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Course Introduction

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Introduction to a course taught in the Harvard Summer School

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• Course Introduction

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