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# Course Introduction

## by Matthew Leingang, Clinical Associate Professor of Mathematics at New York University on Jun 25, 2007

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Introduction to a course taught in the Harvard Summer School

Introduction to a course taught in the Harvard Summer School

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## Course IntroductionPresentation Transcript

• Calculus I and II Math S-1ab Harvard Summer School Summer 2007
• Goals
• Understand functions and their rates of change
• Use functions to study the world
• Work hard
• Learn a lot
• Have fun
• Staff
• Matthew Leingang SC 323 [email_address]
• Jen Balakrishnan (Course Assistant) [email_address]
• Get to Know Indiana “ The Crossroads of America”
• Get to Know Indiana
• Get to Know Indiana
• Get to Know Indiana
• Get to Know Indiana
• Famous Hoosiers
• Hatsumon Problems you will be able to solve after this course 発問
• Hatsumon—Ballistics
• A ball is dropped off the roof of the Science Center. How fast is it going when it hits the ground?
• Hatsumon—Microbiology
• A population of bacteria reproduces asexually, doubling every hour. If the population starts with 100 cells, how many cells are present after 90 minutes?
• Hatsumon—Economics
• In Iceland, a 10% increase in the price of crude oil results in a 1% decrease in oil consumed.
• In China, the same increase in price effects a 0.01% decrease in quantity demanded.
• What do these numbers say about the necessity of oil?
Source: OPEC Review, March 2003
• Hatsumon—Geometry
• What is the volume of a Krispy Kreme Donut?
• Hatsumon—Hydrostatics
• How thick does a dam need to be so as not to collapse from the weight of all the water it’s holding back?
• Hatsumon—Organismal Bio
• How many field mice are needed in a given environment to sustain a population of owls?
• Hatsumon—Numerical Analysis
• What is the 173rd digit of π? The 1000th? 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
• Topics
• Functions
• Differential Calculus
• Limits
• Derivatives
• Rates of Change (with Applications)
• Optimization (with Applications)
• Integral Calculus
• Areas
• Volumes
• Work
• Pressure
• Much, much more!
• Topics
• Sequences and Series
• give a way to solve differential equations and to approximate functions by polynomials
• Differential Equations
• describe the way quantities change with respect to other quantities (e.g., F = ma )
• Class: 10AM–Noon, Monday–Friday
• Discussion Section: 2–3PM, Monday–Friday
• Homework (~20 problems/day)
• Estimated Total: 8 hours/day!
• Textbook
• Single Variable Calculus:Early Transcendentals , by Smith and Minton.
• Available at Harvard Coop and elsewhere
• Other material to be published on course website
• Online Material and Assessments
• ALEKS to refresh your precalculus skills
• MathZone for web material relating to textbook
• Both require registration online and a course code
• Technology
• Calculators and computers are good aids in computational problems and in checking derivations, but…
• … are not allowed on exams
• Do not buy a calculator. Learn to use computer tools (e.g., Mathematica) instead.
• Exams
• Midterm I: Friday July 6
• Midterm II: Friday July 20
• Midterm III: Friday August 3
• All midterms occur in discussion section
• Exams are synthetic (not exactly like homework)
• Final: Tuesday August 14, 8:30AM Location TBA
• Midterms: 3 @ 15%
• Final: 30%
• Homework 25%
• Prerequisites
• Placement test
• Solid foundation of precalculus, including algebra, trigonometry, exponentials, logarithms, and graphing
• MathZone has self-study exercises for this (and all other material in the course).
• ALEKS will assess and help with this
• Course Web Site
• http://my.harvard.edu/k15863
• Available through your HSS portal: http://my.summer.harvard.edu/
• Contains/will contain course documents
• Syllabus
• Handouts
• Old Exams
• Etc.
• Conclusion
• We hope you take and enjoy Math S-1ab!
• Gratuitous Kid Shots