# Syllabus

Harvard College/GSAS: 8434,, Exam Group 1, Spring 2012**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**: Jeanine Sinanan-Singh (jsinanan-singh.harvard.edu) Jared Sawyer (jaredsawyer.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.

**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 1 and April 5, both midterms take place at 6-7:30 PM in Hall E.

-------------------------------------------------------- So Mo Tu We Th Fr Sa -------------------------------------------------------- 22 23 24 25 26 27 28 4 Jan 23, first class 29 30 31 1 2 3 4 5 Feb 5 6 7 8 9 10 11 6 12 13 14 15 16 17 18 7 19 20 21 22 23 24 25 8 Feb 20 Presidents day 26 27 28 29 1 2 3 9 Mar 1 First midterm Hall E 6PM 4 5 6 7 8 9 10 10 11 12 13 14 15 16 17 11 18 19 20 21 22 23 24 12 25 26 27 28 29 30 31 13 1 2 3 4 5 6 7 14 Apr 5 Second midterm Hall E 6PM 8 9 10 11 12 13 14 15 15 16 17 18 19 20 21 16 22 23 24 25 26 27 28 17 29 30 1 2 3 4 5 18 April 26-May 3 Reading period 6 7 8 9 10 11 12 19 May 4 - May 12 Exam period 13 14 15 16 17 18 19 20 20 21 22 23 24 25 26 21 27 28 29 30 31 22

1. What is calculus? Date Day --------------------- 1. What is Calculus? Jan 23 Mon 2. Functions Jan 25 Wed 3. Limits Jan 27 Fri 4 Continuity Jan 30 Mon 5 Intermediate value theorem Feb 1 Wed 6. A fundamental theorem Feb 3 Fri 7. Rate of Change, tangent Feb 6 Mon 8. Derivative as a function Feb 8 Wed 9. Product and Quotient rules Feb 10 Fri 2. The derivative ----------------- 1. Chain rule Feb 13 Mon 2. Critical points and extrema Feb 15 Wed 3. Optimization problems Feb 17 Fri Pesidents day, no class Feb 20 Mon 4. L'Hopital rule Feb 22 Wed 5. Newton method Feb 24 Fri 6 Review for first midterm 3/1/11 Feb 27 Mon 7. Rolles theorem Feb 29 Wed 8. Castastrophe theory Mar 2 Fri 3. The integral --------------- 1. From sums to integrals Mar 6 Mon 2. The fundamental theorem Mar 8 Wed 3. Antiderivatives Mar 10 Fri 4. Computing areas Mar 19 Mon 5. Volume of solids Mar 21 Wed 6. Improper integrals Mar 23 Fri 7. Applications of integration Mar 26 Mon 4. Calculus Techniques ------------------------ 1. Related rates Mar 28 Wed 2. Implicit differentiation Mar 30 Fri 3. Substitution Apr 2 Wed 4 Review for second midterm 4/5/11 Apr 4 Mon 5. Integration by parts Apr 6 Fri 6. Numerical integration Apr 9 Mon 7. Partial fractions Apr 11 Wed 8. Trig substitutions Apr 13 Fri 5. Calculus and the world ------------------------- 1. Calculus and music Apr 16 Mon 2. Calculus and statistics Apr 18 Wed 3. Calculus and economics Apr 20 Fri 1. Calculus and Computing Apr 23 Mon 2. Outlook and review Apr 25 Mon