Calculus III Sections 8 and 9, Fall 2007

The Universe is a grand book which cannot be read until
one first learns to comprehend the language
and become familiar with the characters in which it is composed.
It is written in the language of mathematics.
Galileo Galilei (1564 - 1642) Opere Il Saggiatore p. 171.

Calculus III:

Math 1201 Section 8 (TuTh 1:10pm - 2:25pm)
Math 1201 Section 9 (TuTh 4:10pm - 5:25pm)

Basic course info:

Instructor Prof. Jason Behrstock
627 Mathematics
Email: jason@math.columbia.edu
Website: www.math.columbia.edu/~jason
Office Hours: Tu 2:30-3:30 in 627 Mathematics
Th 2:30-3:30 in 627 Mathematics

Text We will cover Chapters 12, 13, and 14 of:
J. Stewart, Calculus (Early Transcendentals), sixth Edition

Schedule Detailed course schedule and all homework assignments will be posted at:
http://math.columbia.edu/~jason/calc3_07f/calc3hw.html

Calculator You do not need a calculator for this course.
Calculators are not allowed on the tests.

Grade 20% Homework
20% Each of the two midterms
40% Final exam

Teaching Assistants Ivana Medos (Sections 8 and 9)
Email: ivana@math.columbia.edu
Office Hours: TBA.

Shuvojit Ghosh (Section 8)
Email: sg2252@columbia.edu
Office Hours: TBA.

Mikhail Shklyar (Section 9)
Email: ms2756@columbia.edu
Office Hours: Mondays 4-6pm in Barnard help room (Milbank 333).

Overview In the first half of this course we develop a language for describing geometry in two and three dimensions. For example, there are special ways of "multiplying" points in the plane (the product of complex numbers) and points in space (the cross product of vectors), both of which have geometric as well as algebraic significance.

The second half of the course is about differential calculus applied to curves and surfaces in space. The lines and planes studied in the first part here appear as first order approximations, i.e., derivatives. Conics (ellipses and hyperbolas) appear as second order approximations, allowing us to distinguish maxima, minima, and saddle points.

This subject has many application, to name a few: In physics and engineering, complex numbers are used to describe waves, notably the wave functions of quantum mechanics; vector algebra is used to describe (among many other things) electric and magnetic fields. Space curves describe the trajectories of objects moving in those fields. In economics, it is often useful to be able to maximise functions, especially when there are additional constraints.

Goals

make calculations with agility, accuracy, intelligence and flexibility;

explain the basic concepts of calculus clearly and reason logically with them;

solve extended problems, with good judgment in the choice of tools and in checking answers.

Expectations

read each section of the textbook before the material is presented in class;

attend the lectures;

complete all homework assignments;

discuss mathematics with other students.

Help
There are several venues available if you have any questions in this course.

Office hours:See the information above.

TA Office Hours:See the information above.

Mathematics Help Room at Barnard (Check the availablity online.) (333 Milbank Hall, Barnard Campus).

Make appointment: You can meet me after class to arrange an appointment, or send me an email.

Instructor	Prof. Jason Behrstock 627 Mathematics Email: jason@math.columbia.edu Website: www.math.columbia.edu/~jason Office Hours: Tu 2:30-3:30 in 627 Mathematics Th 2:30-3:30 in 627 Mathematics
Text	We will cover Chapters 12, 13, and 14 of: J. Stewart, Calculus (Early Transcendentals), sixth Edition
Schedule	Detailed course schedule and all homework assignments will be posted at: http://math.columbia.edu/~jason/calc3_07f/calc3hw.html
Calculator	You do not need a calculator for this course. Calculators are not allowed on the tests.
Grade	20% Homework 20% Each of the two midterms 40% Final exam
Teaching Assistants	Ivana Medos (Sections 8 and 9) Email: ivana@math.columbia.edu Office Hours: TBA. Shuvojit Ghosh (Section 8) Email: sg2252@columbia.edu Office Hours: TBA. Mikhail Shklyar (Section 9) Email: ms2756@columbia.edu Office Hours: Mondays 4-6pm in Barnard help room (Milbank 333).
Overview	In the first half of this course we develop a language for describing geometry in two and three dimensions. For example, there are special ways of "multiplying" points in the plane (the product of complex numbers) and points in space (the cross product of vectors), both of which have geometric as well as algebraic significance. The second half of the course is about differential calculus applied to curves and surfaces in space. The lines and planes studied in the first part here appear as first order approximations, i.e., derivatives. Conics (ellipses and hyperbolas) appear as second order approximations, allowing us to distinguish maxima, minima, and saddle points. This subject has many application, to name a few: In physics and engineering, complex numbers are used to describe waves, notably the wave functions of quantum mechanics; vector algebra is used to describe (among many other things) electric and magnetic fields. Space curves describe the trajectories of objects moving in those fields. In economics, it is often useful to be able to maximise functions, especially when there are additional constraints.
Goals	make calculations with agility, accuracy, intelligence and flexibility; explain the basic concepts of calculus clearly and reason logically with them; solve extended problems, with good judgment in the choice of tools and in checking answers.
Expectations	read each section of the textbook before the material is presented in class; attend the lectures; complete all homework assignments; discuss mathematics with other students.
Help	There are several venues available if you have any questions in this course. Office hours:See the information above. TA Office Hours:See the information above. Mathematics Help Room at Barnard (Check the availablity online.) (333 Milbank Hall, Barnard Campus). Make appointment: You can meet me after class to arrange an appointment, or send me an email.