Section links/Section 104/Lecture slides
From UBCMATH WIKI
- I will post lecture slides after class. If they don't appear within a day, feel free to contact me to remind me to post them.
- The staged version of each set of slides shows every stage of the slides, as shown in class. The collapsed versions are generally smaller files with all stages collapsed into a single page (sometimes with overlapping text and hard to read).
- As the term progresses, I will fill in the links to this year's slide - red links are empty for now. You can look at last year's slides if I am late to post the new ones (scroll down).
Current year
| Date | Lecture | Staged version | Collapsed version | Description | |
|---|---|---|---|---|---|
| Week 1 | Sep 5 | Lecture 1 | Course info and absorption/consumption by cells | ||
| Sep 7 | Lecture 2 | Asymptotics and an experiment on learning | |||
| Week 2 | Sep 10 | Lecture 3 | Even/odd functions, Hill functions, slopes and derivative. | ||
| Sep 12 | Lecture 4 | Secant lines, tangent lines, and the derivative. | |||
| Sep 14 | Lecture 5 | Limits and continuity. | |||
| Week 3 | Sep 17 | Lecture 6 | Limits, continuity, and differentiability. | ||
| Sep 19 | Lecture 7 | Sketching f'(x) given a graph of f(x). | |||
| Sep 21 | Lecture 8 | Graphing with a spreadsheet. Power rule. | |||
| Week 4 | Sep 24 | Lecture 9 | Power rule. Rules of differentiation (addition, product, chain, quotient). | ||
| Sep 26 | Lecture 10 | Antiderivatives of polynomials. Tangent lines. | |||
| Sep 28 | Lecture 11 | Tangent lines. Linear approximation. | |||
| Week 5 | Oct 1 | Lecture 12 | Newton's method | ||
| Oct 3 | Lecture 13 | Critical points, extrema, the first derivative test, and the second derivative test. | |||
| Oct 5 | Lecture 14 | First derivative test without plugging in numbers, concavity and inflection points. | |||
| Week 6 | Oct 8 | Thanksgiving | |||
| Oct 10 | Lecture 15 | Concavity and inflection points. | |||
| Oct 12 | Lecture 16 | Sign tables and graphing. Absolute extrema. | |||
| Week 7 | Oct 15 | Lecture 17 | Kepler's wedding. Optimal foraging (intro). | ||
| Oct 17 | Lecture 18 | Optimal foraging. Least squares (intro). | |||
| Oct 19 | Lecture 19 | Least squares | |||
| Week 8 | Oct 22 | Lecture 20 | An optimization example. Chain rule intuition. Related rates. | ||
| Oct 24 | Lecture 21 | Implicit differentiation including (1) a tangent line to an implicit function and (2) power rule for non-integer powers. | |||
| Oct 26 | Lecture 22 | Exponential functions and their derivatives. | |||
| Week 9 | Oct 29 | Lecture 23 | Natural log and its derivative, semi-log plots, derivatives of exponential functions. | ||
| Oct 31 | Lecture 24 | Exponential growth, doubling time, half life, characteristic time, linear differential equations. | |||
| Nov 2 | Lecture 25 | Nonlinear differential equations and their qualitative analysis. | |||
| Week 10 | Nov 5 | Lecture 26 | Phase line, examples. | ||
| Nov 7 | Lecture 27 | Phase line. Biological examples (population model with Allee effect, lac operon switch) | |||
| Nov 9 | Lecture 28 | Phase line examples. Newton's Law of Cooling. | |||
| Week 11 | Nov 12 | Remembrance Day (observed) | |||
| Nov 14 | Lecture 29 | Solving y'=ay+b | |||
| Nov 16 | Lecture 30 | Euler's method | |||
| Week 12 | Nov 19 | Lecture 31 | Logistic equation in applications - infectious disease models. | ||
| Nov 21 | Lecture 32 | pdf (guest lecturer in Sec 106 notes) |
Trig review | ||
| Nov 23 | Lecture 33 | Rhythmic processes - finding the trig function that describes an oscillating phenomenon. | |||
| Week 13 | Nov 26 | Lecture 34 | Related rates with trig - Zebra Danio escape response | ||
| Nov 28 | Lecture 35 | Inverse trig functions. Mono-mono twin example. | |||
| Nov 30 | Lecture 36 | Pi pie competition and question session. |
Last year
| Date | Lecture | Staged version | Collapsed version | Description | |
|---|---|---|---|---|---|
| Week 1 | Sep 7 | Lecture 1 | |||
| Sep 9 | Lecture 2 | ||||
| Week 2 | Sep 12 | Lecture 3 | Using asymptotics to graph polynomials, Hill functions. Secant lines to tangent lines. | ||
| Sep 14 | Lecture 4 | From secant line to tangent line. | |||
| Sep 16 | Lecture 5 | Limits, continuity and the definition of the derivative. | |||
| Week 3 | Sep 19 | Lecture 6 | Limits, continuity and differentiability. | ||
| Sep 21 | Lecture 7 | Tangent lines, drawing f'(x) from f(x). | |||
| Sep 23 | Lecture 8 | Graphing f'(x) given f(x). | |||
| Week 4 | Sep 26 | Lecture 9 | Differentiation rules. | ||
| Sep 28 | Lecture 10 | Chain rule, quotient rule, antiderivatives of power functions and polynomials, tangent lines. | |||
| Sep 30 | Lecture 11 | Tangent lines and linear approximation. | |||
| Week 5 | Oct 3 | Lecture 12 | Newton's method. Increasing, decreasing and extrema. | ||
| Oct 5 | Lecture 13 | Newton's method Google sheet example. Critical points, concavity, and inflection points. | |||
| Oct 7 | Lecture 14 | Minima, maxima and inflection points. | |||
| Week 6 | Oct 10 | Thanksgiving | |||
| Oct 12 | Lecture 15 | Using calculus to determine the shape of a function's graph. | |||
| Oct 14 | Lecture 16 | Absolute extrema. Goat enclosure example. Kepler's Wedding. | |||
| Week 7 | Oct 17 | Lecture 17 | Kepler's wedding. Intro to optimal foraging. | ||
| Oct 19 | Lecture 18 | Optimal foraging. Intro to least squares model fitting. | |||
| Oct 21 | Lecture 19 | Least squares model fitting. | |||
| Week 8 | Oct 24 | Lecture 20 | Related rates | ||
| Oct 26 | Lecture 21 | Related rates. Implicit differentiation. | |||
| Oct 28 | Lecture 22 | Power rule for rational powers (using implicit differentiation). Exponential functions and their derivatives. | |||
| Week 9 | Oct 31 | Lecture 23 | Inverse functions: log and its derivative. | ||
| Nov 2 | Lecture 24 | Semi-log plots, exponential derivative, bacterial growth example, exponential function as solution of differential equation. | |||
| Nov 4 | Lecture 25 | Introduction to differential equations (DEs) and qualitative analysis of DEs. | |||
| Week 10 | Nov 7 | Lecture 26 | Qualitative analysis of DEs. Slope fields, phase line, steady states and their stability. | ||
| Nov 9 | Lecture 27 | Qualitative analysis of DEs - examples. | |||
| Nov 11 | Remembrance Day | ||||
| Week 11 | Nov 14 | Lecture 28 | Phase line example. Solving linear DEs. | ||
| Nov 16 | Lecture 29 | Solving linear DEs. | |||
| Nov 18 | Lecture 30 | Wrap up IV drug example and general case of y'=ay+b. | |||
| Week 12 | Nov 21 | Lecture 31 | Euler's method. Logistic equation application - infectious disease | ||
| Nov 23 | Lecture 32 | Logistic equation application - infectious disease. Trig review. | |||
| Nov 25 | Lecture 33 | Trig review. Rhythmic processes. | |||
| Nov 28 | Lecture 34 | Related rates with trig - The Zebra Danio escape response. | |||
| Week 13 | Nov 30 | Lecture 35 | Inverse trig functions and their derivatives. A summary modelling example. | ||
| Dec 2 | Lecture 36 | A collection of multiple choice questions from old exams and quizzes. [not shown in class] |
