Syllabus

Harvard College/GSAS: 8434,, Exam Group 1, Spring 2013
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.

Course assistants:
  • Angeline Baniqued anniebaniqued
  • Jeanine Sinanan-Singh jsinanan-singh
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.

Grades: 20 percent for each midterm, 20 percent for homework and 40 percent for final exam.

MQC the MQC for 1A is in SC 309-A from Sun to Thu 8:30 - 10:30 PM. Calendar: the midterm dates are March ? and April ?, both midterms take place at 6-7:30 PM in Hall ?
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So Mo Tu We Th Fr Sa
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27 28 29 30 31  1  2    4  Jan 28, first class
 3  4  5  6  7  8  9    5
10 11 12 13 14 15 16    6
17 18 19 20 21 22 23    7
24 25 26 27 28  1  2    8  
 3  4  5  6  7  8  9    9  March 7 First midterm  7 PM
10 11 12 13 14 15 16   10
17 18 19 20 21 22 23   11  Spring Break 
24 25 26 27 28 29 30   12
31  1  2  3  4  5  6   13       
 7  8  9 10 11 12 13   14  April 11 Second midterm  7 PM
14 15 16 17 18 19 20   15
21 22 23 24 25 26 27   16
28 29 30  1  2  3  4   17  May 1 Last day of class
 5  6  7  8  9 10 11   18  Reading period
12 13 14 15 16 17 18   19  Exam period

1. What is calculus?                         Date   Day  
---------------------

1. What is Calculus?                         Jan 28 Mon   
2. Functions                                 Jan 30 Wed   
3. Limits                                    Jan  1 Fri   

4  Continuity                                Feb  4 Mon   
5  Intermediate value theorem                Feb  6 Wed   
6. A fundamental theorem                     Feb  8 Fri  

7. Rate of Change, tangent                   Feb 11 Mon   
8. Derivative as a function                  Feb 13 Wed   
9. Product and Quotient rules                Feb 15 Fri   

2. The derivative
-----------------

   Presidents day, no class                  Feb 18 Mon  
1. Chain rule                                Feb 20 Mon   
2. Critical points and extrema               Feb 22 Wed   

3. Optimization problems                     Feb 25 Fri   
4. L'Hopital rule                            Feb 27 Wed   
5. Newton method                             Mar  1 Fri   

6. Rolles theorem                            Mar  4 Mon
7  Review for first midterm                  Mar  6 Wed
                                    ------------------------first mid
8. Castastrophe theory                       Mar  8 Fri  

3. The integral
---------------

1. From sums to integrals                    Mar 11 Mon  
2. The fundamental theorem                   Mar 13 Wed   
3. Antiderivatives                           Mar 15 Fri  

4. Computing areas                           Mar 25 Mon 
5. Volume of solids                          Mar 27 Wed 
6. Improper integrals                        Mar 29 Fri 

7. Applications of integration               Apr  1 Mon 

4. Calculus Techniques
------------------------

1. Related rates                             Apr  3 Wed 
2. Implicit differentiation                  Apr  5 Fri 

4. Substitution                              Apr  8 Mon
3  Review for second midterm                 Apr 10 Wed  
                                    ------------------------second mid
5. Integration by parts                      Apr 12 Fri  

6. Numerical integration                     Apr 15 Mon  
7. Partial fractions                         Apr 17 Wed  
8. Trig substitutions                        Apr 19 Fri  

5. Calculus and the world
-------------------------

1. Calculus and music                        Apr 22 Mon  
2. Calculus and statistics                   Apr 24 Wed  
3. Calculus and economics                    Apr 26 Fri  

1. Calculus and Computing                    Apr 29 Mon  
2. Outlook and review                        May  1 Wed