MATH 102

Differential Calculus with Applications to Life Sciences

University of British Columbia

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.

24HR Notes for MATH 102

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Elyse Yeager

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MATH 102 Lecture 37: 2010 Final exam review lecture
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Mathematics
MATH 102
Elyse Yeager

MATH 102 Syllabus for Elyse Yeager — Fall 2018

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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