# Syllabus

Harvard College/GSAS: 8434,, Exam Group 1, Spring 2014**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 -------------------------------------------------------- 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 171. 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].