Pre-lecture videos
From UBCMATH WIKI
| Date | Topic | Notes | Pre-L WeBWorK | Videos | By | |
|---|---|---|---|---|---|---|
| Week 1 | Sept 3 | Cell size: volume, area. Power functions. | Sec 1.1-1.2 | A1:22 | [1],[2] | LEK |
| Sept 5 | Power functions (cont). Sketching simple polynomials (y=x^3-ax). Example of graphing with spreadsheet. | Sec 1.1, 1.4,1.6 | A1:23 | [3] | LEK | |
| Week 2 | Sept 8 | Sketching simple polynomials (cont). Rational functions, Michaelis-Menten and Hill functions, “limits” at infinity. OSH 1 due! (Section 105, due Tuesday.) |
Sec 1.4, 1.5 | A1: 21,18,29 | SRF1, SRF2, SRF3 | EC |
| Sept 10 | Average rate of change and secant lines. Definition of the derivative. Instantaneous rate of change. | Sec 2.2-2.5 | [4] [5] | WM | ||
| Sept 12 | Limits and continuity, examples. One example of computing derivative of $y=c t^2$ from the definition. | Sec 2.5, Sec 3.2, Appendix D. | A3:28 | [6] [7] | WM | |
| Week 3 | Sept 15 | Derivatives: analytic, and geometric (zoom in on a point). Sketching $f'(x)$ given $f(x)$ (intro). OSH 2 due! (Section 105, due Tuesday.) |
Sec 3.1-3.2 | [8] | WM | |
| Sept 17 | Derivatives (cont): computational (spreadsheet example in class). More examples of sketching $f'(x)$ given $f(x)$ (intro). | Sec 3.2-3.3 | [9] | LEK | ||
| Sept 19 | 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). | Chap 4 | A3: 29,33,34,30,31,22,23,32 | [10] [11] [12] | WM | |
| Week 4 | Sept 22 | Tangent lines and linear approximation. |
Chap 5 | A2: 22, A3: 14,15,16,17, A4: 4,5. A11: 19,20, A12: 4,6. | [13], [14],[15]. | LEK |
| Sept 24 | Introduction to Newton’s method. Sketching the graph of a function using calculus tools: increasing, decreasing, critical points. | End of Chap 5, Sec 6.1 | A12: 7,8,11,12 (NM). A3: 20,21,26,27, A4: 3 (slope). | NM1, NM2,NM3 | EC | |
| Sept 26 | Sketching the graph of a function using calculus tools (cont): concavity and inflection points. | Sec 6.2-6.3 | A4: 10,11,15,20,25 | EC | ||
| Week 5 | Sept 29 | Complete and/or review above topics. OSH 3 due! (Section 105, due Tuesday.) |
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| Sept 30 | MIDTERM 1: 6-7 pm | |||||
| Oct 1 | Finish sketching functions. Introduce simple optimization problem(s). | Sec 6.3-6.4, 7.1 | A3: 25, A4: 1,5,7 (rough sketches). A3: 35, A4: 6,8,9,18,19,27 (crit pts, local min/max). | EC | ||
| Oct 3 | More optimization examples including those with a constraint and those on bounded intervals. Distinction between absolute (global) and local minima and maxima. | 7.1-7.3 | A1: 13, A5: 17, A6: 4,12 ?? (constraint, bndd. int.). A4: 28, 29, 30, 31, 32 (global). | |||
| Week 6 | Oct 6 | Kepler's Wedding - A wine optimization problem. | Sec 7.2 | A1: 11, A6: 14. Leah made up new Q's | [16] | LEK |
| Oct 8 | Optimal Foraging. | Sec 7.4 | Leah made up new Q's | [17] | LEK | |
| Oct 10 | Least Squares - finding the mean of a data set. | Wiki | EC | |||
| Week 7 | Oct 13 | THANKSGIVING - no classes. | ||||
| Oct 15 | Least Squares - finding the best fitting line y=ax through a set of data points. OSH 4 due! (Section 105, due Tuesday.) |
Wiki | EC | |||
| Oct 17 | Chain Rule: examples, applications to optimization problems. | Chap 8 | A7: 1,4 (chain). Need opt ex using chain. | [18](temporary-LEK) | WM | |
| Week 8 | Oct 20 | More Chain Rule: Related Rates and Implicit differentiation. | Chap 9 | A6: 12, A7: 6, 8, 10, 14 (Imp diff). A7: 15, 17, 18 (related rates with chain). | WM | |
| Oct 22 | Exponential functions: intro and motivation, derivative of exponential functions. | Sec 10.1-10.2 | A8: 27, (need more on doubling). A7: 21, 22, A8: 17, 23 (exp deriv).
|
[19],[20] | LEK | |
| Oct 24 | Inverse functions and logarithm, applications of logs. | Sec 10.3-10.4 | A8: 3, 4, 6, 7, 9. (log and log deriv). A8: 5, 12, 13, A7: 23 (work with exp/log). | WM | ||
| Week 9 | Oct 27 | Exponential growth and decay, intro to differential equations, population growth and/or other examples. OSH 5 due! (Section 105, due Tuesday.) |
Sec 11.1-11.2 or 11.3 | A8: 14 (bacterial growth). A8: Problem 29, 30, 34, 35 (simple ODE ex). A8: 32 (2x time). A8: 33, A9: 4,5,6 (radio decay). | [21],[22],[23] | LEK |
| Oct 29 | Solving differential equations of the type $dy/dt=a-by$. | Sec 12.1-12.3 | A9: 7, 14 (write ODE, solve - maybe not pre-L). A9: 2, 3, 8, A11: 18 ($dy/dt=a-by$). | [24], [25] | LEK | |
| Oct 31 | Newton's Law of Cooling (Murder Mystery example). | Sec 12.4 | A9: 11, A11: 17. | LEK | ||
| Week 10 | Nov 3 | Complete and/or review above topics. | Chaps 11-12 | |||
| Nov 4 | MIDTERM 2: 6-7 pm | |||||
| Nov 5 | Solving differential equations approximately using Euler's Method. | Sec 12.4 | No pre-lecture problems. (day after midterm) (A9: 15, A10: 1,2.) | [26] | EC | |
| Nov 7 | Go over midterm. Introduction to nonlinear ODEs, qualitative analysis. | Sec 13.1 | A11: 23, A12: 22. | [27] | LEK | |
| Week 11 | Nov 10 | Geometry of change: (I) Slope fields, (II) State space . OSH 6 due! (Section 105, due Thursday.) |
Sec 13.2 | A12: 20, 21, 25, 26 (log. growth). A11: 2, A12: 16,17. | [28], | LEK |
| Nov 11 | Remembrance Day. University closed. | Sec 13.2 | ||||
| Nov 12 | The Logistic equation (state space and slope field). | Sec 13.2 | A11: 24,25 (ss). A12: 18,23 (slope fields). A12: 24 (stability). | [30],[31] | LEK | |
| Nov 14 | Disease dynamics | Sec 13.3 | [32], | LEK | ||
| Week 12 | Nov 17 | Review of differential equations and/or complete above topics. | Chaps 11-13 | |||
| Nov 19 | Introduction to Trigonometric Functions. | Sec 14.1-14.2 | A9: 16,17,18,19. A10: 6,7,10. | EC | ||
| Nov 21 | Trigonometric Functions and cyclic processes, phase, amplitude, etc. (fitting a sin or cos to a cyclic process), Inverse trig functions. | Sec 14.2-14.3 | A9: 22, A10: 5, 12. | [34] (LEK, temporary) | EC | |
| Week 13 | Nov 24 | Derivatives of trig functions, related rates examples. OSH 7 due! (Section 105, due Tuesday.) |
Sec 15.1-15.2 | A10: 15,16, A11: 3 (trig deriv). A11: 5,6,7,10 (trig rel rate). | WM | |
| Nov 26 | The Escape Response and inverse trig functions. | Sec 15.3 | A10: 8,9,13,14 (inv trig). A10: 18,19,20, A11: 1,9 (inv trig deriv) | [35] | LEK | |
| Nov 28 | Second order ODEs. Complete and/or review trig. | Sec 15.4 | A10: 17 (2nd order ODE). |
New version of table
| Date | Video link | Topic | |
|---|---|---|---|
| Week 1 | Sept 3 | [36] | Power functions. |
| [37] | Cell size and nutrient balance: volume, area. Power functions. | ||
| Sept 5 | [38] | Power functions (cont). Sketching simple polynomials (y=x^3-ax). Example of graphing with spreadsheet. | |
| Week 2 | Sept 8 | [39] | Approximating a rational function near the origin. |
| [40] | Approximating a rational function for large x. Introduction to Hill functions. | ||
| [41] | Sketching Hill functions by hand and by Desmos ([ Demos demo]). Comparing Hill functions with different parameter values. | ||
| Sept 10 | [42] | Average rate of change and secant lines. Definition of the derivative. Instantaneous rate of change. | |
| [43] | Average rate of change and secant lines. Definition of the derivative. Instantaneous rate of change. | ||
| Sept 12 | [44] | Limits and continuity, examples. One example of computing derivative of $y=c t^2$ from the definition. | |
| [45] | Limits and continuity, examples. One example of computing derivative of $y=c t^2$ from the definition. | ||
| Week 3 | Sept 15 | [46] | Derivatives: analytic, and geometric (zoom in on a point). Sketching $f'(x)$ given $f(x)$ (intro). |
| Sept 17 | [47] | Derivatives (cont): computational (spreadsheet example in class). More examples of sketching $f'(x)$ given $f(x)$ (intro). | |
| Sept 19 | [48] | 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). | |
| [49] | 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). | ||
| [50] | 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 | [51] | Tangent lines and linear approximation. |
| [52] | Tangent lines and linear approximation. | ||
| [53] | 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 | [54] | Kepler's Wedding - A wine optimization problem. |
| Oct 8 | [55] | 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 | [56](LEK),WM | Chain Rule: examples, applications to optimization problems. | |
| Week 8 | Oct 20 | WM | More Chain Rule: Related Rates and Implicit differentiation. |
| Oct 22 | [57] | Exponential functions: intro and motivation, derivative of exponential functions. | |
| Oct 22 | [58] | Exponential functions: intro and motivation, derivative of exponential functions. | |
| Oct 24 | WM | Inverse functions and logarithm, applications of logs. | |
| Week 9 | Oct 27 | [59] | Exponential growth and decay, intro to differential equations, population growth and/or other examples. |
| [60] | Exponential growth and decay, intro to differential equations, population growth and/or other examples. | ||
| [61] | Exponential growth and decay, intro to differential equations, population growth and/or other examples. | ||
| Oct 29 | [62] | Solving differential equations of the type $dy/dt=a-by$. | |
| Oct 29 | [63] | 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 | [64] | Solving differential equations approximately using Euler's Method. | |
| Nov 7 | [65] | Go over midterm. Introduction to nonlinear ODEs, qualitative analysis. | |
| Week 11 | Nov 10 | [66] | Geometry of change: (I) Slope fields, (II) State space . |
| [67] | Geometry of change: (I) Slope fields, (II) State space . | ||
| Nov 11 | Remembrance Day. University closed. | ||
| Nov 12 | [68] | The Logistic equation (state space and slope field). | |
| [69] | The Logistic equation (state space and slope field). | ||
| Nov 14 | [70] | Disease dynamics | |
| [71] | Disease dynamics | ||
| Week 12 | Nov 17 | Review of differential equations and/or complete above topics. | |
| Nov 19 | EC | Introduction to Trigonometric Functions. | |
| Nov 21 | [72] (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 | [73] | The Escape Response and trigonometric related rates. | |
| Nov 28 | Second order ODEs. Complete and/or review trig. |
