Math 1b Calculus, Series, and Differential Equations Harvard University Fall 2005

Math 1bCalculus, Series, and Differential Equations

Harvard UniversityFall 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 [email protected](not leingang@fas)Science Center 323Office Hours: Tues., Weds., 1–3pm.

mailto:[email protected]

Get to Know Indiana

QuickTime™ and aTIFF (Uncompressed) decompressor

are needed to see this picture.

Get to Know Indiana



Get to Know Indiana



Get to Know Indiana



Get to Know Indiana



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

Sections

Choose your section by computer:MWF9, 10, 11, 12, 10, 11:30

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/

mailto:[email protected]

http://math.harvard.edu/sectioning/

発問発問Hatsumon

Problems you will be able to solve after this course

Hatsumon – VolumeWhat is the volume of a Krispy Kreme

Donut?





Hatsumon – Microbiology

A population of 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

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 digit of π?

The 1000th? The millionth?QuickTime™ and a

TIFF (Uncompressed) decompressorare needed to see this picture.



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

Course Topics

Techniques and Applications of Integration

Basic Problem: find the area under a curve

Extends to many concepts besides area:VolumeWorkFlux



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

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

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



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

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

Texts

Single Variable Calculus—Concepts and Contexts by James Stewart, ISBN 0-534-41022-7

Available for purchase at the Coop



Texts

Schaum’s Outlines: Precalculus by Fred Safier, ISBN 0-07-057261-5

OptionalCheapAvailable for

purchase at the Coop

Prerequisites

Logical Prerequisite: Calculus

DerivativesDefinition of the

IntegralFundamental

Theorem of Calculus

(Integration by Substitution)

Math 1a or 8 on HMPT2



Logical Prerequisite: Precalculus

FunctionsGraphs of

“famous” functions and manipulating them

TrigonometryLogarithms20 on HMPT1



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



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/

http://www.math.harvard.edu/mwus/

Other Activities

Online Placement Examhttp://math.placement.fas.harvard.edu/



http://math.placement.fas.harvard.edu/

Other Activities

Math Department advice is ongoing; see http://www.math.harvard.edu/sectioning



http://www.math.harvard.edu/sectioning

First Assignments

Read Section 5.1 and 5.2 of the text

Select a section by computeranswer questions online (to appear

later this week)

Conclusion

I hope you take and enjoy Math 1b!

Web site reminder: http://my.harvard.edu/course/math1b

(Gratuitous baby shot)




Documents

Math 1b Calculus, Series, and Differential Equations Harvard University Fall 2005