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Calculus II (Spring 2023) |
Lecture Notes |
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| Notes | Video | |
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1/18/2023: We discussed the main concepts of calculus and practiced finding definite integrals
using substitution. Notes from 1/18/23 |
Video from 1/18/23 | |
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1/20/2023: We practiced finding integrals
using substitution. Notes from 1/20/23 |
Video from 1/20/23 | |
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1/23/2023: We derived the integration by parts formula and used it to calculate
antiderivatives. Notes from 1/23/23 |
Video from 1/23/23, part 1 Video from 1/23/23, part 2 |
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1/25/2023: We discussed the Second Fundamental Theorem of Calculus and did examples of trig integrals. Notes from 1/25/23 |
Video from 1/25/23 | |
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1/27/2023: We found more antiderivatives, some using trig substitution. Notes from 1/27/23 |
Video from 1/27/23 | |
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2/3/2023: We worked on long division and partial fractions. Notes from 2/3/23 |
Video from 2/3/23 | |
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2/6/2023: More on long division and partial fractions. Notes from 2/6/23 |
Video from 2/6/23 | |
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2/13/2023: We did some improper integrals and discussed indeterminant forms
of limits. Notes from 2/13/23 |
Video from 2/13/23 | |
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2/15/2023: We discussed l'Hopital's Rule, indeterminant forms of limits, and improper integrals. Notes from 2/15/23 |
Video from 2/15/23 | |
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2/17/2023: We discussed determining if improper integrals converge. Notes from 2/17/23 |
Video from 2/17/23 | |
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2/20/2023: We discussed inequalities of functions and improper integrals. Notes from 2/20/23 |
Video from 2/20/23 | |
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2/22/2023: We discussed inequalities of functions and improper integrals. We also used
integrals to find the area between curves. Notes from 2/22/23 |
Video from 2/22/23 | |
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2/24/2023: We found areas between curves and derived a volume formula. Notes from 2/24/23 |
Video from 2/24/23 | |
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2/27/2023: We used integrals to find various volumes. Notes from 2/27/23 |
Video from 2/27/23 | |
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3/1/2023: We the volume of a solid torus 4 different ways. Notes from 3/1/23 |
Video from 3/1/23 | |
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3/3/2023: We calculated volumes of solids of revolution. Notes from 3/3/23 |
Video from 3/3/23 | |
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3/6/2023: We reviewed how to determine if improper integrals converge or diverge. Notes from 3/6/23 |
Video from 3/6/23 | |
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3/10/2023: We computed the volume of a square pyramid, and we introduced the idea of computing the length
of a curve using an integral. Notes from 3/10/23 |
Video from 3/10/23 | |
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3/20/2023: We computed the length of a curve, and we introduced the idea of computing the surface area
of a surface of revolution. Notes from 3/20/23 |
Video from 3/20/23 | |
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3/22/2023: We computed surface area of a couple of surfaces of revolution and introduced the hyperbolic trig functions.
We also discussed volumes of solids with given bases and cross sections of similar shapes. Finally, we started
discussing using definite integrals to compute work (from physics). Notes from 3/22/23 |
Video from 3/22/23 | |
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3/24/2023: We computed the work required to pump gas out of a container. Notes from 3/24/23 |
Video from 3/24/23 | |
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3/27/2023: We computed the work required to move objects away from the Earth using Newton's Law
of Universal Gravitation. Notes from 3/27/23 |
Video from 3/27/23 | |
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3/29/2023: We discussed sequences defined in closed form and through recursive formulas.
We saw how to find limits of such sequences. Notes from 3/29/23 |
Video from 3/29/23 | |
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3/31/2023: We discussed limits of sequences. Notes from 3/31/23 |
Video from 3/31/23 | |
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4/5/2023: We derived formulas for finite and infinite geometric series. We also discussed telescoping series
and the comparison test for convergence of series. Notes from 4/5/23 |
Video from 4/5/23 | |
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4/10/2023: We discussed the review for test 3. Updated review solutions |
Video from 4/10/23 | |
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4/14/2023: We discussed the integral test and p-series test and limit comparison test. Corrected Notes from 4/14/23 |
Video from 4/14/23 | |
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4/17/2023: We determined series convergence via the integral test and limit comparison test. We also
started discussing Taylor polynomials and Taylor series. Notes from 4/17/23 |
Video from 4/17/23 | |
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4/19/2023: We discovered more ways of finding Taylor polynomials and Taylor series for functions. Notes from 4/19/23 |
Video from 4/19/23 | |
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4/21/2023: We discussed the alternating series test, the ratio and root tests, and the binomial Taylor expansion. Notes from 4/21/23 |
Video from 4/21/23 | |
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4/24/2023: We found limits using Taylor series, and we also used the ratio and root tests to figure out if series converge or not. Notes from 4/24/23 |
Video from 4/24/23 | |
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4/26/2023: We discussed evaluating infinite sums, intervals of convergence of power series. We also began discussing parametric equations and polar coordinates. Notes from 4/26/23 |
Video from 4/26/23 | |
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5/1/2023: We computed lengths of curves given by parametric equations. We also computed areas of regions in polar graphs. Notes from 5/1/23 |
Video from 5/1/23 | |
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5/3/2023: We worked on practice exam questions. Notes from 5/3/23 |
Video from 5/3/23 | |