# Syllabus

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

-------------------------------------------------------- So Mo Tu We Th Fr Sa -------------------------------------------------------- 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 period1. 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