Mathematics 16A, Fall 2005

Analytic Geometry and Calculus

Professor Bernd Sturmfels

Office hours: Wednesdays and Thursdays 10:00-11:00am
Office location and phone: 925 Evans Hall, 642 4687
email: bernd@math.berkeley.edu

Our class meets in 10 Evans on Tuesday and Thursdays from 8:00am until 9:30am.
Participation in the class, even in this large lecture course, is strongly encouraged.

Graduate Student Instructors:

Text book: L.J. Goldstein, D.C. Lay, and D.I. Schneider, Calculus and its Applications , 10th edition, Prentice Hall.
We will cover Chapters 0-6.

Grading: Quizzes 5 %, Homework 10 %, Midterms 25 % each, Final 35 %. The final exam score will override any lower midterm score. This means that, a posteriori, your final exam may count as 60 % or 85 % instead of 35 %.

Quizzes: Five quizzes will be given during the main lecture. These will occur on randomly selected dates. You may use your book and your notes during a quiz. There will be no make-up quizzes. Don't worry about missing a lecture that has a quiz: a perfect score on all homeworks and exams (i.e. 95 % in total) will suffice to get the course grade A+.

Midterms: Midterm 1 is held in class on Thursday, September 29 and covers material of the text book through Section 2.2. Midterm 2 is held in class on Tuesday, November 8, and covers Chapter 2, 3 and 4 of the text book. A brief review session is held during the class prior to each midterm. No books, notes, calculators, scratch paper or collaboration are permitted at any exam. Student photo ID and a blue-covered exam booklet are required at the midterms and final exam. No make-up midterms will be given; instead, missing midterm scores will be overridden by the final exam score.
Click on the following links to retrieve (in pdf): Midterm 1, Solutions to Midterm 1, Midterm 2, Solutions to Midterm 2.

Final Exam: The final exam will be held from 12:30 to 3:30 on Friday, December 16, in 100 Haas Pavillion. and will cover the material from the entire course. There will be no make-up final exam. If you are unable to attend the final exam due to documented and unexpected circumstances beyond your control, and you have a C average on the previous coursework, an incomplete may be assigned.
Click on the following links to retrieve (in pdf): Final Exam , Solution to Final Exam.

Homework: A range of problems covering the lecture material of each week is due on Tuesday of the following week. Please hand your homework to your GSI. No late homework can be accepted, as solution will be posted shortly after the due date.

Here are the assigned homework problems. Click on the due date (any time after that date) to see the solutions. Your GSI will grade two problems per homework set carefully, and he will spot-check the others. The problems which will be graded more carefully are marked by an asterisk.

Homework # 1 (due September 6): 0.1: 19,42,50; 0.2: 7,16,17,29; 0.3: 9,34*,37; 0.4: 3,19,29,40*; 0.5: 11,37,50,93; 0.6: 13,19,20,39.

Homework # 2 (due September 13): 1.1: 6,12,24,30,40,58; 1.2: 2,3,8,14,15,16,17,18,25; 1.3: 14*,18,28,42,48*,54.

Homework # 3 (due September 20): 1.4: 12,14,33,40,54,55,58; 1.6: 14,17,40,43*,48,53; 1.7: 9,15,25,30,32; 1.8: 3,5,8,12*,13,21.

Homework # 4 (due September 27): 2.1: 5,6,11,15,28,29,33,37,41,43; 2.2: 3,8,15,21,24,26,31,34*,40*.

Homework # 5 (due October 11): 2.3: 12,18,24,26,36; 2.4: 4,8,12,22,29,30,32; 2.5: 10,12,16,20,24; 2.6: 4,8,24,26,27.

Homework # 6 (due October 18): 2.7: 2,6,9,12*,14,22; 3.1: 2,6,12,18,32*,38,44,52,54,66; 3.2: 4,10,16,20.

Homework # 7 (due October 25): 3.2: 28,34,42,46,49,54,61*,62; 3.3: 6,14,22,26,34,38,42,46; 4.1: 2,4*.

Homework # 8 (due November 1): 4.1: 24, 30 ; 4.2: 10, 24, 28*, 30, 32 ; 4.3: 12, 20, 33,34, 36, 44 ; 4.4: 10, 14,18,30,36,40*.

Homework # 9 (due November 15): 5.1: 2, 6, 12, 20*, 26; 5.2: 2, 8, 10*, 12, 24, 25, 26.

Homework # 10 (due November 22): 5.3: 2, 10, 14, 18, 20, 24; 5.4: 2, 4, 6, 8, 9, 12; Suppl.Ex.(Chap 5): 2, 23.

Homework # 11 (due November 29): 6.1: 2, 10, 12, 16*, 20, 24, 26, 34, 36, 39, 43, 44*, 46, 48, 50, 54.

Homework # 12 (due December 6): 6.2: 8,12,16,20,22,26,28; 6.3: 2,6,12,14,26*,38,40,45; 6.4: 2,6,22,28*.

Course Outline:

August 30, September 1: Chapter 0: Functions
September 6, 8: 1.1-1.2. Slope of Line and a Curve, 1.3. The Derivative
September 13, 15: 1.4, 1.6, 1.7, 1.8. More on Derivatives
September 20, 22: 2.1. Graphs of Functions, 2.2. First and Second Derivative Rules,
September 27, 29: Review, First Midterm
October 4,6: 2.3, 2.4. Curve Sketching, 2.5, 2.6, Optimization Problems,
October 11, 13: 2.7 Applications to Business and Economics, 3.1. Product and Quotient Rules,
October 18, 20: 3.2. Chain Rule, Power Rule, 3.3. Implicit Differentiation
October 25, 27: 4.1, 4.2, 4.3. Exponential Function, 4.4. Natural Logarithm
November 1, 3: 4.5, 4.6. Derivative and Other Properties, Review
November 8, 10: Second Midterm, 5.1. Exponential Growth and Decay, 5.2. Compound Interest,
November 15, 17: 5.3. Natural Logarithm in Economics, 5.4 Further Exponential Models
November 22: 6.1. Antidifferentiation
November 29, December 1: 6.2 Areas and Riemann Sums, 6.3 Definite Integrals 6.4, Areas in the Plane
December 6, 8: 6.5 Applications of the Definite Integral, Review.