Difference between revisions of "Pre-lecture videos"

From UBCMATH WIKI
Jump to: navigation, search
 
(12 intermediate revisions by 3 users not shown)
Line 1: Line 1:
 +
<!-- Number of views as of Sept 6, 2016: 78,801 -->
 +
 
{| width=100% class="calendar plainlinks"
 
{| width=100% class="calendar plainlinks"
  
Line 34: Line 36:
 
|
 
|
 
|[http://youtu.be/kuMWI8kL1wI]
 
|[http://youtu.be/kuMWI8kL1wI]
−
|Sketching Hill functions by hand and by Desmos ([[Online_interactive_tools|see Hill functions demo]]). Comparing Hill functions with different parameter values.
+
|Sketching Hill functions by hand and by Desmos ([[Videos and demos|see Hill functions demo]]). Comparing Hill functions with different parameter values.
  
 
|- class="EvenWeek"
 
|- class="EvenWeek"
 
|
 
|
 
|
 
|
−
|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.
+
|See video [1] above for an introduction to even and odd functions and also Sec 1.4 and Appendix C.4 of the OpenBook (a.k.a."Course Notes").
  
 
|- class="EvenWeek"
 
|- class="EvenWeek"
Line 75: Line 77:
 
|[https://www.youtube.com/watch?v=HNXv3bmMGZ0&index=2&list=UUNHASevzeyPH-OZMax8iMAA]
 
|[https://www.youtube.com/watch?v=HNXv3bmMGZ0&index=2&list=UUNHASevzeyPH-OZMax8iMAA]
 
|Derivatives of polynomials.
 
|Derivatives of polynomials.
−
 
−
|- class="OddWeek"
 
−
|
 
−
|[https://www.youtube.com/watch?v=twnyZasD-d4&index=3&list=UUNHASevzeyPH-OZMax8iMAA]
 
−
|Rules of differentiation:  Antiderivatives of polynomials.
 
  
 
|- class="OddWeek"
 
|- class="OddWeek"
Line 88: Line 85:
 
|- class="NewWeek EvenWeek"
 
|- class="NewWeek EvenWeek"
 
|id="week4"|Week 4
 
|id="week4"|Week 4
 +
|[https://www.youtube.com/watch?v=twnyZasD-d4&index=3&list=UUNHASevzeyPH-OZMax8iMAA]
 +
|Rules of differentiation:  Antiderivatives of polynomials.
 +
 +
|- class="EvenWeek"
 +
|
 
|[http://www.educreations.com/lesson/view/equation-of-a-tangent-line/23143393/?s=JD4d1l&ref=app]
 
|[http://www.educreations.com/lesson/view/equation-of-a-tangent-line/23143393/?s=JD4d1l&ref=app]
 
|Equation of a Tangent line.
 
|Equation of a Tangent line.
Line 106: Line 108:
 
|Introduction to Newton’s method - how it works and the formula for successive estimates.  
 
|Introduction to Newton’s method - how it works and the formula for successive estimates.  
  
−
|- class="EvenWeek"
+
|- class="NewWeek OddWeek"
−
|
+
|id="week5"|Week 5
 
|[http://youtu.be/TcPb4zkWEfo]
 
|[http://youtu.be/TcPb4zkWEfo]
 
|Introduction to Newton’s method - how to carry it out with a spreadsheet.
 
|Introduction to Newton’s method - how to carry it out with a spreadsheet.
  
−
|- class="EvenWeek"
+
|- class="OddWeek"
 
|
 
|
 
|[http://youtu.be/9nRU0V_3vjw]
 
|[http://youtu.be/9nRU0V_3vjw]
 
|Introduction to Newton’s method - how to choose a good $x_0$.
 
|Introduction to Newton’s method - how to choose a good $x_0$.
  
−
|- class="NewWeek OddWeek"
+
|- class="OddWeek"
−
|id="week5"|Week 5
+
|
 
|[https://www.youtube.com/watch?v=sDSt0G6dpzg]
 
|[https://www.youtube.com/watch?v=sDSt0G6dpzg]
 
|Increasing, decreasing and critical points.
 
|Increasing, decreasing and critical points.
Line 200: Line 202:
 
|[http://www.educreations.com/lesson/view/simple-differential-equation-problem/14300182/?s=GCrISn&ref=app]
 
|[http://www.educreations.com/lesson/view/simple-differential-equation-problem/14300182/?s=GCrISn&ref=app]
 
|A simple differential equation problem.
 
|A simple differential equation problem.
−
 
−
|- class="OddWeek"
 
−
|
 
−
|[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 $dy/dt=a-by$.
 
  
 
|- class="NewWeek EvenWeek"
 
|- class="NewWeek EvenWeek"
Line 229: Line 226:
 
|id="week11"|Week 11
 
|id="week11"|Week 11
 
|[http://www.educreations.com/lesson/view/solving-a-diffl-eq-dy-dt-a-by/23385476/?s=ObLqjR&ref=app].
 
|[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 $dy/dt=a-by$ (same as [39]).
+
|Solving differential equations of the type $dy/dt=a-by$.
  
 
|- class="OddWeek"
 
|- class="OddWeek"
Line 241: Line 238:
 
|Solving differential equations approximately using Euler's Method - spreadsheet.
 
|Solving differential equations approximately using Euler's Method - spreadsheet.
  
−
|- class="OddWeek EvenWeek"
+
|- class="NewWeek EvenWeek"
 
|id="week12"|Week 12
 
|id="week12"|Week 12
 
|[http://www.educreations.com/lesson/view/disease-dynamics-i/23465001/?s=pJChZV&ref=app]
 
|[http://www.educreations.com/lesson/view/disease-dynamics-i/23465001/?s=pJChZV&ref=app]
 
|Disease dynamics I
 
|Disease dynamics I
  
−
|- class="OddWeek"
+
|- class="EvenWeek"
 
|
 
|
 
|[http://www.educreations.com/lesson/view/disease-dynamics-ii/23465479/?s=EG7QeI&ref=app]
 
|[http://www.educreations.com/lesson/view/disease-dynamics-ii/23465479/?s=EG7QeI&ref=app]
 
|Disease dynamics II
 
|Disease dynamics II
  
−
|- class="OddWeek"
+
|- class="EvenWeek"
 
|
 
|
 
|[https://www.youtube.com/watch?v=vg1hmGI2WDM], [https://www.youtube.com/watch?v=XZ6O4dWaeZ0]
 
|[https://www.youtube.com/watch?v=vg1hmGI2WDM], [https://www.youtube.com/watch?v=XZ6O4dWaeZ0]
 
|Introduction to Trigonometric Functions and review of trigonometric identities.
 
|Introduction to Trigonometric Functions and review of trigonometric identities.
  
−
|- class="OddWeek"
+
|- class="EvenWeek"
 
|
 
|
 
|[http://www.educreations.com/lesson/view/periodic-function/14693344/?s=kxJDte&ref=app] (LEK),EC
 
|[http://www.educreations.com/lesson/view/periodic-function/14693344/?s=kxJDte&ref=app] (LEK),EC

Latest revision as of 13:17, 12 September 2017


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 1.4 and Appendix C.4 of the OpenBook (a.k.a."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] Using a spreadsheet to graph a function and its (approximate) derivative.
[13] Derivatives of polynomials.
[14] Rules of differentiation: Product and quotient rules.
Week 4 [15] Rules of differentiation: Antiderivatives of polynomials.
[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.
Week 5 [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.
[24] Largest area of a rectangle inscribed in a semicircle
[25] Absolute Maximum and Minimum Values of a Function - Calculus I
Week 6 [26] Kepler's Wedding - A wine optimization problem. (Blooper alert: want to get most wine for given budget)
[27] Optimal Foraging.
Week 7 [28] Least Squares - finding the best fitting line y=ax through a set of data points. See also the Fitting data supplement to the course notes.
[29] Chain Rule: general introduction with examples
[30] Chain Rule: an applications to optimization problems involving plovers and crocodiles.
Week 8 [31] Implicit differentiation.
[32] Related Rates.
[33] Exponential functions and doubling.
[34] Exponential functions: derivative of $a^x$.
Week 9 [35] Inverse functions and logarithm, applications of logs.
[36] Differential equations for growth and decay.
[37] A differential equation for human population growth.
[38] A simple differential equation problem.
Week 10 [39] Geometry of change: (I) Slope fields.
[40] Geometry of change: (II) State space. This one is more relevant to the pre-lecture questions but you should watch both.
[41] The Logistic equation I (state space and slope field).
[42] The Logistic equation II (state space and slope field).
Week 11 [43]. Solving differential equations of the type $dy/dt=a-by$.
[44] Solving differential equations approximately using Euler's Method - theory.
[45] Solving differential equations approximately using Euler's Method - spreadsheet.
Week 12 [46] Disease dynamics I
[47] Disease dynamics II
[48], [49] Introduction to Trigonometric Functions and review of trigonometric identities.
[50] (LEK),EC Trigonometric Functions and cyclic processes, phase, amplitude, etc. (fitting a sin or cos to a cyclic process), Inverse trig functions.
Week 13 [51] Derivatives of trig functions, related rates examples.
[52][53] The Escape Response and trigonometric related rates.
Retrieved from "https://wiki.math.ubc.ca/mathbook/M102/index.php?title=Pre-lecture_videos&oldid=7803"