1.3
Sustainability and energy balance on Earth
The sustainability of life on Earth depends on a balance between the incoming
energy from the sun and the outgoing energy lost from radiation into space.
1. Energy input from the sun is given by the equation
f a cu lty of science
d epa r tm ent of m athema tic s
MATH 895-4 Fall 2010
Course Schedule
MATH 154, S UMMARY #6
Summary
Week
Date
Sections
from FS2009
Part/ References
Topic/Sections
Notes/Speaker
Continuity.
We
see the notionSymbolic
of continuity:
a f
MATH 895-4 Fall 2010
Course Schedule
f a cu lty of sc ie nce
d ep ar tment of mathem atics
Lecture outline
Week
Date
1
Sept 7
Sections
from FS2009
I.1, I.2, I.3
Part/ References
Topic/Sections
Combinatorial
Structures
FS: Part A.1, A.2
Comtet74
Handout #1
MATH 895-4 Fall 2010
Course Schedule
f a cu lty of science
d epa r tm ent of m athema tic s
MATH 154, A SSIGNMENT #1
Due date: Friday September 12, 2:30PM
Week
Date
Sections
from FS2009
Part/ References
Topic/Sections
Notes/Speaker
Please
attach
cover pag
14
Qualitative methods for differential equations
Not all differential equations are easily solved analytically. Furthermore,
even when we find the analytic solution, it is not necessarily easy to interpret,
graph, or understand. This situation motivates
MATH 895-4 Fall 2010
Course Schedule
f a cu lty of science
d epa r tm ent of m athema tic s
Lecture outline
Week
Date
Sections
from FS2009
1
Sept 7
I.1, I.2, I.3
5
Oct 5
III.1, III.2
Part/ References
4.1: D EFINITION OF DERIVATIVE
Topic/Sections
Notes/Spe
MATH 895-4 Fall 2010
Course Schedule
f a cu lty of sc ie nce
d ep ar tment of mathem atics
MATH 154, A SSIGNMENT #2
Due date: Friday, September 19, 2:30PM
Week
Date
Sections
from FS2009
Part/ References
Topic/Sections
Notes/Speaker
Please
attach
cover pag
TA N G E N T L I N E S , L I N E A R A P P ROX I M AT I O N , A N D N E W T O N S M E T H O D
5.5
119
Harder problems: finding the point of tangency
Section 5.4 Learning goals
1. Find a tangent line to a function that goes through a point that is not
nece
5
Tangent lines, linear approximation, and Newtons method
5.1
The equation of a tangent line
The two most common forms for the equation of a line are:
y = mx + b (m is the slope and b is the y-intercept)
y y1 = m(x x1 ) (m is the slope and (x1 , y1 ) is
S O LV I N G D I F F E R E N T I A L E Q UAT I O N S
Here, the first term is the rate of production and the second term is the
rate of decay. The net rate of change of the chemical concentration is then
the difference of the two. The constants Kin > 0, >
14
Periodic and trigonometric functions
Nature abounds with examples of cyclic processes. Perhaps most familiar
is the continually repeating heartbeat that accompanies us through life.
Electrically active muscles power the heart. That electrical activity
192
DIFFERENTIAL CALCULUS FOR THE LIFE SCIENCES
y x x
1 y x y
y2 + x2
1
d2y
y
=
=
=
= 3.
dx2
y2
y2
y3
y
Substituting y = 3/2 from part (a) yields
d2y
dx2
Mastered Material Check
8
1
= (
.
=
3 3/2)
( 3/2)3
We used the equation of the circle, and our resul
15
Cycles, periods, and rates of change
15.1 Derivatives of trigonometric functions
Section 15.1 Learning goals
1. Use the definition of the derivative to calculate the derivatives of sin(x)
and cos(x).
2. Using the quotient rule, compute derivatives of t
7
Optimization
Calculus was developed to solve practical problems. In this chapter, we showcase a variety of problems where finding the largest, the smallest, or the
best answer is the goal. The techniques developed earlier are put to use. In
particular,
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SIMON FRASER UNIVERSITY
DEPARTMENT OF MATHEMATICS
Midterm 1 v1
MATH 154 - D100 Fall 2016
Instructor: Matt DeVos
October 2015, 8:30 - 9:20 am
Name: (please print)
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SIMON FRASER UNIVERSITY
DEPARTMENT OF MATHEMATICS
Midterm 1 v2
MATH 154 - D100 Fall 2015
Instructor: Matt DeVos
October 2015. 8:30 9:20 am
Name: (please print)
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MATH 895-4 Fall 2010
Course Schedule
f a cu lty of sc ie nce
1.2: E LEMENTARY F UNCTIONS
d ep ar tment of mathem atics
Lecture outline
Week
Date
1
Sept 7
Sections
from FS2009
I.1, I.2, I.3
Part/ References
Topic/Sections
Combinatorial
Structures
FS: Part
MATH 895-4 Fall 2010
Course Schedule
f a cu lty of science
d epa r tm ent of m athema tic s
Lecture outline
Week
Date
1
Sept 7
Sections
from FS2009
I.1, I.2, I.3
Part/ References
Topic/Sections
Combinatorial
Structures
FS: Part A.1, A.2
Comtet74
Handout #
MATH 895-4 Fall 2010
Course Schedule
f a cu lty of science
d epa r tm ent of m athema tic s
MATH 154, S UMMARY #4
Summary
Week
Date
Sections
from FS2009
Part/ References
Topic/Sections
Notes/Speaker
This
week
topic
the notion of Symbolic
limit,methods
and
f a cu lty of science
d epa r tm ent of m athema tic s
MATH 895-4 Fall 2010
Course Schedule
MATH 154, S UMMARY #3
Summary
Week
Date
Sections
from FS2009
Part/ References
Topic/Sections
Notes/Speaker
This
week
we focused on graphing.Symbolic
A key
point th
M ATH 155
C HAPTER 7
Our central method for solving differential equations is as follows:
Separation of Variables. A differential equation involving a function y
and its derivative dy
dt is separable if treating dy and dt as differentials, it can
be writt
M ATH 155
C HAPTER 7
Chapter 7 Differential Equations
Definition. A differential equation is an equation concerning functions (so
to the left and right of the = sign are functions which are exactly equal)
that involves derivatives.
Example. y 00 = 4y + 4x
M ATH 155
7.3
C HAPTER 7
Density Dependent Growth
History! Thomas Malthus wrote a series of papers starting in 1798 in
which he argued that the human population was undergoing exponential
growth, but the increase in food production was only linear. He ant
M ATH 155
C HAPTER 7
Our central method for solving differential equations is as follows:
Separation of Variables. A differential equation involving a function y
and its derivative dy
dt is separable if treating dy and dt as differentials, it can
be writt
M ATH 155
5.4
C HAPTER 5
Length of a curve
In this section we compute lengths of curves. Lets start with an easy one:
(x2; y2)
(x1; y1)
Problem. What is the length of the line segment from (x1 , y1 ) to (x2 , y2 )?
Question. How might we compute the lengt