Math 1b Calculus, Series, and Differential Equations Harvard University Fall 2005 http://my.harvard.edu/course/math1bSlide 2
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 contentionsSlide 3
Course Head Dr. Matthew Leingang firstname.lastname@example.org ( not leingang@fas) Science Center 323 Office Hours: Tues., Weds., 1–3pm.Slide 4
Get to Know IndianaSlide 5
Get to Know IndianaSlide 6
Get to Know IndianaSlide 7
Get to Know IndianaSlide 8
Get to Know IndianaSlide 9
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 workloadSlide 10
Sections Choose your segment by PC : MWF9, 10, 11, 12, T 10, 11:30Slide 11
Sections Choose your segment by PC : MWF9 , 10, 11, 12 , T 10, 11:30 With adequate enlistment To area from a UNIX incite: ssh email@example.com More data on flyer and at http://math.harvard.edu/separating/Slide 12
発問 Hatsumon Problems you will have the capacity to unravel after this courseSlide 13
Hatsumon – Volume What is the volume of a Krispy Kreme Donut?Slide 14
Hatsumon – Microbiology A populace of microorganisms duplicates abiogenetically. How might you anticipate the development of the populace after some time?Slide 15
Hatsumon – Fluid Dynamics A gap is punched close to the base of a tank How long does it take for the tank to deplete?Slide 16
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?Slide 17
Hatsumon – Numerical Analysis What is the 173rd digit of π? The 1000th? The millionth?Slide 18
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 BourbakiSlide 19
Course TopicsSlide 20
Techniques and Applications of Integration Basic Problem: discover the range under a bend Extends to numerous ideas other than territory: Volume Work FluxSlide 21
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 DynamicsSlide 22
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 SeriesSlide 23
Course ExpectationsSlide 24
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 classSlide 25
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 reviewSlide 26
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 14Slide 27
Breakdown of your course reviewSlide 28
Grading Scale Could be balanced for value ("on the bend")— up, yet not down Pluses and minuses will likewise be resolved in definite examinationSlide 29
Texts Single Variable Calculus—Concepts and Contexts by James Stewart, ISBN 0-534-41022-7 Available for buy at the CoopSlide 30
Texts Schaum\'s Outlines: Precalculus by Fred Safier, ISBN 0-07-057261-5 Optional Cheap Available for buy at the CoopSlide 31
Logical Prerequisite: Calculus Derivatives Definition of the Integral Fundamental Theorem of Calculus (Integration by Substitution) Math 1a or 8 on HMPT2Slide 33
Logical Prerequisite: Precalculus Functions Graphs of "renowned" capacities and controlling them Trigonometry Logarithms 20 on HMPT1Slide 34
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 1bSlide 35
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 understudySlide 36
Resources Your segment\'s issue session Math Question Center (Sunday–Thursday, 8–10pm, Loker Commons) Your TF\'s available time My office hoursSlide 37
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/Slide 38
Other Activities Online Placement Exam http://math.placement.fas.harvard.edu/Slide 39
Other Activities Math Department guidance is progressing; see http://www.math.harvard.edu/separatingSlide 40
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)Slide 41
Conclusion I trust you take and appreciate Math 1b! Site update: http://my.harvard.edu/course/math1b (Gratuitous infant shot)
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