Math 1b
Calculus, Series, and
Differential Equations
Harvard University
Fall 2005
http:/my.harvard.edu/course/math1b
Course Goals
Learn the techniques of calculus
for analyzing functions
Learn how to
Maths Counts
Insights into Lesson
Study
1
Presentation Secondary School:
Listowel:
Jacqueline Normile, Norma Dowling and Elaine
Hickey.
Sixth Year.
Associating derivatives with slopes of tangent
li
What is Calculus?
Origin of calculus
The word Calculus comes from the
Greek name for pebbles
Pebbles were used for counting and
doing simple algebra
Google answer
A method of computation or calcula
Spreadsheet Software as a Teaching Tool
for Introductory Mathematics Courses
Shuzo Takahashi
Arizona Winter School 2002
March 10, 2002
Abstract
I will talk about one way to use spreadsheets
(Excel) in
9.1 Power Series
Start with a square one
unit by one unit:
1 1 1 1 1 1
1
2 4 8 16 32 64
1
8
1
2
1
64
1
16
1
1
4
This is an example of an
infinite series.
This series converges
(approaches a limiting
4.1 Extreme Values of
Functions
Absolute extreme values are either maximum or
minimum points on a curve.
They are sometimes called global extremes.
They are also sometimes called absolute extrema.
(Ex
10.1 Parametric Functions
In chapter 1, we talked about parametric
equations.
Parametric equations can be used to describe
motion that is not a function.
x f t
y g t
If f and g have derivatives at t,
7.1 Integrals as Net Change
A honey bee makes several trips from the hive to a flower
garden. What is the total distance traveled by the bee?
ft
min
200ft
200ft
200 200 200 100 700
minutes
200ft
100ft
2.1 Rates of Change and Limits
Suppose you drive 200 miles, and it takes you 4 hours.
Then your average speed is:
mi
200 mi 4 hr 50
hr
distance
x
average speed
elapsed time
t
If you look at your spee
6.1 Antiderivatives with
Slope Fields
Consider:
then:
y x 2 3
y x 2 5
or
y2 x
y 2 x
It doesnt matter whether the constant was 3 or -5, since
when we take the derivative the constant disappears.
Howeve
8.1 LHpitals Rule
Actually, LHpitals Rule was
developed by his teacher
Johann Bernoulli. De
LHpital paid Bernoulli for
private lessons, and then
published the first Calculus
book based on those lesson
5.1 Estimating with Finite
Sums
Consider an object moving at a constant rate of 3 ft/sec.
Since rate . time = distance: 3t d
If we draw a graph of the velocity, the distance that the
object travels is