Difference between revisions of "Math100Videos"
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| + | The videos below were made by Elyse Yeager for her Math 100 class at UBC. Due to the substantial overlap between the content of Math 100 and Math 102, we include them here for your use. Keep in mind that different courses and textbooks use slightly different conventions. | ||
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|[https://youtu.be/PI5mlJpLBhw] | |[https://youtu.be/PI5mlJpLBhw] | ||
| Limits at infinity | | Limits at infinity | ||
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|- class="NewWeek EvenWeek" | |- class="NewWeek EvenWeek" | ||
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| Before we learn the formal definition of a continuous function, dwell a little on what it means for a function's limit to differ from its value at a point. Being used to this behaviour will help you build intuition about continuity. | | Before we learn the formal definition of a continuous function, dwell a little on what it means for a function's limit to differ from its value at a point. Being used to this behaviour will help you build intuition about continuity. | ||
| − | |- | + | |-class="EvenWeek" |
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| Limits, Continuity, IVT | | Limits, Continuity, IVT | ||
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|Strategies for evaluating limits; continuity; Intermediate Value Theorem | |Strategies for evaluating limits; continuity; Intermediate Value Theorem | ||
| − | |- | + | |-class="EvenWeek" |
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| Extra: continuity | | Extra: continuity | ||
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|Think you understand continuity? Test yourself with a graph that has no limit... anywhere. (This video goes beyond the course material. Think of it as recreational.) | |Think you understand continuity? Test yourself with a graph that has no limit... anywhere. (This video goes beyond the course material. Think of it as recreational.) | ||
| − | |- | + | |-class="NewWeek OddWeek" |
|Derivatives | |Derivatives | ||
| Intro to Derivatives | | Intro to Derivatives | ||
| Line 58: | Line 59: | ||
|Introduction to derivatives: interpretations, derivatives at a point, derivatives of a function | |Introduction to derivatives: interpretations, derivatives at a point, derivatives of a function | ||
| − | |- | + | |-class="OddWeek" |
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|Graphing Derivatives | |Graphing Derivatives | ||
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| Use the graph of a function to create the graph of its derivative. Review the interpretation of positive and negative derivatives, and get used to looking at a line and intuiting its slope. | | Use the graph of a function to create the graph of its derivative. Review the interpretation of positive and negative derivatives, and get used to looking at a line and intuiting its slope. | ||
| − | |- | + | |-class="OddWeek" |
| | | | ||
|Tangent Lines | |Tangent Lines | ||
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|Find the tangent line to a curve; calculate derivatives using simple rules. | |Find the tangent line to a curve; calculate derivatives using simple rules. | ||
| − | |- | + | |-class="NewWeek EvenWeek" |
|Differentiation | |Differentiation | ||
| Product and Quotient Rules | | Product and Quotient Rules | ||
| Line 76: | Line 77: | ||
| Derivatives of Products and Ratios | | Derivatives of Products and Ratios | ||
| − | |- | + | |-class="EvenWeek" |
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| Exponential | | Exponential | ||
| Line 82: | Line 83: | ||
| Product rule and derivatives of exponential functions | | Product rule and derivatives of exponential functions | ||
| − | |- | + | |-class="EvenWeek" |
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| Trigonometric | | Trigonometric | ||
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|Derivatives of trigonometric functions. | |Derivatives of trigonometric functions. | ||
| − | |- | + | |-class="EvenWeek" |
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| Chain Rule | | Chain Rule | ||
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| Derivatives of compound functions. | | Derivatives of compound functions. | ||
| − | + | |-class="EvenWeek" | |
| − | + | | | |
| − | + | | Review: Inverse Functions | |
| − | + | |[https://youtu.be/HiWYatEbNFw] | |
| − | + | | Inverse functions. | |
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| + | |-class="EvenWeek" | ||
| + | | | ||
| + | | Logarithms | ||
| + | |[https://youtu.be/FMYIvZVzGlc] | ||
| + | | Logarithmic functions and logarithmic differentiation. | ||
| + | |- class="NewWeek OddWeek" | ||
| + | | Rates of Change | ||
| + | | Rates of Change | ||
| + | |[https://youtu.be/3LMjCwvqAqw] | ||
| + | | Rates of Change | ||
| + | |||
| + | |- class="OddWeek" | ||
| + | | | ||
| + | |Exponential change | ||
| + | |[https://youtu.be/eblBM7tvRLY] | ||
| + | |Exponential growth and decay, such as radioactive decay, compound interest, and population growth. Introduction to differential equations. | ||
| + | |||
| + | |- class="OddWeek" | ||
| + | | | ||
| + | |Newton's Law of Cooling | ||
| + | |[https://youtu.be/ug3k4fqQfbU] | ||
| + | | Exponential rates of change applied to cooling bodies. | ||
|- class="NewWeek EvenWeek" | |- class="NewWeek EvenWeek" | ||
| + | | Related Rates | ||
| + | | | ||
| + | |[https://youtu.be/_G5dx3-J-uE] | ||
| + | | Calculating the rate of change in systems with lots of interconnected changing parts. | ||
| + | |||
| + | |- class="NewWeek OddWeek" | ||
| + | | Polynomial Approximations | ||
| + | | First Approximations | ||
| + | |[https://youtu.be/cYtRR2NVeY0] | ||
| + | |Estimating the value of a function with a constant, linear, or quadratic approximation. | ||
| + | |||
| + | |- class="OddWeek" | ||
| | | | ||
| − | |[ | + | |Error Bounding |
| − | | | + | |[https://youtu.be/QavL2wnf8qk] |
| + | | Give an approximation of a function, and bound the error you introduced. | ||
| − | |- class=" | + | |- class="OddWeek" |
| + | | | ||
| | | | ||
| − | |[ | + | |[https://youtu.be/VbjR6JF1OG4] |
| − | | | + | |If you are given an error tolerance, which approximation should you use? |
| − | |- class="EvenWeek" | + | |- class="NewWeek EvenWeek" |
| + | | Optimization | ||
| + | | Extrema | ||
| + | |[https://youtu.be/pxMPYzEm_-o] | ||
| + | |Finding maxima and minima of a function. | ||
| + | |||
| + | |-class="EvenWeek" | ||
| | | | ||
| − | |[ | + | | Optimization |
| − | | | + | |[https://youtu.be/IxYA1IWs2R4] |
| + | |Second derivative test; solving an optimization word problem | ||
| − | |- class="EvenWeek" | + | |-class="EvenWeek" |
| | | | ||
| | | | ||
| − | | | + | |[https://youtu.be/E-20K2Mby60] |
| + | | Another optimization word problem | ||
| − | |- class=" | + | |- class="NewWeek OddWeek" |
| − | | | + | | Mean Value Theorem |
| − | |[https:// | + | | Rolle's Theorem |
| − | | | + | |[https://youtu.be/WBvTXxzhg9A] |
| + | | A differentiable function that takes the same value twice has a horizontal tangent line somewhere. | ||
| − | |- class=" | + | |-class="OddWeek" |
| | | | ||
| − | |[https:// | + | | Mean Value Theorem |
| − | | | + | |[https://youtu.be/3lardKQbD_I] |
| + | | A differentiable function has a point where its instantaneous rate of change is equal to is average rate of change over an interval. | ||
| − | |- class="EvenWeek" | + | |-class="NewWeek EvenWeek" |
| + | |Curve Sketching | ||
| + | | Curve Sketching 1 | ||
| + | |[https://youtu.be/XjuyNjKEAcg] | ||
| + | | Sketching a curve using its domain and asymptotes. | ||
| + | |||
| + | |-class="EvenWeek" | ||
| | | | ||
| − | |[https:// | + | | Curve Sketching 2 |
| − | | | + | |[https://youtu.be/m4GeiEsEzXk] |
| + | |Sketching a curve using the first two derivatives. | ||
| − | |- class="EvenWeek" | + | |-class="EvenWeek" |
| | | | ||
| − | |[https:// | + | | Symmetry |
| − | | | + | |[https://youtu.be/vYZF078-Zow] |
| − | + | | Even and odd functions. | |
| + | |-class="NewWeek OddWeek" | ||
| + | | L'Hospital's Rule | ||
| + | | | ||
| + | |[https://youtu.be/VJ7DlV1vp8o] | ||
| + | | Using l'Hospital's rule in a variety of situations | ||
|} | |} | ||
Latest revision as of 13:58, 18 August 2017
The videos below were made by Elyse Yeager for her Math 100 class at UBC. Due to the substantial overlap between the content of Math 100 and Math 102, we include them here for your use. Keep in mind that different courses and textbooks use slightly different conventions.
| Topic | Link | Video contents | |
|---|---|---|---|
| Limits | Limits and tangent lines | [1] | Average and Instantaneous Velocity; secant and tangent line; limit notation |
| One-sided limits | [2] | A simple example motivating one-sided limits | |
| Limits, continued | [3] | Sometimes limits don't exist; one-sided limits; calculating limits | |
| Limits at Infinity | [4] | Limits at infinity | |
| Continuity | Intro to Continuity | [5] | Before we learn the formal definition of a continuous function, dwell a little on what it means for a function's limit to differ from its value at a point. Being used to this behaviour will help you build intuition about continuity. |
| Limits, Continuity, IVT | [6] | Strategies for evaluating limits; continuity; Intermediate Value Theorem | |
| Extra: continuity | [7] | Think you understand continuity? Test yourself with a graph that has no limit... anywhere. (This video goes beyond the course material. Think of it as recreational.) | |
| Derivatives | Intro to Derivatives | [8] | Introduction to derivatives: interpretations, derivatives at a point, derivatives of a function |
| Graphing Derivatives | [9] | Use the graph of a function to create the graph of its derivative. Review the interpretation of positive and negative derivatives, and get used to looking at a line and intuiting its slope. | |
| Tangent Lines | [10] | Find the tangent line to a curve; calculate derivatives using simple rules. | |
| Differentiation | Product and Quotient Rules | [11] | Derivatives of Products and Ratios |
| Exponential | [12] | Product rule and derivatives of exponential functions | |
| Trigonometric | [13] | Derivatives of trigonometric functions. | |
| Chain Rule | [14] | Derivatives of compound functions. | |
| Review: Inverse Functions | [15] | Inverse functions. | |
| Logarithms | [16] | Logarithmic functions and logarithmic differentiation. | |
| Rates of Change | Rates of Change | [17] | Rates of Change |
| Exponential change | [18] | Exponential growth and decay, such as radioactive decay, compound interest, and population growth. Introduction to differential equations. | |
| Newton's Law of Cooling | [19] | Exponential rates of change applied to cooling bodies. | |
| Related Rates | [20] | Calculating the rate of change in systems with lots of interconnected changing parts. | |
| Polynomial Approximations | First Approximations | [21] | Estimating the value of a function with a constant, linear, or quadratic approximation. |
| Error Bounding | [22] | Give an approximation of a function, and bound the error you introduced. | |
| [23] | If you are given an error tolerance, which approximation should you use? | ||
| Optimization | Extrema | [24] | Finding maxima and minima of a function. |
| Optimization | [25] | Second derivative test; solving an optimization word problem | |
| [26] | Another optimization word problem | ||
| Mean Value Theorem | Rolle's Theorem | [27] | A differentiable function that takes the same value twice has a horizontal tangent line somewhere. |
| Mean Value Theorem | [28] | A differentiable function has a point where its instantaneous rate of change is equal to is average rate of change over an interval. | |
| Curve Sketching | Curve Sketching 1 | [29] | Sketching a curve using its domain and asymptotes. |
| Curve Sketching 2 | [30] | Sketching a curve using the first two derivatives. | |
| Symmetry | [31] | Even and odd functions. | |
| L'Hospital's Rule | [32] | Using l'Hospital's rule in a variety of situations |
