# Syllabus

Harvard College/GSAS: 8434,, Exam Group 1, Spring 2010-2011**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.

-------------------------------------------------------- So Mo Tu We Th Fr Sa -------------------------------------------------------- 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 ---------------------------------------------------------

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