# Pre-lecture videos

From UBCMATH WIKI

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.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. |