University of Wisconsin-Madison
University of Wisconsin-Madison
Mathematics Department

Math 221 Lectures 2 and 3
Calculus and Analytic Geometry
Lecturer: Arun Ram

Syllabus

Fall 2006


Text: The textbook for the course is Thomas' Calculus, Eleventh edition, Addison-Wesley.

Midterm and Final Exams: The exam problems will be taken from the homework assignments, verbatim. There will never be a surprise problem on the exams. In general, the exams are a random selection of 10 problems from the relevant homework assignments. The way the exams are constructed means that you get can excellent scores on the exams by learning how to write clear, correct, solutions to the homework problems at 1/3 the rate that it takes Prof. Ram to write them. You can go watch Prof. Ram do homework problems every Sunday afternoon from 1:30-4:30pm in B239.

Schedule of topics: The following is the schedule of topics to be covered, including the corresponding section in the text and the approximate timing during the semester. We will go in the general order Chapter 1, 7, 3, 2, 5, 6. This is ordering is helpful because it provides, early in the semester, lots of interesting functions to use for examples and it allows us to practice algebra before getting into the delicacies of what "closer and closer" (i.e. limits) really means. For each week of class the relevant sections in the book are listed. If a given section is listed it means that there is some material in that section which might be useful for a full understanding of the material. It does not mean that we will cover the whole section in that particular week nor does it mean that every student will need to read that section in order to understand the material for that week. Everybody learns differently.

Lecture 1: Wednesday September 6, 2006, Numbers, Sections 1.1, A.5

Lecture 2: Friday September 8, 2006, Functions, Sections 7.1, 7.2, 7.3, 7.4, 7.7, 7.8 and some of Section 11.7 and 11.8

Lecture 3: Monday September 11, 2006, Angles, Section 1.6, HW1 due

Lecture 4: Wednesday September 13, 2006, Examples

Lecture 5: Friday September 15, 2006, Derivatives, Section 3.2, 3.4

Lecture 6: Monday September 18, 2006, Chain rule, Section 3.5 HW2 due

Lecture 7: Wednesday September 20, 2006, Derivatives at a point, Implicit differentiation, Section 3.1, 3.6

Lecture 8: Friday September 22, 2006, Parametric equations, Examples, Section 3.5

Lecture 9: Monday September 25, 2006, Examples, HW3 due

Lecture 10: Wednesday September 27, 2006, Taylor's theorem, Section 3.8, 11.8

Lecture 11: Friday September 29, 2006, Examples, Section 2.1

Lecture 12: Monday October 2, 2006, Limits, Section 2.2, HW4 due

Lecture 13: Wednesday October 4, 2006, Examples, Section 2.4

Lecture 13: Friday October 6, 2006, Graphing, Sections 1.2, 1.3, 1.5

MIDTERM EXAM 1: Monday October 9, 2006, HW5 due, Midterm covers HW1-5

Lecture 15: Wednesday October 11, 2006, Continuous functions, Section 2.6

Lecture 16: Friday October 13, 2006, Increasing, decreasing and concavity, Section 2.7, 4.3, 4.4

Lecture 17: Monday October 16, 2006, Critical points, asymptotes and points of inflection, Sections 2.5, 4.1 HW6 due

Lecture 18: Wednesday October 18, 2006, Rolle's theorem and the mean value theorem, Section 4.2

Lecture 19: Friday October 20, 2006, Tangents and normals, Section 2.7

Lecture 20: Monday October 23, 2006, Optimization, maxima and minima, Section 4.5, HW7 due

Lecture 21: Wednesday October 25, 2006, Related rates, Section 3.7

Lecture 22: Friday October 27, 2006, Examples

MIDTERM EXAM II: Monday October 30, 2006, HW8 due, Midterm covers HW6-8

Lecture 23:Wednesday November 1, 2006, Integrals--backwards of the derivative, Section 5.5

Lecture 24: Friday November 3, 2006, Substitution--backwards of the chain rule, Section 5.5

Lecture 25: Monday November 6, 2006, Definite integrals, Sections 5.1, 5.2, 5.3, HW9 due

Lecture 26: Wednesday November 8, 2006, The fundamental Theorem of Calculus, Section 5.4, 5.6

Lecture 27: Friday November 10, 2006, Areas, Section 5.6

Lecture 28: Monday November 13, 2006, Volumes, Sections 6.1, 6.2, HW10 due

Lecture 29: Wednesday November 15, 2006, Examples

Lecture 30: Friday November 17, 2006, Length, Section 6.3

Lecture 31: Monday November 20, 2006, Surface area, Section 6.5, HW11 due

Lecture 32: Wednesday November 22, 2006, Average values and center of mass, Sections 5.2, 6.4

THANKSGIVING: Friday November 24, 2006

MIDTERM EXAM III :Monday November 27, 2006, HW12 due, Midterm covers HW9-12

Lecture 33: Wednesday November 29, 2006, Motion

Lecture 34: Friday December 1, 2006, Applications of the exponential function, Section 7.5

Lecture 35: Monday December 4, 2006, Logarithmic differentiation, Section 7.2, No HW due

Lecture 36: Wednesday December 6, 2006, L'Hopital's rule, Section 4.6

Lecture 37: Friday December 8, 2006, Review, HW13 due

Lecture 38: Monday December 11, 2006, Review

Lecture 39: Wednesday December 13, 2006, Review

Lecture 40: Friday December 15, 2006, Review, HW14 due

Final Exam: 7:45am Wednesday December 20, 2006