Syllabus

Harvard College/GSAS: 8434,, Exam Group 1, Spring 2010-2011
Instructor: Oliver Knill

Meeting time: Monday/Wednesday/Friday at 10 in 309, and a weekly problem section to be arranged.

The development of calculus by Newton and Leibniz ranks among the greatest intellectual achievements of the past millennium. This course will help you see why. How does differential calculus treat rates of change? How does integral calculus deal with accumulation? And how does the fundamental theorem of calculus link the two? These ideas will be applied to problems from many other disciplines. We do not go chronologically through the textbook but use a slightly streamlined path which will allow us to spend the last week with applying the material. The handouts will guide you.

Gen Ed: This course, when taken for a letter grade, meets the General Education requirement for Empirical and Mathematical Reasoning or the Core area requirement for Quantitative Reasoning.

Prerequisite: A solid background in precalculus.

Calendar: the midterm dates are March 1 and April 5, both midterms take place at 7 PM in Hall D.
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So Mo Tu We Th Fr Sa    
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23 24 25 26 27 28 29    1   Jan 24 first class
30 31  1  2  3  4  5    2  
 6  7  8  9 10 11 12    3
13 14 15 16 17 18 19    4                           
20 21 22 23 24 25 26    5   Feb 21, Presidents day 
27 28  1  2  3  4  5    6   March 1. First midterm Hall D
 6  8  9 10 11 12 13    7
13 15 16 17 18 19 20        March 13-March 19 Spring break
20 21 22 23 24 25 26    8   March 23: Brian lecture I
27 28 29 30 31  1  2    9
 3  4  5  6  7  8  9   10   April 5. Second midterm Hall D
10 11 12 13 14 15 16   11   April 15. Brian lecture II
17 18 19 20 21 22 23   12
24 25 26 27 28 29 30   13   April 20. Brian lecture III
 1  2  3  4  5  6  7        April 29-May 6, Reading period
 8  9 10 11 12 13 14        Review: 9'th and final exam 14'th
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1. What is calculus?                         Date   Day  References 
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1. What is Calculus?                         Jan 24 Mon  Oliver 
2. Functions                                 Jan 26 Wed  Johnny  1.2
3. Limits                                    Jan 28 Fri  Johnny  2.2

4  Continuity                                Jan 31 Mon  Johnny  2.4
5  Intermediate value theorem                Feb  2 Wed  Johnny  2.4
6. A fundamental theorem                     Feb  4 Fri  Oliver

7. Rate of Change, tangent                   Feb  7 Mon  Johnny  2.6
8. Derivative as a function                  Feb  9 Wed  Johnny  2.7
9. Product and Quotient rules                Feb 11 Fri  Johnny  3.2

2. The derivative
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1. Chain rule                                Feb 14 Mon  Johnny  3.2
2. Critical points and extrema               Feb 16 Wed  Johnny  4.2
3. Optimization problems                     Feb 18 Fri  Johnny  4.2

   Pesidents day, no class                   Feb 21 Mon  

4. L'Hopital rule                            Feb 23 Wed  Johnny  4.5
5. Newton method                             Feb 25 Fri  Johnny  4.7 

6  Review for first midterm  3/1/11          Feb 28 Mon  Oliver   
7. Rolles theorem                            Mar  2 Wed  Johnny  4.3
8. Castastrophe theory                       Mar  4 Fri  Oliver

3. The integral
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1. From sums to integrals                    Mar  8 Mon  Johnny 5.1 
2. The fundamental theorem                   Mar 10 Wed  Johnny 5.4 
3. Antiderivatives                           Mar 12 Fri  Johnny 5.4 

4. Computing areas                           Mar 21 Wed  Johnny 6.1
5. Volume of solids                          Mar 23 Fri  Johnny 6.2 
6. Improper integrals                        Mar 25 Mon  Johnny 5.10 

7. Applications of integration               Mar 28 Mon  Johnny 6.5 

4. Calculus Techniques
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1. Related rates                             Mar 30 Wed  Johnny 3.4
2. Implicit differentiation                  Apr  1 Fri  Johnny 3.5

3  Review for second midterm 4/5/11          Apr  4 Mon  Oliver 
4. Substitution                              Apr  6 Wed  Johnny 5.5 
5. Integration by parts                      Apr  8 Fri  Johnny 5.6

6. Numerical integration                     Apr 11 Mon  Johnny 5.9
7. Partial fractions                         Apr 13 Wed  Johnny 5.7
8. Trig substitutions                        Apr 15 Fri  Johnny 5.7

5. Calculus and the world
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1. Calculus and music                        Apr 18 Mon  Oliver
2. Calculus and statistics                   Apr 20 Wed  Bryan
3. Calculus and economics                    Apr 22 Fri  Oliver

4. Calculus and artificial intelligence      Apr 25 Mon  Oliver
5. The lighter side                          Apr 27 Wed  Oliver