Transcript Introduction - Department of Mathematics

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 model complex situations
with mathematics
 To read, write, and critique
mathematical arguments
Course Head
 Dr. Matthew Leingang
[email protected]
(not leingang@fas)
Science Center 323
Office Hours: Tues., Weds., 1–3pm.
Get to Know Indiana
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, T10, 11:30
Sections
 Choose your section by computer:
MWF9, 10, 11, 12, T10, 11:30
With sufficient enrollment
 To section from a UNIX prompt:
ssh [email protected]
 More information on flyer and at
http://math.harvard.edu/sectionin
g/
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 bacteria
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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 to
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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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“Overarethree
needed tocenturies
see this picture. of
constant
use have not completely dulled
this incomparable instrument.”—
Nicholas Bourbaki
Course Topics
Techniques and Applications
of Integration
 Basic Problem: find
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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
n
n 1
2


2
6
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
Exams
 Technique Test:
October 6 and 13
(second is optional;
maximum counts)
 Two midterm exams:
Thursday, October 27
and December 1
 Final Exam
(cumulative)
tentatively scheduled
for January 14
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Breakdown of your course
grade
20%
Midterm I
25%
Midterm II
35%
Final
15%
Homework
10%
Technique Test
5%
Pre-class Reading Assignments
100%
Total
Grading Scale
 Could be adjusted
90%
A
80%
B
65%
C
50%
D
for equity (“on the
curve”)—up, but not
down
 Pluses and minuses
will also be
determined in final
analysis
Texts
 Single Variable
Calculus—Concepts
and Contexts by
James Stewart, ISBN
0-534-41022-7
 Available for
purchase at the
Coop
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Texts
 Schaum’s Outlines:
Precalculus by Fred
Safier, ISBN 0-07057261-5
 Optional
 Cheap
 Available for
purchase at the
Coop
Prerequisites
Logical Prerequisite: Calculus
 Derivatives
 Definition of the
Integral
 Fundamental
Theorem of Calculus
 (Integration by
Substitution)
 Math 1a or 8 on
HMPT2
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Logical Prerequisite:
Precalculus
 Functions
 Graphs of “famous”
functions and
manipulating them
 Trigonometry
 Logarithms
 20 on HMPT1
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For those who have taken
AP Calculus BC
 Math 1a and 1b
together cover the
Calculus BC syllabus
 Math 1b does more
than what’s on the BC,
with different emphasis
 You will still find lots to
learn in Math 1b
For those who have taken
AP Calculus AB
 Some of your
classmates will have
seen some of this
material before
 We are committed to
supporting all qualified
students
Resources
 Your section’s problem
session
 Math Question Center
(Sunday–Thursday, 8–
10pm, Loker Commons)
 Your TF’s office hours
 My office hours
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Math Warm-Up Series
 Brush-up on some precalculus topics
(trig, logs, algebra)
 Advice on study skills and course
selection
 http://www.math.harvard.edu/mwus/
Other Activities
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 Online Placement Exam
http://math.placement.fas.harvard.edu/
Other Activities
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 Math Department advice is ongoing; see
http://www.math.harvard.edu/sectioning
First Assignments
 Read Section 5.1 and 5.2 of the text
 Select a section by computer
 answer questions online (to appear
later this week)
Conclusion
 I hope you take and
enjoy Math 1b!
 Web site reminder:
http://my.harvard.e
du/course/math1b
 (Gratuitous baby
shot)