Go here for the 8/25 video.
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| 8/29/22: Review of trig...
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Go here for the 8/29 video.
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8/30/22: We finished the review of trig and evaluated more limits.
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Go here for the sagemath code for one example.
Go here for the sagemath code for another example.
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Go here for the 8/30 video.
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| 9/1/22: We discussed continuity, properties of limits, squeeze theorem, and algebraic techniques of
evaluating limits.
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Go here for the 9/1 video.
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9/6/22: We discussed properties of limits and the three special limits.
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Go here for the sagemath code
investigating the slope of $y=a^x$ for different values of $a$.
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Go here for the 9/6 video.
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9/8/22: We did lots of limit calculations, and also showed how to do different levels
of numerical precision on Sagemath.
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Go here for the sagemath code.
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Go here for the 9/8 video.
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| 9/12/22: We discussed more examples of
evaluating limits.
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Go here for the 9/12 video.
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| 9/13/22: We discussed examples of limits and finding tangent lines by taking limits of secant lines.
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Go here for the 9/13 video.
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| 9/15/22: We discussed tangent lines and the derivative.
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Go here for the 9/15 video.
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| 9/22/22: We derived more formulas for the derivative.
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Go here for the 9/22 video.
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| 9/26/22: We derived even more formulas for the derivative.
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Go here for the 9/26 video.
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| 9/27/22: We derived formulas for the derivative of products, quotients,
trig functions, exponential functions.
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Go here for the 9/27 video.
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| 9/29/22: We derived the chain rule and inverse function theorem, and
we utilized them to compute several derivatives.
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Go here for the 9/29 video.
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| 10/3/22: We completed our derivation of fast derivative formulas.
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Go here for the 10/3 video.
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| 10/4/22: We computed more examples of derivatives and also
learned about implicit differentiation.
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Go here for the 10/4 video.
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| 10/10/22: We applied the derivative to a couple of related rates questions.
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Go here for the 10/10 video.
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| 10/11/22: We did more examples of related rates questions.
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Go here for the 10/11 video.
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| 10/17/22: We discussed using the first and second derivative to
find geometric properties of graphs.
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Go here for the 10/17 video.
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10/18/22: We used the first and second derivative to classify critical points
of functions and to find inflection points.
Here is the sagemath code we used to find and graph critical points and inflection points.
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Go here for the 10/18 video.
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| 10/20/22: We worked examples of applications of derivatives: related rates, critical points, inflection points.
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Go here for the 10/20 video.
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| 10/25/22: We worked optimization problems.
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Go here for the 10/25 video.
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| 10/27/22: We worked more optimization problems.
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Go here for the 10/27 video.
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| 10/31/22: We solved some spooky optimization problems.
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Go here for the 10/31 video.
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11/1/22: We solved some projectile motion problems.
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Go here to see the sagemath code for view a function and its first and second derivative on the same graph.
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Go here for the 11/1 video.
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11/3/22: We worked on summation notation and finding sums of numbers,
used to compute total distance traveled from velocity data.
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* Go here to see the sagemath code used to create lists of numbers and to add them up.
* Go here for the more advanced sagemath code used to calculate distance and change the interval size.
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Go here for the 11/3 video.
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11/7/22: We worked on computing total distance traveled from velocity data, using sagemath/python.
* Go here to see the sagemath code that was the starting point of working with your team.
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Go here for the 11/7 video.
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11/8/22: We worked on changing interval sizes in computing total distance traveled from velocity data, using sagemath/python.
* Go here to see the first sagemath code used in class.
* Go here to see the second sagemath code used in class.
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Go here for the 11/8 video.
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11/10/22: We discussed properties of summations and found and used formulas for them.
We also discussed geometric series.
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Go here for the 11/10 video.
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11/14/22: We reviewed and also summed a couple of geometric series.
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Go here for the 11/14 video.
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11/17/22: We discussed the definite integral and computed some examples.
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Go here for the 11/17 video.
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11/28/22: We computed another example of a limit of Riemann sums, and then we
learned about Rolle's Theorem, the Mean Value Theorem, and the FUNdamental Theorem of Calculus.
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Go here for the 11/28 video.
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11/29/22: We did examples of computing integrals using the Fundamental Theorem
of Calculus. We introduced the method of subsitution.
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Go here for the 11/29 video.
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12/1/22: We did more examples of subsitution. We also used an integral to derive the
well-known formula for the volume of a cone.
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Go here for the 12/1 video.
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12/5/22: We did more examples of subsitution and discussed the Second Fundamental Theorem of Calculus.
* Go here for the notes.
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Go here for the 12/5 video.
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12/6/22: We did examples of using the Second Fundamental Theorem of Calculus.
We also discussed Newton's method of finding solutions to equations. We also answered questions about the review for the final exam.
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Go here for the 12/6 video.
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