Description

Math 1b Analytics, Arrangement, and Differential Mathematical statements. Harvard College Fall 2005 http://my.harvard.edu/course/math1b. Course Objectives. Take in the strategies of analytics for dissecting capacities Figure out how to model complex circumstances with arithmetic

Transcripts

Math 1b Calculus, Series, and Differential Equations Harvard University Fall 2005 http://my.harvard.edu/course/math1b

Course Goals Learn the methods of analytics for breaking down capacities Learn how to model complex circumstances with arithmetic To peruse, compose, and evaluate scientific contentions

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

Get to Know Indiana

Get to Know Indiana

Get to Know Indiana

Get to Know Indiana

Get to Know Indiana

Other showing staff Faculty individuals or Teaching Fellows in arithmetic Majority of direction happens in segment , three hours/week All segments cover same subjects and have a similar workload

Sections Choose your segment by PC : MWF9, 10, 11, 12, T 10, 11:30

Sections Choose your segment by PC : MWF9 , 10, 11, 12 , T 10, 11:30 With adequate enlistment To area from a UNIX incite: ssh section@ulam.fas.harvard.edu More data on flyer and at http://math.harvard.edu/separating/

発問 Hatsumon Problems you will have the capacity to unravel after this course

Hatsumon – Volume What is the volume of a Krispy Kreme Donut?

Hatsumon – Microbiology A populace of microorganisms duplicates abiogenetically. How might you anticipate the development of the populace after some time?

Hatsumon – Fluid Dynamics A gap is punched close to the base of a tank How long does it take for the tank to deplete?

Hatsumon – Organismal Bio Owls eat mice. What will happen to the owl populace when the mouse populace is split by starvation? To what extent until we see a change?

Hatsumon – Numerical Analysis What is the 173rd digit of π? The 1000th? The millionth?

All of these issues (and some more) can be tackled with Calculus! " Over three centuries of consistent utilize have not totally dulled this unique instrument. "— Nicholas Bourbaki

Course Topics

Techniques and Applications of Integration Basic Problem: discover the range under a bend Extends to numerous ideas other than territory: Volume Work Flux

Differential Equations depict the way amounts change concerning different amounts (for example, time) The laws of science are effectively communicated by DE F=ma (more troublesome when F relies on upon position, or on time) Newton\'s Law of Cooling Population Dynamics

Approximate many confused capacities by straightforward polynomials Solve differential conditions Our computerized world would be inconceivable without them—how does your number cruncher know sin(0.1) to 8 digits? Interminable Series

Course Expectations

Pre-class Reading Assignments Reading assignments the prior night class Go to course site to answer addresses Your showing kindred will utilize this data to set up a tweaked class

Homework Assigned every day, due the following No late homework! If you don\'t mind keep up. Drop one week\'s worth in calculation of conclusive review

Exams Technique Test: October 6 and 13 (second is discretionary; most extreme tallies) Two midterm exams: Thursday, October 27 and December 1 Final Exam (aggregate) probably booked for January 14

Breakdown of your course review

Grading Scale Could be balanced for value ("on the bend")— up, yet not down Pluses and minuses will likewise be resolved in definite examination

Texts Single Variable Calculus—Concepts and Contexts by James Stewart, ISBN 0-534-41022-7 Available for buy at the Coop

Texts Schaum\'s Outlines: Precalculus by Fred Safier, ISBN 0-07-057261-5 Optional Cheap Available for buy 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

Logical Prerequisite: Precalculus Functions Graphs of "renowned" capacities and controlling them Trigonometry Logarithms 20 on HMPT1

For the individuals who have taken AP Calculus BC Math 1a and 1b together cover the Calculus BC syllabus Math 1b accomplishes more than what\'s on the BC, with various accentuation You will even now discover parts to learn in Math 1b

For the individuals who have taken AP Calculus AB Some of your schoolmates will have seen some of this material before We are focused on supporting every single qualified understudy

Resources Your segment\'s issue session Math Question Center (Sunday–Thursday, 8–10pm, Loker Commons) Your TF\'s available time My office hours

Math Warm-Up Series Brush-up on some precalculus subjects (trig, logs, polynomial math) Advice on study aptitudes and course choice http://www.math.harvard.edu/mwus/

Other Activities Online Placement Exam http://math.placement.fas.harvard.edu/

Other Activities Math Department guidance is progressing; see http://www.math.harvard.edu/separating

First Assignments Read Section 5.1 and 5.2 of the content Select a segment by PC answer questions on the web (to seem in the not so distant future)

Conclusion I trust you take and appreciate Math 1b! Site update: http://my.harvard.edu/course/math1b (Gratuitous infant shot)