Difference between revisions of "Pre-lecture videos"
From UBCMATH WIKI
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|Using a spreadsheet to graph a function and its (approximate) derivative. | |Using a spreadsheet to graph a function and its (approximate) derivative. | ||
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Revision as of 16:15, 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] | 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 | ||
| 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. | |
| [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. |
