Difference between revisions of "Pre-lecture videos"
From UBCMATH WIKI
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|[http://youtu.be/v13aqQaMaSE] | |[http://youtu.be/v13aqQaMaSE] | ||
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|[https://www.youtube.com/watch?v=E-owZqDrTkE&list=UUNHASevzeyPH-OZMax8iMAA] | |[https://www.youtube.com/watch?v=E-owZqDrTkE&list=UUNHASevzeyPH-OZMax8iMAA] | ||
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|[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] | ||
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|[http://www.educreations.com/lesson/view/kepler-s-wedding/23147433/?s=uq5ffc&ref=app] | |[http://www.educreations.com/lesson/view/kepler-s-wedding/23147433/?s=uq5ffc&ref=app] | ||
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|[http://www.educreations.com/lesson/view/differential-equation-for-exponential-growth-and-d/23382026/?s=GyshbX&ref=app] | |[http://www.educreations.com/lesson/view/differential-equation-for-exponential-growth-and-d/23382026/?s=GyshbX&ref=app] | ||
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|[http://www.educreations.com/lesson/view/geometry-of-change-i/23430270/?s=pB3DZB&ref=app] | |[http://www.educreations.com/lesson/view/geometry-of-change-i/23430270/?s=pB3DZB&ref=app] | ||
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Revision as of 13:50, 1 September 2014
Date | Video link | Topic | |
---|---|---|---|
Week 1 | Sept 3 | [1] | Power functions. |
[2] | Cell size and nutrient balance: volume, area. Power functions. | ||
Sept 5 | [3] | Power functions (cont). Sketching simple polynomials (y=x^3-ax). Example of graphing with spreadsheet. | |
Week 2 | Sept 8 | [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 ([ Demos demo]). Comparing Hill functions with different parameter values. | ||
Sept 10 | [7] | Average rate of change and secant lines. Definition of the derivative. Instantaneous rate of change. | |
[8] | Average rate of change and secant lines. Definition of the derivative. Instantaneous rate of change. | ||
Sept 12 | [9] | Limits and continuity, examples. One example of computing derivative of $y=c t^2$ from the definition. | |
[10] | Limits and continuity, examples. One example of computing derivative of $y=c t^2$ from the definition. | ||
Week 3 | Sept 15 | [11] | Derivatives: analytic, and geometric (zoom in on a point). Sketching $f'(x)$ given $f(x)$ (intro). |
Sept 17 | [12] | Derivatives (cont): computational (spreadsheet example in class). More examples of sketching $f'(x)$ given $f(x)$ (intro). | |
Sept 19 | [13] | 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). | |
[14] | 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). | ||
[15] | 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). | ||
Week 4 | Sept 22 | [16] | Tangent lines and linear approximation. |
[17] | Tangent lines and linear approximation. | ||
[18] | Tangent lines and linear approximation. | ||
Sept 24 | NM1 | Introduction to Newton’s method. Sketching the graph of a function using calculus tools: increasing, decreasing, critical points. | |
NM2 | Introduction to Newton’s method. Sketching the graph of a function using calculus tools: increasing, decreasing, critical points. | ||
NM3 | Introduction to Newton’s method. Sketching the graph of a function using calculus tools: increasing, decreasing, critical points. | ||
Sept 26 | EC | Sketching the graph of a function using calculus tools (cont): concavity and inflection points. | |
Week 5 | Sept 29 | ||
Sept 30 | MIDTERM 1: 6-7 pm | ||
Oct 1 | EC | Finish sketching functions. Introduce simple optimization problem(s). | |
Oct 3 | More optimization examples including those with a constraint and those on bounded intervals. Distinction between absolute (global) and local minima and maxima. | ||
Week 6 | Oct 6 | [19] | Kepler's Wedding - A wine optimization problem. |
Oct 8 | [20] | Optimal Foraging. | |
Oct 10 | EC | Least Squares - finding the mean of a data set. | |
Week 7 | Oct 13 | THANKSGIVING - no classes. | |
Oct 15 | EC | Least Squares - finding the best fitting line y=ax through a set of data points. | |
Oct 17 | [21](LEK),WM | Chain Rule: examples, applications to optimization problems. | |
Week 8 | Oct 20 | WM | More Chain Rule: Related Rates and Implicit differentiation. |
Oct 22 | [22] | Exponential functions: intro and motivation, derivative of exponential functions. | |
Oct 22 | [23] | Exponential functions: intro and motivation, derivative of exponential functions. | |
Oct 24 | WM | Inverse functions and logarithm, applications of logs. | |
Week 9 | Oct 27 | [24] | Exponential growth and decay, intro to differential equations, population growth and/or other examples. |
[25] | Exponential growth and decay, intro to differential equations, population growth and/or other examples. | ||
[26] | Exponential growth and decay, intro to differential equations, population growth and/or other examples. | ||
Oct 29 | [27] | Solving differential equations of the type $dy/dt=a-by$. | |
Oct 29 | [28] | 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 | [29] | Solving differential equations approximately using Euler's Method. | |
Nov 7 | [30] | Go over midterm. Introduction to nonlinear ODEs, qualitative analysis. | |
Week 11 | Nov 10 | [31] | Geometry of change: (I) Slope fields, (II) State space . |
[32] | Geometry of change: (I) Slope fields, (II) State space . | ||
Nov 11 | Remembrance Day. University closed. | ||
Nov 12 | [33] | The Logistic equation (state space and slope field). | |
[34] | The Logistic equation (state space and slope field). | ||
Nov 14 | [35] | Disease dynamics | |
[36] | Disease dynamics | ||
Week 12 | Nov 17 | Review of differential equations and/or complete above topics. | |
Nov 19 | EC | Introduction to Trigonometric Functions. | |
Nov 21 | [37] (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 | [38] | The Escape Response and trigonometric related rates. | |
Nov 28 | Second order ODEs. Complete and/or review trig. |