Topics to be covered | Youtube links |
1. Functions and models 1.1: Four ways to represent a function Ex: 2,4,7–10, 31-55,72–78
| https://youtu.be/GY6Q2f2kvY0 https://youtu.be/djT6-YamHaA https://youtu.be/Si2vmzUWfJE https://youtu.be/djT6-YamHaA
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1.2: Mathematical models: A catalog of essential functions Ex: 1-5,6,8,9 1.3: New functions from old functions Ex:1, 3, 5-7, 9-24, 27, 33-36, 39, 43- 47, 49, 50, 51, 61
| https://youtu.be/-oGTA1Nem6o |
https://youtu.be/Ecfw12xUxe0 https://youtu.be/VM3iMj0BwLE https://youtu.be/ZFPkQkURSxk https://youtu.be/fKyBOLsqRlo https://youtu.be/0uiUIjkSjb8
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1.5: Exponential functions Ex: 1,3,11–21,33 1.6: Inverse functions and logarithms Ex: 3–18,21-31,35–41,47–57,63–72,75 | https://youtu.be/RAYmoFWePn4 https://youtu.be/pQinmTySE3w https://youtu.be/AwkiuW18rdU https://youtu.be/6WMZ7J0wwMI https://youtu.be/LRbi_pMX1DM
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2. Limits and derivatives 2.2 The limit of a function Ex: 7,8,15–17,29-33,38 2.3 Calculating limits using the limit laws Ex: 1, 2, 7, 9-32, 37, 39, 41–46, 48, 49, 51, 52 § 2.5: 2.5 Continuity Ex: 4, 18, 20, 23, 33, 35–39, 43, 45- 47, 51-54, 57, 58, 65, 67 | https://youtu.be/YNstP0ESndU https://youtu.be/jfEmtHyUmpY https://youtu.be/y0LfEW2lm2I https://youtu.be/q7kxe6T0E14 https://youtu.be/6e4Wtgc43KQ
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2.6: Limits at infinity; Horizontal asymptotes Ex: 3,7,15–38,41–46,48,52-56 2.7: Derivatives and rate of change Ex: 27,29,31,33-38,53,54 2.8: The derivative as a function Ex: 1,3,23,29,37-40
| https://youtu.be/NmLljBAg82o |
https://youtu.be/-aTLjoDT1GQ https://youtu.be/IWpsnR2uRus https://youtu.be/5yfh5cf4-0w |
3. Differentiation rules 3.1: Derivatives of polynomials and exponential functions Ex: 3–36, 44, 46, 52-55, 57, 68, 70, 74, 75, 77 3.2: The product and quotient rules Ex: 3-9, 11-13, 16-25, 27, 33, 39, 43, 48, 49, 52, 54
| https://youtu.be/17X5g9QArTc
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3.3: Derivatives of trigonometric functions Ex: 1–16, 21–24, 30, 39–49, 52 3.4: The chain rule Ex: 7–17, 23-45, 50, 51, 53, 56, 59, 61, 63, 65, 66, 69, 95-97
| https://youtu.be/_niP0JaOgHY |
https://youtu.be/HaHsqDjWMLU |
3.5: Implicit differentiation Ex: 55–21, 24, 26, 37, 49-60, 75-78 3.6: Derivatives of logarithmic functions Ex: 2-23, 26, 27, 29, 33, 41-52, 53, 55
| https://youtu.be/LGY-DjFsALc |
https://youtu.be/5-TKfOzwu9w |
3.10: Linear approximations and differentials Ex: 2, 3, 6–11, 13, 15, 17, 19, 20, 23–31 3.11: Hyperbolic Functions Ex: 7–21, 23, 31, 33, 35, 40, 41, 43, 45, 47, 54
| https://youtu.be/FIbpibkywmk |
https://youtu.be/uQmNyBztsas |
4. Applications of differentiation 4.1: Maximum and minimum values Ex: 9, 11, 13, 29–45, 47–62, 65–68 4.2: The mean value theorem Ex: 2, 5, 7, 9, 11, 15, 17, 19, 23, 25 4.3: How derivatives affect the shape of a graph Ex:5–7, 9, 11, 13, 15-17, 19, 25, 31, 37-53
| https://youtu.be/9wEHwFrUyOU https://youtu.be/SL2RobwU_M4 https://youtu.be/Dyl7jPlJXOM https://youtu.be/WCq3sRzsJfs
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4. Applications of 4.4: Indefinite forms and L'Hopital's rule Ex: 1–66, 74, 89, 90
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4.5: Summary of curve sketching Ex: 5, 9, 13, 17, 19, 24, 25, 29, 30, 37, 43, 45, 54, 66-69
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5. Integrals 5.2: The definite integral Ex: 34–42,47–50 5.3: The fundamental theorem of calculus Ex: 2, 7–44, 55–62
| https://youtu.be/6WUjbJEeJwM |
https://youtu.be/Gc3QvUB0PkI |
5.4: Indefinite integrals and the net change theorem Ex: 2,5–18,21–46,49,50 5.5: The substitution rule Ex: 7–48, 53–74, 74, 78, 79, 85, 86
| https://youtu.be/iezOIYwMpsA |
https://youtu.be/sdYdnpYn-1o
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