Difference between revisions of "Pre-lecture videos"
From UBCMATH WIKI
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|Sept 3 | |Sept 3 | ||
|[https://www.educreations.com/lesson/view/power-functions/23591979/?s=T9jC77&ref=app] | |[https://www.educreations.com/lesson/view/power-functions/23591979/?s=T9jC77&ref=app] | ||
− | |Power functions. | + | |Power functions - when is $x^n>$x^m$. Even and odd functions. |
|- class="OddWeek" | |- class="OddWeek" |
Revision as of 15:54, 4 September 2014
Date | Video link | Video topic | |
---|---|---|---|
Week 1 | Sept 3 | [1] | Power functions - when is $x^n>$x^m$. Even and odd functions. |- class="OddWeek" | | |[http://www.educreations.com/lesson/view/cell-size/23429678/?s=6FnDiS&ref=app] |Cell size and nutrient balance: volume, area. Power functions. |- class="OddWeek" | |Sept 5 |[http://www.educreations.com/lesson/view/graphing-a-simple-polynomial/23126849/?s=W2B6ko&ref=app] |Power functions (cont). Sketching simple polynomials (y=x^3-ax). |- class="NewWeek EvenWeek" |id="week2"|Week 2 |Sept 8 |[http://youtu.be/v13aqQaMaSE] |Approximating a rational function near the origin. |- class="EvenWeek" | | |[http://youtu.be/cXYCX8YBEVw] |Approximating a rational function for large x. Introduction to Hill functions. |- class="EvenWeek" | | |[http://youtu.be/kuMWI8kL1wI] |Sketching Hill functions by hand and by Desmos ([ Demos demo]). Comparing Hill functions with different parameter values. |- class="EvenWeek" | |Sept 10 |[https://www.youtube.com/watch?v=-yXuSU_jHQ4&list=UUNHASevzeyPH-OZMax8iMAA] |Average rate of change and secant lines. Definition of the derivative. Instantaneous rate of change. |- class="EvenWeek" | | |[https://www.youtube.com/watch?v=PT2XNveWFoI&list=UUNHASevzeyPH-OZMax8iMAA] |Average rate of change and secant lines. Definition of the derivative. Instantaneous rate of change. |- class="EvenWeek" | |Sept 12 |[https://www.youtube.com/watch?v=2Yn05jvl0vI&list=UUNHASevzeyPH-OZMax8iMAA] |Limits and continuity, examples. One example of computing derivative of $y=c t^2$ from the definition. |- class="EvenWeek" | | |[https://www.youtube.com/watch?v=z4ED7eiNhBM&list=UUNHASevzeyPH-OZMax8iMAA] |Limits and continuity, examples. One example of computing derivative of $y=c t^2$ from the definition. |- class="NewWeek OddWeek" |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). |- class="OddWeek" | |Sept 17 |[https://www.youtube.com/watch?v=aDJ0J9Z239s&feature=youtu.be] |Derivatives (cont): computational (spreadsheet example in class). More examples of sketching $f'(x)$ given $f(x)$ (intro). |- class="OddWeek" | |Sept 19 |[https://www.youtube.com/watch?v=HNXv3bmMGZ0&index=2&list=UUNHASevzeyPH-OZMax8iMAA] |Rules of differentiation: Product and quotient rules. Antiderivatives of power functions. Application to falling ball, motion of Listeria. Sketching $f(x)$ given $f'(x)$ (intro). |- class="OddWeek" | | |[https://www.youtube.com/watch?v=twnyZasD-d4&index=3&list=UUNHASevzeyPH-OZMax8iMAA] |Rules of differentiation: Product and quotient rules. Antiderivatives of power functions. Application to falling ball, motion of Listeria. Sketching $f(x)$ given $f'(x)$ (intro). |- class="OddWeek" | | |[https://www.youtube.com/watch?v=giENfOUvE08&list=UUNHASevzeyPH-OZMax8iMAA&index=1] |Rules of differentiation: Product and quotient rules. Antiderivatives of power functions. Application to falling ball, motion of Listeria. Sketching $f(x)$ given $f'(x)$ (intro). |- 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] |Tangent lines and linear approximation. |- class="EvenWeek" | | |[http://www.educreations.com/lesson/view/generic-tangent-line-and-intro-to-newton-s-method/23145498/?s=Ha5C44&ref=app] |Tangent lines and linear approximation. |- class="EvenWeek" | | |[http://www.educreations.com/lesson/view/linear-approximation/23185994/?s=AN5Da8&ref=app] |Tangent lines and linear approximation. |- class="EvenWeek" | |Sept 24 |[http://youtu.be/teRQpllWtaI] |Introduction to Newton’s method. Sketching the graph of a function using calculus tools: increasing, decreasing, critical points. |- class="EvenWeek" | | |[http://youtu.be/TcPb4zkWEfo] |Introduction to Newton’s method. Sketching the graph of a function using calculus tools: increasing, decreasing, critical points. |- class="EvenWeek" | | |[http://youtu.be/9nRU0V_3vjw] |Introduction to Newton’s method. Sketching the graph of a function using calculus tools: increasing, decreasing, critical points. |- class="EvenWeek" | |Sept 26 |EC |Sketching the graph of a function using calculus tools (cont): concavity and inflection points. |- class="NewWeek OddWeek" |id="week5"|Week 5 |Sept 29 | | |- class="OddWeek" | |Sept 30 | |'''MIDTERM 1: 6-7 pm''' |- class="OddWeek" | |Oct 1 |EC |Finish sketching functions. Introduce simple optimization problem(s). |- class="OddWeek" | |Oct 3 | |More optimization examples including those with a constraint and those on bounded intervals. Distinction between absolute (global) and local minima and maxima. |- 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. |- class="EvenWeek" | |Oct 8 |[http://www.educreations.com/lesson/view/optimal-foraging/23177297/?s=UledUg&ref=app] |Optimal Foraging. |- class="EvenWeek" | |Oct 10 |EC |Least Squares - finding the mean of a data set. |- class="NewWeek OddWeek" |id="week7"|Week 7 |Oct 13 | |THANKSGIVING - no classes. |- class="OddWeek" | |Oct 15 |EC ||Least Squares - finding the best fitting line y=ax through a set of data points. |- class="OddWeek" | |Oct 17 |[http://www.educreations.com/lesson/view/optimization-problem/14708865/?s=SmFwgM&ref=app](LEK),WM |Chain Rule: examples, applications to optimization problems. |- class="NewWeek EvenWeek" |id="week8"|Week 8 |Oct 20 |WM |More Chain Rule: Related Rates and Implicit differentiation. |- class="EvenWeek" | |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. |- class="EvenWeek" | |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. |- class="EvenWeek" | |Oct 24 |WM |Inverse functions and logarithm, applications of logs. |- 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" | | |[http://youtu.be/5UFVLtEjUKo] |Exponential growth and decay, intro to differential equations, population growth and/or other examples. |- class="OddWeek" | | |[http://www.educreations.com/lesson/view/simple-differential-equation-problem/14300182/?s=GCrISn&ref=app] |Exponential growth and decay, intro to differential equations, population growth and/or other examples. |- class="OddWeek" | |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 $dy/dt=a-by$. |- 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 $dy/dt=a-by$. |
Oct 31 | LEK | Newton's Law of Cooling (Murder Mystery example). | |
Week 10 | Nov 3 | Complete and/or review above topics. | |
Nov 4 | MIDTERM 2: 6-7 pm | ||
Nov 5 | [2] | Solving differential equations approximately using Euler's Method. | |
Nov 7 | [3] | Go over midterm. Introduction to nonlinear ODEs, qualitative analysis. | |
Week 11 | Nov 10 | [4] | Geometry of change: (I) Slope fields, (II) State space . |
[5] | Geometry of change: (I) Slope fields, (II) State space . | ||
Nov 11 | Remembrance Day. University closed. | ||
Nov 12 | [6] | The Logistic equation (state space and slope field). | |
[7] | The Logistic equation (state space and slope field). | ||
Nov 14 | [8] | Disease dynamics | |
[9] | Disease dynamics | ||
Week 12 | Nov 17 | Review of differential equations and/or complete above topics. | |
Nov 19 | EC | Introduction to Trigonometric Functions. | |
Nov 21 | [10] (LEK),EC | Trigonometric Functions and cyclic processes, phase, amplitude, etc. (fitting a sin or cos to a cyclic process), Inverse trig functions. | |
Week 13 | Nov 24 | WM | Derivatives of trig functions, related rates examples. |
Nov 26 | [11] | The Escape Response and trigonometric related rates. | |
Nov 28 | Second order ODEs. Complete and/or review trig. |