Difference between revisions of "Math100Videos"
From UBCMATH WIKI
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− | |- |Limits | + | |- |
− | |[https:// | + | |Limits |
− | | | + | |Limits and tangent lines |
+ | |[https://youtu.be/abeuHo-fbSc] | ||
+ | |Average and Instantaneous Velocity; secant and tangent line; limit notation | ||
|- class="OddWeek" | |- class="OddWeek" |
Revision as of 13:16, 18 August 2017
Topic | Video link | Video contents | |
---|---|---|---|
Limits | Limits and tangent lines | [1] | Average and Instantaneous Velocity; secant and tangent line; limit notation |
[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: 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. |