Difference between revisions of "Pre-lecture videos"

Revision as of 16:10, 8 September 2015

	Video link	Video contents
Week 1	[1]	Power functions - when is $x^n>x^m$ and where do they intersect. Introduction to even and odd functions.
	[2]	Cell size and nutrient balance: cell volume and area and the role of power functions in describing cell size limitations.
	[3]	Sketching simple polynomials (y=x^3-ax).
Week 2	[4]	Approximating a rational function near the origin.
	[5]	Approximating a rational function for large x. Introduction to Hill functions.
	[6]	Sketching Hill functions by hand and by Desmos (see Hill functions demo). Comparing Hill functions with different parameter values.
		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.
	[7]	Average rate of change and secant lines. Instantaneous rate of change.
	[8]	Definition of the derivative.
	[9]	Continuity - definition and examples of three types of discontinuities.
	[10]	Examples of computing the derivative of a function from the definition of the derivative.
Week 3	[11]	Derivatives: analytic, and geometric (zoom in on a point). Sketching $f'(x)$ given $f(x)$ (intro).
	[12] NEW!!	Using a spreadsheet to graph a function and its (approximate) derivative.
	[13]	Derivatives of polynomials.
	[14]	Rules of differentiation: Antiderivatives of polynomials.
	[15]	Rules of differentiation: Product and quotient rules.
Week 4	[16]	Equation of a Tangent line.
	[17]	Generic Tangent line and intro to Newton's method.
	[18]	Tangent lines and linear approximation.
	[19]	Introduction to Newton’s method - how it works and the formula for successive estimates.
	[20]	Introduction to Newton’s method - how to carry it out with a spreadsheet.
	[21]	Introduction to Newton’s method - how to choose a good $x_0$.
	[22]	Increasing, decreasing and critical points.
	[23]	Concavity and inflection points.
Week 5
		MIDTERM 1: 6-7 pm
	EC	Finish sketching functions. Introduce simple optimization problem(s).
		More optimization examples including those with a constraint and those on bounded intervals. Distinction between absolute (global) and local minima and maxima.
Week 6	[24]	Kepler's Wedding - A wine optimization problem. (Blooper alert: want to get most wine for given budget)
	[25]	Optimal Foraging.
	[26],[27],[28]	Least Squares - finding the mean of a data set. See also the Fitting data supplement to the course notes.
Week 7		THANKSGIVING - no classes.
	See Oct 10	Least Squares - finding the best fitting line y=ax through a set of data points.
	[29], [30]	Chain Rule: examples, applications to optimization problems.
Week 8	[31][32]	More Chain Rule: Related Rates and Implicit differentiation.
	[33]	Exponential functions: intro and motivation, derivative of exponential functions.
	[34]	Exponential functions: intro and motivation, derivative of exponential functions.
	[35]	Inverse functions and logarithm, applications of logs.
Week 9	[36]	Exponential growth and decay, intro to differential equations, population growth and/or other examples.
	[37]	Exponential growth and decay, intro to differential equations, population growth and/or other examples.
	[38]	Exponential growth and decay, intro to differential equations, population growth and/or other examples.
	[39]	Solving differential equations of the type $dy/dt=a-by$.
	[40]	Solving differential equations of the type $dy/dt=a-by$.
	LEK	Newton's Law of Cooling (Murder Mystery example).
Week 10		Complete and/or review above topics.
		MIDTERM 2: 6-7 pm
	[41], [42]	Solving differential equations approximately using Euler's Method.
	[43]	Geometry of change: (I) Slope fields.
	[44]	Geometry of change: (II) State space. This one is more relevant to the pre-lecture questions but you should watch both.
Week 11	[45]	Geometry of change: (I) Slope fields.
	[46]	Geometry of change: (II) State space.
		Remembrance Day. University closed.
	[47]	The Logistic equation (state space and slope field).
	[48]	The Logistic equation (state space and slope field).
	[49]	Disease dynamics
	[50]	Disease dynamics
Week 12		Review of differential equations and/or complete above topics.
	[51], [52]	Introduction to Trigonometric Functions and review of trigonometric identities.
	[53] (LEK),EC	Trigonometric Functions and cyclic processes, phase, amplitude, etc. (fitting a sin or cos to a cyclic process), Inverse trig functions.
Week 13	[54]	Derivatives of trig functions, related rates examples.
	[55][56]	The Escape Response and trigonometric related rates.
		Second order ODEs. Complete and/or review trig.

Difference between revisions of "Pre-lecture videos"

Revision as of 16:10, 8 September 2015

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-|Sept 3
 |[https://www.educreations.com/lesson/view/power-functions/23591979/?s=T9jC77&ref=app]
 |Power functions - when is $x^n>x^m$ and where do they intersect. Introduction to even and odd functions.
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-|
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 |[http://www.educreations.com/lesson/view/cell-size/23429678/?s=6FnDiS&ref=app]
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-|Sept 5
 |[http://www.educreations.com/lesson/view/graphing-a-simple-polynomial/23126849/?s=W2B6ko&ref=app]
 |Sketching simple polynomials (y=x^3-ax).
@@ Line 27: / Line 23: @@
 |- class="NewWeek EvenWeek"
 |id="week2"|Week 2
-|Sept 8
 |[http://youtu.be/v13aqQaMaSE]
 |Approximating a rational function near the origin.
 |- class="EvenWeek"
-|
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 |[http://youtu.be/cXYCX8YBEVw]
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-|Sept 10
 |[https://www.youtube.com/watch?v=-yXuSU_jHQ4&list=UUNHASevzeyPH-OZMax8iMAA]
 |Average rate of change and secant lines. Instantaneous rate of change.
 |- class="EvenWeek"
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 |[https://www.youtube.com/watch?v=PT2XNveWFoI&list=UUNHASevzeyPH-OZMax8iMAA]
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-|Sept 12
 |[https://www.youtube.com/watch?v=2Yn05jvl0vI&list=UUNHASevzeyPH-OZMax8iMAA]
 |Continuity - definition and examples of three types of discontinuities.
 |- class="EvenWeek"
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 |[https://www.youtube.com/watch?v=z4ED7eiNhBM&list=UUNHASevzeyPH-OZMax8iMAA]
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 |id="week3"|Week 3
-|Sept 15
 |[https://www.youtube.com/watch?v=E-owZqDrTkE&list=UUNHASevzeyPH-OZMax8iMAA]
 |Derivatives: analytic, and geometric (zoom in on a point). Sketching $f'(x)$ given $f(x)$ (intro).
@@ Line 81: / Line 68: @@
 |- class="OddWeek"
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-|Sept 17-19
 |[https://www.educreations.com/lesson/view/using-a-spreadsheet-to-graph-a-function-and-its-de/24158741/?s=5I7yPP&ref=app] NEW!!
 |Using a spreadsheet to graph a function and its (approximate) derivative.
 |- class="OddWeek"
-|
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 |[https://www.youtube.com/watch?v=HNXv3bmMGZ0&index=2&list=UUNHASevzeyPH-OZMax8iMAA]
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 |- class="NewWeek EvenWeek"
 |id="week4"|Week 4
-|Sept 22
 |[http://www.educreations.com/lesson/view/equation-of-a-tangent-line/23143393/?s=JD4d1l&ref=app]
 |Equation of a Tangent line.
 |- 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]
@@ Line 116: / Line 97: @@
 |- class="EvenWeek"
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 |[http://www.educreations.com/lesson/view/linear-approximation/23185994/?s=AN5Da8&ref=app]
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 |- class="EvenWeek"
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-|Sept 24
 |[http://youtu.be/teRQpllWtaI]
 |Introduction to Newton’s method - how it works and the formula for successive estimates.
 |- class="EvenWeek"
-|
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 |[http://youtu.be/TcPb4zkWEfo]
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 |[https://www.youtube.com/watch?v=sDSt0G6dpzg]
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-|Sept 26
 |[http://youtu.be/_bRBbdsV7Hs]
 |Concavity and inflection points.
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-|Sept 29
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-|Sept 30
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 |<span class="emphasize">'''MIDTERM 1: 6-7 pm'''</span>
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 |- class="OddWeek"
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-|Oct 1
 |EC
 |Finish sketching functions. Introduce simple optimization problem(s).
@@ Line 172: / Line 144: @@
 |- class="OddWeek"
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-|Oct 3
 |
 |More optimization examples including those with a constraint and those on bounded intervals. Distinction between absolute (global) and local minima and maxima.
@@ Line 178: / Line 149: @@
 |- class="NewWeek EvenWeek"
 |id="week6"|Week 6
-|Oct 6
 |[http://www.educreations.com/lesson/view/kepler-s-wedding/23147433/?s=uq5ffc&ref=app]
 |Kepler's Wedding - A wine optimization problem. (Blooper alert: want to get most wine for given budget)
@@ Line 184: / Line 154: @@
 |- class="EvenWeek"
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-|Oct 8
 |[http://www.educreations.com/lesson/view/optimal-foraging/23177297/?s=UledUg&ref=app]
 |Optimal Foraging.
@@ Line 190: / Line 159: @@
 |- class="EvenWeek"
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-|Oct 10
 |[http://youtu.be/MB5zGQuDK5s],[http://slesse.math.ubc.ca/Teaching/Screencasts/LinearRegression1.mov],[http://slesse.math.ubc.ca/Teaching/Screencasts/LinearRegression2.mov]
 |Least Squares - finding the mean of a data set. See also the [[Course notes/Fitting data - least squares| Fitting data]] supplement to the course notes.
@@ Line 196: / Line 164: @@
 |- class="NewWeek OddWeek"
 |id="week7"|Week 7
-|Oct 13
 |
 |THANKSGIVING - no classes.
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-|Oct 15
 |See Oct 10
 ||Least Squares - finding the best fitting line y=ax through a set of data points.
@@ Line 208: / Line 174: @@
 |- class="OddWeek"
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-|Oct 17
 |[http://www.educreations.com/lesson/view/optimization-problem/14708865/?s=SmFwgM&ref=app], [https://www.youtube.com/watch?v=-1A7ZbO5dDY&feature=youtu.be]
 |Chain Rule: examples, applications to optimization problems.
@@ Line 214: / Line 179: @@
 |- class="NewWeek EvenWeek"
 |id="week8"|Week 8
-|Oct 20
 |[https://www.youtube.com/watch?v=CPIt13UItqI][https://www.youtube.com/watch?v=ERZAbNW3x0w]
 |More Chain Rule: Related Rates and Implicit differentiation.
@@ Line 220: / Line 184: @@
 |- class="EvenWeek"
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-|Oct 22
 |[http://www.educreations.com/lesson/view/exponential-functions-and-doublings/23173031/?s=tzmKvB&ref=app]
 |Exponential functions: intro and motivation, derivative of exponential functions.
@@ Line 226: / Line 189: @@
 |- class="EvenWeek"
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-|Oct 22
 |[http://www.educreations.com/lesson/view/derivative-of-a-x/23176738/?s=hQQTNF&ref=app]
 |Exponential functions: intro and motivation, derivative of exponential functions.
@@ Line 232: / Line 194: @@
 |- class="EvenWeek"
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-|Oct 24
 |[https://www.youtube.com/watch?v=qrEuGgjVuqI&feature=youtu.be]
 |Inverse functions and logarithm, applications of logs.
@@ Line 238: / Line 199: @@
 |- class="NewWeek OddWeek"
 |id="week9"|Week 9
-|Oct 27
 |[http://www.educreations.com/lesson/view/differential-equation-for-exponential-growth-and-d/23382026/?s=GyshbX&ref=app]
 |Exponential growth and decay, intro to differential equations, population growth and/or other examples.
 |- class="OddWeek"
-|
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 |[http://youtu.be/5UFVLtEjUKo]
@@ Line 249: / Line 208: @@
 |- class="OddWeek"
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 |[http://www.educreations.com/lesson/view/simple-differential-equation-problem/14300182/?s=GCrISn&ref=app]
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-|Oct 29
 |[http://www.educreations.com/lesson/view/solving-de-checking-that-a-function-is-a-solution/23384860/?s=qwZb1k&ref=app]
 |Solving differential equations of the type $dy/dt=a-by$.
@@ Line 262: / Line 219: @@
 |- class="OddWeek"
 |
-|Oct 29
 |[http://www.educreations.com/lesson/view/solving-a-diffl-eq-dy-dt-a-by/23385476/?s=ObLqjR&ref=app]
 |Solving differential equations of the type $dy/dt=a-by$.
@@ Line 268: / Line 224: @@
 |- class="OddWeek"
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-|Oct 31
 |LEK
 |Newton's Law of Cooling (Murder Mystery example).
@@ Line 274: / Line 229: @@
 |- class="NewWeek EvenWeek"
 |id="week10"|Week 10
-|Nov 3
 |
 |Complete and/or review above topics.
@@ Line 280: / Line 234: @@
 |- class="EvenWeek"
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-|Nov 4
 |
 |<span class="emphasize">'''MIDTERM 2: 6-7 pm'''</span>
@@ Line 286: / Line 239: @@
 |- class="EvenWeek"
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-|Nov 5
 |[https://www.youtube.com/watch?v=Yga2chpiLtc], [http://slesse.math.ubc.ca/Teaching/Screencasts/EulersMethod.mov]
 |Solving differential equations approximately using Euler's Method.
@@ Line 292: / Line 244: @@
 |- class="EvenWeek"
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-|Nov 7
 |[http://www.educreations.com/lesson/view/geometry-of-change-i/23430270/?s=pB3DZB&ref=app]
 |Geometry of change: (I) Slope fields.
 |- class="EvenWeek"
-|
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 |[http://www.educreations.com/lesson/view/geometry-of-change-ii/23430914/?s=T8tWAw&ref=app]
@@ Line 304: / Line 254: @@
 |- class="NewWeek OddWeek"
 |id="week11"|Week 11
-|Nov 10
 |[http://www.educreations.com/lesson/view/geometry-of-change-i/23430270/?s=pB3DZB&ref=app]
 |Geometry of change: (I) Slope fields.
 |- class="OddWeek"
-|
 |
 |[http://www.educreations.com/lesson/view/geometry-of-change-ii/23430914/?s=T8tWAw&ref=app]
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 |- class="OddWeek"
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-|Nov 11
 |
 |Remembrance Day. University closed.
@@ Line 322: / Line 269: @@
 |- class="OddWeek"
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-|Nov 12
 |[http://www.educreations.com/lesson/view/logistic-equation/23431216/?s=2GkGkB&ref=app]
 |The Logistic equation (state space and slope field).
 |- class="OddWeek"
-|
 |
 |[http://www.educreations.com/lesson/view/slope-field-for-a-differential-equation/14300653/?s=c6aBLN&ref=app]
@@ Line 334: / Line 279: @@
 |- class="OddWeek"
 |
-|Nov 14
 |[http://www.educreations.com/lesson/view/disease-dynamics-i/23465001/?s=pJChZV&ref=app]
 |Disease dynamics
 |- class="OddWeek"
-|
 |
 |[http://www.educreations.com/lesson/view/disease-dynamics-ii/23465479/?s=EG7QeI&ref=app]
@@ Line 346: / Line 289: @@
 |- class="NewWeek EvenWeek"
 |id="week12"|Week 12
-|Nov 17
 |
 |Review of differential equations and/or complete above topics.
@@ Line 352: / Line 294: @@
 |- class="EvenWeek"
 |
-|Nov 19
 |[https://www.youtube.com/watch?v=vg1hmGI2WDM], [https://www.youtube.com/watch?v=XZ6O4dWaeZ0]
 |Introduction to Trigonometric Functions and review of trigonometric identities.
@@ Line 358: / Line 299: @@
 |- class="EvenWeek"
 |
-|Nov 21
 |[http://www.educreations.com/lesson/view/periodic-function/14693344/?s=kxJDte&ref=app] (LEK),EC
 |Trigonometric Functions and cyclic processes, phase, amplitude, etc. (fitting a sin or cos to a cyclic process), Inverse trig functions.
@@ Line 364: / Line 304: @@
 |- class="NewWeek OddWeek"
 |id="week13"|Week 13
-|Nov 24
 |[http://youtu.be/mdYuQ2NDVgA]
 |Derivatives of trig functions, related rates examples.
@@ Line 370: / Line 309: @@
 |- class="OddWeek"
 |
-|Nov 26
 |[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.
@@ Line 376: / Line 314: @@
 |- class="OddWeek"
 |
-|Nov 28
 |
 |Second order ODEs. Complete and/or review trig.
 |}