Syllabus

Harvard College/GSAS: 8434,, Exam Group 1, Spring 2014
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:
  • Emma Rausch (erausch@college.harvard.edu)
  • Cody Kiechle (ckiechle@college.harvard.edu)
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 Math question center 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 ?
--------------------------------------------------------
So Mo Tu We Th Fr Sa
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26 27 28 29 30 31  1    1  Jan 27, first class
 2  3  4  5  6  7  8    2
 9 10 11 12 13 14 15    3
16 17 18 19 20 21 22    4
23 24 25 26 27 28  1    5
 2  3  4  5  6  7  8    6  March 4  First midterm  7 PM
 9 10 11 12 13 14 15    7
17 18 19 20 21 22 23    8  Spring Break: March 15-23 
16 17 18 19 20 21 22    9
23 24 25 26 27 28 29   10
30 31  1  2  3  4  5   10       
 6  7  8  9 10 11 12   11  April 8 Second midterm  7 PM
13 14 15 16 17 18 19   15
20 21 22 23 24 25 26   16
27 28 29 30  1  2  3   14  April 30, last day of spring class
 4  5  6  7  8  9 10   15  Reading period
11 12 13 14 15 16 17   16  Final Exam date:  May 17

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

1. What is Calculus?                         Jan 27 Mon   
2. Functions                                 Jan 29 Wed   
3. Limits                                    Jan 31 Fri   

4  Continuity                                Feb  3 Mon   
5  Intermediate value theorem                Feb  5 Wed   
6. A fundamental theorem                     Feb  7 Fri  

7. Rate of Change, tangent                   Feb 10 Mon   
8. Derivative as a function                  Feb 12 Wed   
9. Product and Quotient rules                Feb 14 Fri   

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

   Presidents day, no class                  Feb 17 Mon  
1. Chain rule                                Feb 19 Mon   
2. Critical points and extrema               Feb 21 Wed   

3. Optimization problems                     Feb 24 Fri   
4. L'Hopital rule                            Feb 26 Wed   
5. Newton method                             Mar 28 Fri   

6  Review for first midterm                  Mar  3 Mon
                                    ----------------Tue ----first mid 
7. Rolles theorem                            Mar  5 Wed
8. Castastrophe theory                       Mar  7 Fri  

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

1. From sums to integrals                    Mar 10 Mon  
2. The fundamental theorem                   Mar 12 Wed   
3. Antiderivatives                           Mar 14 Fri  

4. Computing areas                           Mar 24 Mon 
5. Volume of solids                          Mar 26 Wed 
6. Improper integrals                        Mar 28 Fri 

7. Applications of integration               Mar 31 Mon 

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

1. Related rates                             Apr  2 Wed 
2. Implicit differentiation                  Apr  4 Fri 

3  Review for second midterm                 Apr  7 Mon  
                                    --------------- Tue ----second mid
4. Substitution                              Apr  9 Wed 
5. Integration by parts                      Apr 11 Fri  

6. Numerical integration                     Apr 14 Mon  
7. Partial fractions                         Apr 16 Wed  
8. Trig substitutions                        Apr 18 Fri  

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

1. Calculus and music                        Apr 21 Mon  
2. Calculus and statistics                   Apr 23 Wed  
3. Calculus and economics                    Apr 25 Fri  

1. Calculus and Computing                    Apr 28 Mon  
2. Outlook and review                        May 30 Wed   last day of classes

Our final exam takes place in May 17, 2014. See
the exam schedule [PDF].