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Calculus I (Fall 2023) |
Lecture Notes |
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| Notes | Video | |
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8/21/2023: We reviewed precalculus. Notes from 8/21/23 |
Video from 8/21/23 | |
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8/23/2023: We discussed a little bit of sagemath and a lot more of trig. Notes from 8/23/23 |
Video from 8/23/23 | |
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8/25/2023: We discussed limits, algebraically, numerically, and graphically, and
we derived one special limit. Notes from 8/25/23 |
Video from 8/25/23 | |
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8/28/2023: We noted the three special limits and worked examples of computing
limits. Notes from 8/28/23 |
Video from 8/28/23 | |
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8/30/2023: We noted the three special limits and worked examples of computing
limits. Notes from 8/30/23 |
Video from 8/30/23 | |
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9/1/2023: We computed more examples of limits and introduced the definition of
the derivative and its interpretation. Notes from 9/1/23 |
Video from 9/1/23 | |
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9/6/2023: We went over some homework and did more examples of computing the
derivative using the definition. Notes from 9/6/23 |
Video from 9/6/23 | |
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9/8/2023: We proved the formulas for the derivative of power functions, for the
derivative of $\sin(x)$ and of $e^x$ using the definition. Notes from 9/8/23 |
Video from 9/8/23 | |
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9/11/2023: We proved the product rule and used it in a few examples. Notes from 9/11/23 |
Video from 9/11/23 | |
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9/13/2023: We did more examples of using the power rule and product rule, looked at
examples of functions that are not differentiable, and then we
proved the quotient rule. Notes from 9/13/23 |
Video from 9/13/23 | |
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9/15/2023: We did examples of using the product and quotient rule, then proved the chain rule
and used it in several examples. Notes from 9/15/23 |
Video from 9/15/23 | |
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9/18/2023: We did examples of taking derivatives using shortcut rules, and then we
worked on projectile motion. Notes from 9/18/23 |
Video from 9/18/23 | |
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9/20/2023: We finished our projectile motion questions and then reviewed the test on Friday. Notes from 9/20/23 |
Video from 9/20/23 | |
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9/25/2023: We discussed a couple of other aspects of projectile motion. After that, we worked on implicit differentiation. Notes from 9/25/23 |
Video from 9/25/23 | |
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9/27/2023: We considered the implicit differentiation example discussed previously.
We used sagemath to numerically compute the points of our curve where the tangent line
is vertical. Notes from 9/27/23 Sagemath code used |
Video from 9/27/23 | |
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9/29/2023: We derived the formulas of the derivatives of inverse functions. Notes from 9/29/23 |
Video from 9/29/23 | |
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10/2/2023: We started working on related rates problems. Notes from 10/2/23 |
Video from 10/2/23 | |
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10/4/2023: We discussed related rates and estimates using derivatives. Notes from 10/4/23 |
Video from 10/4/23 | |
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10/9/2023: We did more examples of related rates problems. Notes from 10/9/23 |
Video from 10/9/23 | |
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10/11/2023: We discussed related rates questions a little more and discussed the differential and linearizations. Notes from 10/11/23 |
Video from 10/11/23 | |
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10/13/2023: We discussed critical points and how to classify them using the derivative. Notes from 10/13/23 |
Video from 10/13/23 | |
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10/16/2023: We worked on second derivatives and finding absolute maxima and minima. Notes from 10/16/23 |
Video from 10/16/23 | |
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10/18/2023: We discussed second derivative and concavity and showed how to compute
derivatives on sagemath. Notes from 10/18/23 |
Video from 10/18/23 | |
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10/20/2023: We did lots of examples. Notes from 10/20/23 |
Video from 10/20/23 | |
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10/25/2023: We solved a couple of optimization problems. Notes from 10/25/23 |
Video from 10/25/23 | |
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10/27/2023: We solved some max/min problems and learned l'Hopital's Rule. Notes from 10/27/23 |
Video from 10/27/23 | |
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10/30/2023: We solved some max/min problems and practiced using l'Hopital's Rule. Notes from 10/30/23 |
Video from 10/30/23 | |
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11/1/2023: We solved another max/min problem. Notes from 11/1/23 |
Video from 11/1/23 | |
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11/3/2023: We discussed optimization with projectile motion, Rolle's Theorem and the
Mean Value Theorem, and we introduced the definition of the definite integral. Notes from 11/3/23 |
Video from 11/3/23 | |
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11/6/2023: We showed how to find a point on an ellipse closest to an outside point in three
different ways. Notes from 11/6/23 |
Video from 11/6/23 | |
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11/8/2023: We finished an exercise from last time, and we derived some summation formulas.
We then started to use them in computing a definite integral. Notes from 11/8/23 |
Video from 11/8/23 | |
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11/10/2023: We computed definite integrals using the definition and then proved the fundamental theorem of calculus. Notes from 11/10/23 |
Video from 11/10/23 | |
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11/13/2023: We discussed definite integrals, average values, and the first and second fundamental theorems of calculus. Notes from 11/13/23 |
Video from 11/13/23 | |
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11/15/2023: We worked on finding definite and indefinite integrals using the fundamental theorem of calculus
and the method of substitution.
Notes from 11/15/23 |
Video from 11/15/23 | |
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11/17/2023: We worked on the method of substitution to solve integration questions.
Notes from 11/17/23 |
Video from 11/17/23 | |
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11/27/2023: We worked on questions involving the second fundamental theorem of calculus,
the substitution method of integration, and finding the area between curves.
Notes from 11/27/23 |
Video from 11/27/23 | |
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12/01/2023: We reviewed questions concerning integrals and optimization. We also
worked on strategies for determining whether integrals can be computed by hand or not.
Notes from 12/01/23 |
Video from 12/01/23 | |
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12/04/2023: We reviewed.
Notes from 12/04/23 |
Video from 12/04/23 | |
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12/06/2023: We reviewed.
Notes from 12/06/23 |
Video from 12/06/23 | |