Math 1 b Calculus Series and Differential Equations

Math 1 b Calculus, Series, and Differential Equations Harvard University Fall 2005 http: //my. harvard. edu/course/math 1 b

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

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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: MWF 9, 10, 11, 12, T 10, 11: 30

Sections Choose your section by computer: MWF 9, 10, 11, 12, T 10, 11: 30 With sufficient enrollment To section from a UNIX prompt: ssh section@ulam. fas. harvard. edu More information on flyer and at http: //math. harvard. edu/sectionin g/

発問 Hatsumon Problems you will be able to solve after this course

Hatsumon – Volume What 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 173 rd digit of π? The 1000 th? The millionth?

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: 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?

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 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

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 1 a or 8 on HMPT 2

Logical Prerequisite: Precalculus Functions Graphs of “famous” functions and manipulating them Trigonometry Logarithms 20 on HMPT 1

For those who have taken AP Calculus BC Math 1 a and 1 b together cover the Calculus BC syllabus Math 1 b does more than what’s on the BC, with different emphasis You will still find lots to learn in Math 1 b

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– 10 pm, 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/