90 Math 1b Calculus, Series, and Differential Equations

Math 1b
Calculus, Series, and
Differential Equations
Harvard University
Fall 2005
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Course Goals
 Learn the techniques of calculus for analyzing

functions
 Learn how to model complex situations with

mathematics
 To read, write, and critique mathematical

arguments


Course Head
 Dr. Matthew Leingang


(not leingang@fas)
Science Center 323
Office Hours: Tues., Weds., 1–3pm.


Get to Know Indiana

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Get to Know Indiana

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Get to Know Indiana

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Get to Know Indiana

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Get to Know Indiana

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Other teaching staff
 Faculty members or Teaching Fellows in

mathematics
 Majority of instruction takes place in section,

three hours/week
 All sections cover same topics and have the

same workload


Sections
 Choose your section by computer:

MWF9, 10, 11, 12, ΤΘ10, 11:30


Sections
 Choose your section by computer:

MWF9, 10, 11, 12, ΤΘ10, 11:30
With sufficient enrollment

 To section from a UNIX prompt:

ssh
 More information on flyer and at

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発発

Hatsumon

Problems you will be able to
solve after this course


Hatsumon – Volume
 What is the volume of a Krispy Kreme

Donut?

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Hatsumon – Microbiology
 A population of

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bacteria reproduces
asexually. How can
you predict the growth
of the population over
time?


Hatsumon – Fluid
Dynamics
 A hole is punched

near the bottom
of a tank
 How long does it
take for the tank
to drain?


Hatsumon – Organismal
Bio
 Owls eat mice.
 What will happen

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to the owl

population when
the mouse
population is
halved by
starvation?
 How long until we
notice a change?


Hatsumon – Numerical
Analysis
 What is the 173rd

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digit of π?
 The 1000th?
 The millionth?


All of these problems (and
many more) can be solved
with Calculus!
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neededcenturies
to see this picture.
“Overarethree

of
constant use have not
completely dulled this
incomparable instrument.”—
Nicholas Bourbaki


Course Topics


Techniques and
Applications of Integration
 Basic Problem:

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find the area
under a curve
 Extends to many
concepts besides
area:
 Volume
 Work
 Flux


Differential Equations
 describe the way quantities change with

respect to other quantities (for instance,
time)
 The laws of science are easily expressed
by DE
 F=ma (more difficult when F depends on

position, or on time)
 Newton’s Law of Cooling
 Population Dynamics


Infinite Series
 Approximate many

complicated
functions by simple
polynomials
 Solve differential
equations
 Our digital world
would be impossible
without them—how
does your calculator
know sin(0.1) to 8
digits?

1 π
∑ n2 = 6
n =1

∞

2


Course Expectations


Pre-class Reading
Assignments
 Reading assignments

the night before class
 Go to course web site
to answer questions
 Your teaching fellow
will use this
information to
prepare a customized
class


Homework
 Assigned each

day, due the next
 No late
homework!
Please keep up.
 Drop one week’s

worth in
computation of
final grade