Difference between revisions of "Math100Videos"

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<!-- Number of views as of Sept 6, 2016: 78,801 -->
 
<!-- Number of views as of Sept 6, 2016: 78,801 -->
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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.
  
 
{| width=100% class="calendar plainlinks"
 
{| width=100% class="calendar plainlinks"
  
 
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|-
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!width=8% | Topic
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!width=15% |  
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!width=10%|Video link
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!width=5%|Link
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!width=64%|Video contents
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!width=65%|Video contents
  
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|-  
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|- class="NewWeek OddWeek"
 
|Limits
 
|Limits
 
|Limits and tangent lines
 
|Limits and tangent lines
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|- class="OddWeek"
 
|- class="OddWeek"
 
|
 
|
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|[http://www.educreations.com/lesson/view/cell-size/23429678/?s=6FnDiS&ref=app]
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|One-sided limits
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|Cell size and nutrient balance: cell volume and area and the role of power functions in describing cell size limitations.
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|[https://youtu.be/z6bxo3esANE]
 +
|A simple example motivating one-sided limits
  
 
|- class="OddWeek"
 
|- class="OddWeek"
 
|
 
|
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|[http://www.educreations.com/lesson/view/graphing-a-simple-polynomial/23126849/?s=W2B6ko&ref=app]
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|Limits, continued
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|Sketching simple polynomials (y=x^3-ax).
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|[https://youtu.be/gdpUAJViM64]
 +
|Sometimes limits don't exist; one-sided limits; calculating limits
  
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|- class="NewWeek EvenWeek"
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|-class="OddWeek"
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|id="week2"|Week 2
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|[http://youtu.be/v13aqQaMaSE]
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|Approximating a rational function near the origin.
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|- class="EvenWeek"
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|
 
|
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|[http://youtu.be/cXYCX8YBEVw]
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| Limits at Infinity
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|Approximating a rational function for large x. Introduction to Hill functions.
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|[https://youtu.be/PI5mlJpLBhw]
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| Limits at infinity
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|- class="EvenWeek"
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|
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|[http://youtu.be/kuMWI8kL1wI]
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|Sketching Hill functions by hand and by Desmos ([[Videos and demos|see Hill functions demo]]). Comparing Hill functions with different parameter values.
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|- class="EvenWeek"
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|
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|
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|See video [1] above for an introduction to even and odd functions and also Sec 1.2.3 and Appendix C.D of the course notes.
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|- class="EvenWeek"
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|
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|[https://www.youtube.com/watch?v=-yXuSU_jHQ4&list=UUNHASevzeyPH-OZMax8iMAA]
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|Average rate of change and secant lines. Instantaneous rate of change.
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|- class="EvenWeek"
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|
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|[https://www.youtube.com/watch?v=PT2XNveWFoI&list=UUNHASevzeyPH-OZMax8iMAA]
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|Definition of the derivative.
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−
|- class="EvenWeek"
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|
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|[https://www.youtube.com/watch?v=2Yn05jvl0vI&list=UUNHASevzeyPH-OZMax8iMAA]
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|Continuity - definition and examples of three types of discontinuities.
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−
 
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|- class="EvenWeek"
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|
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|[https://www.youtube.com/watch?v=z4ED7eiNhBM&list=UUNHASevzeyPH-OZMax8iMAA]
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|Examples of computing the derivative of a function from the definition of the derivative.
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|- class="NewWeek OddWeek"
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|id="week3"|Week 3
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|[https://www.youtube.com/watch?v=E-owZqDrTkE&list=UUNHASevzeyPH-OZMax8iMAA]
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|Derivatives: analytic, and geometric (zoom in on a point). Sketching $f'(x)$ given $f(x)$ (intro).
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|- class="OddWeek"
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|
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|[https://www.educreations.com/lesson/view/using-a-spreadsheet-to-graph-a-function-and-its-de/24158741/?s=5I7yPP&ref=app]
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|Using a spreadsheet to graph a function and its (approximate) derivative.
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−
 
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|- class="OddWeek"
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|
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|[https://www.youtube.com/watch?v=HNXv3bmMGZ0&index=2&list=UUNHASevzeyPH-OZMax8iMAA]
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|Derivatives of polynomials.
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−
 
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|- class="OddWeek"
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−
|
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−
|[https://www.youtube.com/watch?v=giENfOUvE08&list=UUNHASevzeyPH-OZMax8iMAA&index=1]
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|Rules of differentiation:  Product and quotient rules.
+
  
 
|- class="NewWeek EvenWeek"
 
|- class="NewWeek EvenWeek"
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|id="week4"|Week 4
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| Continuity
−
|[https://www.youtube.com/watch?v=twnyZasD-d4&index=3&list=UUNHASevzeyPH-OZMax8iMAA]
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| Intro to Continuity
−
|Rules of differentiation:  Antiderivatives of polynomials.
+
|[https://youtu.be/tR5EkjCH9GU]
 +
| 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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|-class="EvenWeek"
 
|
 
|
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|[http://www.educreations.com/lesson/view/equation-of-a-tangent-line/23143393/?s=JD4d1l&ref=app]
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| Limits, Continuity, IVT
−
|Equation of a Tangent line.
+
|[https://youtu.be/zDuCAB1fx-o]
 +
|Strategies for evaluating limits; continuity; Intermediate Value Theorem
  
−
|- class="EvenWeek"
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|-class="EvenWeek"
 
|
 
|
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|[http://www.educreations.com/lesson/view/generic-tangent-line-and-intro-to-newton-s-method/23145498/?s=Ha5C44&ref=app]
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| Extra: continuity
−
|Generic Tangent line and intro to Newton's method.
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|[https://youtu.be/0ftIwSH9y4E]
 +
|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="EvenWeek"
+
|-class="NewWeek OddWeek"
−
|
+
|Derivatives
−
|[http://www.educreations.com/lesson/view/linear-approximation/23185994/?s=AN5Da8&ref=app]
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| Intro to Derivatives
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|Tangent lines and linear approximation.
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|[https://youtu.be/FOVKHhHIx90]
 +
|Introduction to derivatives: interpretations, derivatives at a point, derivatives of a function
  
−
|- class="EvenWeek"
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|-class="OddWeek"
 
|
 
|
−
|[http://youtu.be/teRQpllWtaI]
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|Graphing Derivatives
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|Introduction to Newton’s method - how it works and the formula for successive estimates.  
+
|[https://youtu.be/pe43D7BPHQw]
 +
| 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="NewWeek OddWeek"
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|-class="OddWeek"
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|id="week5"|Week 5
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|[http://youtu.be/TcPb4zkWEfo]
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|Introduction to Newton’s method - how to carry it out with a spreadsheet.
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−
 
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|- class="OddWeek"
+
 
|
 
|
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|[http://youtu.be/9nRU0V_3vjw]
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|Tangent Lines
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|Introduction to Newton’s method - how to choose a good $x_0$.
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|[https://youtu.be/D5M8dE7W874]
 +
|Find the tangent line to a curve; calculate derivatives using simple rules.
  
−
|- class="OddWeek"
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|-class="NewWeek EvenWeek"
−
|
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|Differentiation
−
|[https://www.youtube.com/watch?v=sDSt0G6dpzg]
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| Product and Quotient Rules
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|Increasing, decreasing and critical points.
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|[https://youtu.be/QHQp0PXS43E]
 +
| Derivatives of Products and Ratios
  
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|- class="OddWeek"
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|-class="EvenWeek"
 
|
 
|
−
|[http://youtu.be/_bRBbdsV7Hs]
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| Exponential
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|Concavity and inflection points.
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|[https://youtu.be/Vzs646Y5lNA]
−
 
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| Product rule and derivatives of exponential functions
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|- class="OddWeek"
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 +
|-class="EvenWeek"
 
|
 
|
−
|[https://www.youtube.com/watch?v=wNMK92GVTO8]
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| Trigonometric
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|Largest area of a rectangle inscribed in a semicircle
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|[https://youtu.be/BnxDzjYynAQ]
 +
|Derivatives of trigonometric functions.
  
−
|- class="OddWeek"
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|-class="EvenWeek"
 
|
 
|
−
|[https://www.youtube.com/watch?v=JIQTPlBs154]
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| Chain Rule
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|Absolute Maximum and Minimum Values of a Function - Calculus I
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|[https://youtu.be/kSL7atf0Omw]
 +
| Derivatives of compound functions.
  
−
|- class="NewWeek EvenWeek"
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|-class="EvenWeek"
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|id="week6"|Week 6
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|  
−
|[http://www.educreations.com/lesson/view/kepler-s-wedding/23147433/?s=uq5ffc&ref=app]
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| Review: Inverse Functions
−
|Kepler's Wedding - A wine optimization problem. (Blooper alert: want to get most wine for given budget)
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|[https://youtu.be/HiWYatEbNFw]
 +
| Inverse functions.
  
−
|- class="EvenWeek"
+
|-class="EvenWeek"
 
|
 
|
−
|[http://www.educreations.com/lesson/view/optimal-foraging/23177297/?s=UledUg&ref=app]
+
| Logarithms
−
|Optimal Foraging.
+
|[https://youtu.be/FMYIvZVzGlc]
 +
| Logarithmic functions and logarithmic differentiation.
  
 
|- class="NewWeek OddWeek"
 
|- class="NewWeek OddWeek"
−
|id="week7"|Week 7
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| Rates of Change
−
|[http://youtu.be/MB5zGQuDK5s]
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| Rates of Change
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|Least Squares -  finding the best fitting line y=ax through a set of data points. See also the [[Course notes/Fitting data - least squares| Fitting data]] supplement to the course notes.
+
|[https://youtu.be/3LMjCwvqAqw]
 +
| Rates of Change
  
 
|- class="OddWeek"
 
|- class="OddWeek"
 
|
 
|
−
|[https://www.youtube.com/watch?v=-1A7ZbO5dDY&feature=youtu.be]
+
|Exponential change
−
|Chain Rule: general introduction with examples
+
|[https://youtu.be/eblBM7tvRLY]
−
 
+
|Exponential growth and decay, such as radioactive decay, compound interest, and population growth. Introduction to differential equations.
 +
 
|- class="OddWeek"
 
|- class="OddWeek"
 
|
 
|
−
|[http://www.educreations.com/lesson/view/optimization-problem/14708865/?s=SmFwgM&ref=app]
+
|Newton's Law of Cooling
−
|Chain Rule: an applications to optimization problems involving plovers and crocodiles.
+
|[https://youtu.be/ug3k4fqQfbU]
 +
| Exponential rates of change applied to cooling bodies.
  
 
|- class="NewWeek EvenWeek"
 
|- class="NewWeek EvenWeek"
−
|id="week8"|Week 8
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| Related Rates  
−
|[https://www.youtube.com/watch?v=CPIt13UItqI]
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|  
−
|Implicit differentiation.
+
|[https://youtu.be/_G5dx3-J-uE]
−
 
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| Calculating the rate of change in systems with lots of interconnected changing parts.
−
|- class="EvenWeek"
+
−
|
+
−
|[https://www.youtube.com/watch?v=ERZAbNW3x0w]
+
−
|Related Rates.
+
−
 
+
−
|- class="EvenWeek"
+
−
|
+
−
|[http://www.educreations.com/lesson/view/exponential-functions-and-doublings/23173031/?s=tzmKvB&ref=app]
+
−
|Exponential functions and doubling.
+
−
 
+
−
|- class="EvenWeek"
+
−
|
+
−
|[http://www.educreations.com/lesson/view/derivative-of-a-x/23176738/?s=hQQTNF&ref=app]
+
−
|Exponential functions: derivative of $a^x$.
+
  
 
|- class="NewWeek OddWeek"
 
|- class="NewWeek OddWeek"
−
|id="week9"|Week 9
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| Polynomial Approximations
−
|[https://www.youtube.com/watch?v=qrEuGgjVuqI&feature=youtu.be]
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| First Approximations
−
|Inverse functions and logarithm, applications of logs.
+
|[https://youtu.be/cYtRR2NVeY0]
 +
|Estimating the value of a function with a constant, linear, or quadratic approximation.
  
 
|- class="OddWeek"
 
|- class="OddWeek"
 
|
 
|
−
|[http://www.educreations.com/lesson/view/differential-equation-for-exponential-growth-and-d/23382026/?s=GyshbX&ref=app]
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|Error Bounding
−
|Differential equations for growth and decay.
+
|[https://youtu.be/QavL2wnf8qk]
 +
| Give an approximation of a function, and bound the error you introduced.
  
 
|- class="OddWeek"
 
|- class="OddWeek"
 
|
 
|
−
|[http://youtu.be/5UFVLtEjUKo]
 
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|A differential equation for human population growth.
 
−
 
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|- class="OddWeek"
 
 
|
 
|
−
|[http://www.educreations.com/lesson/view/simple-differential-equation-problem/14300182/?s=GCrISn&ref=app]
+
|[https://youtu.be/VbjR6JF1OG4]
−
|A simple differential equation problem.
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|If you are given an error tolerance, which approximation should you use?
  
 
|- class="NewWeek EvenWeek"
 
|- class="NewWeek EvenWeek"
−
|id="week10"|Week 10
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| Optimization
−
|[http://www.educreations.com/lesson/view/geometry-of-change-i/23430270/?s=pB3DZB&ref=app]
+
| Extrema
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|Geometry of change: (I) Slope fields.
+
|[https://youtu.be/pxMPYzEm_-o]
 +
|Finding maxima and minima of a function.
  
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|- class="EvenWeek"
+
|-class="EvenWeek"
 
|
 
|
−
|[http://www.educreations.com/lesson/view/geometry-of-change-ii/23430914/?s=T8tWAw&ref=app]
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| Optimization
−
|Geometry of change: (II) State space. This one is more relevant to the pre-lecture questions but you should watch both.
+
|[https://youtu.be/IxYA1IWs2R4]
 +
|Second derivative test; solving an optimization word problem
  
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|- class="EvenWeek"
+
|-class="EvenWeek"
 
|
 
|
−
|[http://www.educreations.com/lesson/view/logistic-equation/23431216/?s=2GkGkB&ref=app]
 
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|The Logistic equation I (state space and slope field).
 
−
 
−
|- class="EvenWeek"
 
 
|
 
|
−
|[http://www.educreations.com/lesson/view/slope-field-for-a-differential-equation/14300653/?s=c6aBLN&ref=app]
+
|[https://youtu.be/E-20K2Mby60]
−
|The Logistic equation II (state space and slope field).
+
| Another optimization word problem
  
 
|- class="NewWeek OddWeek"
 
|- class="NewWeek OddWeek"
−
|id="week11"|Week 11
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| Mean Value Theorem
−
|[http://www.educreations.com/lesson/view/solving-a-diffl-eq-dy-dt-a-by/23385476/?s=ObLqjR&ref=app].
+
| Rolle's Theorem
−
|Solving differential equations of the type $dy/dt=a-by$.
+
|[https://youtu.be/WBvTXxzhg9A]
 +
| A differentiable function that takes the same value twice has a horizontal tangent line somewhere.
  
−
|- class="OddWeek"
+
|-class="OddWeek"
 
|
 
|
−
|[https://www.youtube.com/watch?v=Yga2chpiLtc]
+
| Mean Value Theorem
−
|Solving differential equations approximately using Euler's Method - theory.
+
|[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="OddWeek"
+
|-class="NewWeek EvenWeek"
−
|
+
|Curve Sketching
−
|[https://www.youtube.com/watch?v=z7Kbp8hl950]
+
| Curve Sketching 1
−
|Solving differential equations approximately using Euler's Method - spreadsheet.
+
|[https://youtu.be/XjuyNjKEAcg]
 +
| Sketching a curve using its domain and asymptotes.
  
−
|- class="NewWeek EvenWeek"
+
|-class="EvenWeek"
−
|id="week12"|Week 12
+
−
|[http://www.educreations.com/lesson/view/disease-dynamics-i/23465001/?s=pJChZV&ref=app]
+
−
|Disease dynamics I
+
−
 
+
−
|- class="EvenWeek"
+
 
|
 
|
−
|[http://www.educreations.com/lesson/view/disease-dynamics-ii/23465479/?s=EG7QeI&ref=app]
+
| Curve Sketching 2
−
|Disease dynamics II
+
|[https://youtu.be/m4GeiEsEzXk]
 +
|Sketching a curve using the first two derivatives.
  
−
|- class="EvenWeek"
+
|-class="EvenWeek"
 
|
 
|
−
|[https://www.youtube.com/watch?v=vg1hmGI2WDM], [https://www.youtube.com/watch?v=XZ6O4dWaeZ0]
+
| Symmetry
−
|Introduction to Trigonometric Functions and review of trigonometric identities.
+
|[https://youtu.be/vYZF078-Zow]
 +
| Even and odd functions.  
  
−
|- class="EvenWeek"
+
|-class="NewWeek OddWeek"
 +
| L'Hospital's Rule
 
|
 
|
−
|[http://www.educreations.com/lesson/view/periodic-function/14693344/?s=kxJDte&ref=app] (LEK),EC
+
|[https://youtu.be/VJ7DlV1vp8o]
−
|Trigonometric Functions and cyclic processes, phase, amplitude, etc. (fitting a sin or cos to a cyclic process), Inverse trig functions.
+
| Using l'Hospital's rule in a variety of situations
−
 
+
−
|- class="NewWeek OddWeek"
+
−
|id="week13"|Week 13
+
−
|[http://youtu.be/mdYuQ2NDVgA]
+
−
|Derivatives of trig functions, related rates examples.
+
−
 
+
−
|- class="OddWeek"
+
−
|
+
−
|[http://www.educreations.com/lesson/view/visual-angles/23504229/?s=0mhFFb&ref=app][https://www.educreations.com/lesson/view/visual-angles-part-2-escape-response/26980643/?s=YzbN0D&ref=app]
+
−
|The Escape Response and trigonometric related rates.
+
−
 
+
 
|}
 
|}

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
Retrieved from "https://wiki.math.ubc.ca/mathbook/M102/index.php?title=Math100Videos&oldid=7503"