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Functions, derivatives, optimization, growth and decay, discrete probability. Please consult the Faculty of Science Credit Exclusion List: www.students.ubc.ca/calendar/index.cfm?tree=12,215,410,414.

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Calendar

The calendar is based on sections meeting MWF; sections will naturally diverge somewhat from each other and from the

calendar.

Abbreviations:

OSH: Old-School Homework. Apply principals from class to solve contextual problems. Practice thinking critically and

creatively.

WW: WeBWorK weekly assignments.

PL: Pre-Lecture WeBWorK assignments. Read the text before class to prepare; answer questions in WeBWorK based on

your reading.

WW CL: WeBWorK course logistics assignment

WW DT: WeBWorK diagnostic test

Date What's

due Lecture topic Course notes

Week

1

Sep

5Cell size: volume, area. Power functions. Sec 1.1-1.2

Sep

7

Power functions (cont). Sketching simple

polynomials (y=x^3-ax). Sec 1.1, 1.4,1.6

Week

2

Sep

10 WW CL

Sketching simple polynomials (cont). Rational

functions, Michaelis-Menten and Hill functions,

“limits” at infinity.

Sec 1.4, 1.5

Sep

11 PL2.1

Sep

12 OSH 0

Average rate of change and secant lines.

Definition of the derivative. Instantaneous rate of

change.

Sec 2.2-2.5

Sep

13 PL2.2

Sep

14 OSH 1

Limits and continuity, examples. One example of

computing derivative of from the

definition.

Sec 2.5, 3.2, Appendix D.

Sep

16 WW DT

Week

3

Sep

17 PL3.1 Derivatives: analytic, and geometric (zoom in on a

point). Sketching given (intro). Sec 3.1-3.2

Sep

19 PL3.2

Derivatives (cont): computational (spreadsheet

example in class). More examples of sketching

given (intro).

Sec 3.2-3.3

Sep

20 WW 2

Sep Rules of differentiation: Power rule, sum rule, Sec 4.1

21 product rule.

Week

4

Sep

24 PL4.1

Chain rule (intro) and quotient rules.

Antiderivatives of power functions and

applications.

Sec 4.1-4.2

Sep

26 PL4.2 Sketching given (intro using

polynomial). Tangent lines. sec 4.3, 5.1-5.2

Sep

27 WW 3

Sep

28 OSH 2 Linear approximation. Newton’s method (intro). Sec 5.3-5.5

Week

5

Oct

1PL5.1

Newton’s method (examples). Sketching the

graph of a function using calculus tools:

increasing, decreasing, critical points, concavity

and inflection points.

Sec 6.1-6.3

Oct

3PL5.2 Sketching (cont). Sec 6.1-6.3

Oct

4WW 4

Oct

5Sketching (cont). Sec 6.1-6.3

Week

6

Oct

8THANKSGIVING - no classes.

Oct

10 PL6.2 Absolute (global) extrema. Optimization,

examples. Sec 6.3.1, 7.1-7.3

Oct

11 WW 5

Oct

12 OSH 3 Kepler's wedding. Sec 7.2

Week

7

Oct

15 PL7.1 Optimal Foraging - an optimization problem

emphasizing biological interpretation. Sec 7.4

Oct

17 PL7.2

Least Squares - minimizing residuals to find the

best fitting model for a set of data points: (1)

constant and (2) .

Supplement

(https://wiki.math.ubc.ca/mathbook/M102/Course_notes/F

_least_squares)

Oct

18 WW 6

Oct

19 OSH4 Least Squares spreadsheet demo. Chain Rule:

examples, applications to optimization problems.

Supplement

(https://wiki.math.ubc.ca/mathbook/M102/Course_notes/F

_least_squares) , Chap 8

Week

8

Oct

22

PL8.1 Related Rates. Sec 9.1

Oct

24 PL8.2 Implicit differentiation Sec 9.2

Oct

25 MIDTERM

Midterm information

(https://canvas.ubc.ca/courses/6219/pages/midterm-

information)

Oct

26 WW 7 Exponential functions: intro and motivation,

derivative of exponential functions. Sec 10.1-10.2

Week

9

Oct

29 PL9.1 Inverse functions and logarithm, applications of

logs. Sec 10.3-10.4

Oct

31 PL9.2

Exponential growth and decay, intro to differential

equations, population growth and/or other

examples.

Sec 11.1; 11.2 or 11.3

Nov

1WW 8

Nov

2

Introduction to nonlinear ODEs, qualitative

analysis. Sec 13.1

Week

10

Nov

5PL10.1 Slope fields with logistic equation as example. Sec 13.2

Nov

7PL10.2 State-space diagrams and examples (logistic). Sec 13.2

Nov

8WW 9

Nov

9OSH 5

Solving differential equations of the type

.

Week

11

Nov

12 Remembrance Day. University closed. Sec 12.1-12.3

Nov

13 PL11.1 Sec 12.1-12.3

Nov

14 PL11.2

Solving differential equations of the type

(cont). Newton's Law of Cooling. Sec 12.3

Nov

15 WW 10

Nov

16

Solving differential equations approximately using

Euler's Method. Sec 12.4

Week

12

Nov

19 PL12.1 Disease dynamics. Sec 13.3

Nov

21

PL12.2 Introduction to Trigonometric Functions. Sec 14.1-14.2

Nov

22 WW 11

Nov

23 OSH6

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

Week

13

Nov

26 PL13.1 Derivatives of trig functions, related rates

examples. Sec 15.1-15.2

Nov

28 PL13.2 The Escape Response and inverse trig functions. Sec 15.3

Nov

29 WW 12

Nov

30 Complete and/or review trig.

WW 13 The final WeBWorK assignment will be due during

the week following the end of classes.

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