Math 1b Calculus, Series, and Differential Equations Harvard University Fall 2005 .
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Math 1bCalculus, Series, and Differential Equations
Harvard UniversityFall 2005
http://my.harvard.edu/course/math1b
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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
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Course Head
Dr. Matthew [email protected](not leingang@fas)Science Center 323Office Hours: Tues., Weds., 1–3pm.
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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
Other teaching staff
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Sections
Choose your section by computer:MWF9, 10, 11, 12, 10, 11:30
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Sections
Choose your section by computer:MWF9, 10, 11, 12, 10, 11:30With sufficient enrollment
To section from a UNIX prompt:ssh [email protected]
More information on flyer and athttp://math.harvard.edu/sectioning/
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発問発問Hatsumon
Problems you will be able to solve after this course
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Hatsumon – VolumeWhat is the volume of a Krispy Kreme
Donut?
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Hatsumon – Microbiology
A population of bacteria reproduces asexually. How can you predict the growth of the population over time?
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Hatsumon – Fluid Dynamics
A hole is punched near the bottom of a tank
How long does it take for the tank to drain?
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Hatsumon – Organismal Bio
Owls eat mice. What will happen
to the owl population when the mouse population is halved by starvation?
How long until we notice a change?
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Hatsumon – Numerical Analysis
What is the 173rd digit of π?
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All of these problems (and many more) can be solved
with Calculus!
“Over three centuries of constant use have not completely dulled this incomparable instrument.”—Nicholas Bourbaki
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Course Topics
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Techniques and Applications of Integration
Basic Problem: find the area under a curve
Extends to many concepts besides area:VolumeWorkFlux
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Differential Equations
describe the way quantities change with respect to other quantities (for instance, time)
The laws of science are easily expressed by DEF=ma (more difficult when F depends on
position, or on time)Newton’s Law of CoolingPopulation Dynamics
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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
n2n=1
∞
∑ =π 2
6
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Course Expectations
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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
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Homework
Assigned each day, due the next
No late homework! Please keep up.
Drop one week’s worth in computation of final grade
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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
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Grading Scale
90% A
80% B
65% C
50% D
Could be adjusted for equity (“on the curve”)—up, but not down
Pluses and minuses will also be determined in final analysis
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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 0-07-057261-5
OptionalCheapAvailable for
purchase at the Coop
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Prerequisites
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Logical Prerequisite: Calculus
DerivativesDefinition of the
IntegralFundamental
Theorem of Calculus
(Integration by Substitution)
Math 1a or 8 on HMPT2
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Logical Prerequisite: Precalculus
FunctionsGraphs of
“famous” functions and manipulating them
TrigonometryLogarithms20 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
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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
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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/
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Other Activities
Online Placement Examhttp://math.placement.fas.harvard.edu/
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Other Activities
Math Department advice is ongoing; see http://www.math.harvard.edu/sectioning
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First Assignments
Read Section 5.1 and 5.2 of the text
Select a section by computeranswer questions online (to appear
later this week)
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Conclusion
I hope you take and enjoy Math 1b!
Web site reminder: http://my.harvard.edu/course/math1b
(Gratuitous baby shot)