# AUBG, Math & Sci Dept, Fall 2009

Syllabus

**AUBG, Math & Sci Dept, Fall 2009 **

**MAT 212: Calculus III (or Multivariate Calculus)**

required for Math Major & Minor;

prerequisites: Calculus I (MAT 103) and Linear Algebra (MAT 105) or equivalent; of Calculus II (MAT 104) we will need the sections on exp/log functions, techniques of integration

### Alexander GANCHEV

, ,

office 304 (new bulding), phone: 480, office hours: Tue & Wed 9:30-10:30

Time and venue: TF 16:00-17:15, room 002 NAB

**Course description: **The course is an introduction to multivariate calculus. The course extends techniques of calculus in one variable to two and three dimensions. (Vectors, and Geometry of Space. Quadratic surfaces, Space curves, Cylindrical and Spherical Coordinates. Partial derivatives, and extreme value problems for functions of several variables – Lagrange multipliers. Double and triple integrals. Iterated integrals and applications. )

**Course objectives** (Student Learning Outcomes):

At the end of the course the student should be able:

- To work with vector functions and apply partial derivatives to identify some geometrical characteristics of curves and surfaces
- To use partial derivatives to minimum/maximum problems with and without constraints
- To evaluate multiple integrals
- To use multiple integrals to evaluate volumes of solids, surface areas and lengths of curves

The above is a list of technical math skills we want to develop but what is more important

we want to learn to think creatively, be able to attack a problem you have not seen before, develop tools for that, develop a mathematical model for a given “real life” situation.

Prerequisites: The main prerequisite for this course is Calculus 1 (MAT 103). Calculus is about approximating complicated function with linear functions, hence another prerequisite for Calculus is the geometry and algebra of things linear, i.e., Linear Algebra.

Textbook:J. Stewart, Calculus, 5th (or 3rd) edition,

(Brooks/Cole Publishing Company, Pacific Grove, 2003)

Assessment: Your grade will be formed by

short quizzes, oral exams, projects 100 points

midterm 80

final exam 120

______

total 300

The duration of a short quiz will be from 5 to 10 min and may consist of up to 10 problems. The duration of the midterm exam will be a full class period and may consist 6 or more problems (some will be routine but do expect also several nontrivial problems). The final will be comprehensive, i.e., over all the material covered by the course. Every class sessions I will ask for volunteers to do problems on the board (if there are no volunteers then I will just call some name from the class list) which could count to the oral exam credit and at the last weeks of class we will have oral exams sessions.

**Points/Grade Map:**

D-> 135, D > 150, D+ > 165, C- > 180, C > 195, C+ > 210,

B- > 225, B > 240, B+ > 255, A- > 270, A > 285

Exam policies: During quizzes, exams and the final all that you will need and will be allowed to use is a pen/pencil and a notebook that I will give you (no textbooks, notes, calculators, mobile telephones or other electronic gadgets, sheets of paper etc., no sheets of paper flying around the room, etc.). I will assign seats before the exam, i.e., before the exam you may help me pull the tables apart and wait to be assigned a seat. You should work strictly by yourself – you should not communicate in any way with your classmates – violation of this will be considered cheating with all the ensuing consequences (see the AUBG documentation for the consequences of cheating). Cheating is not only talking to the person next to you (talking about anything: math, the problems, the weather, last nights party …) but also intentionally making your work available to others during the exam.

Attendance: Students are expected to attend classes regularly and should comply with the university attendance policies. I expect you to come to class prepared (having read the assigned text if there is such) and to show active participation during the lecture.

Assignments: Often I will assign sections from the textbook for you to read ahead and from time to time I will make reading quizzes to check if you have read the assigned part. I will also expect that on the average you spend about 6 hours per week (on top of the regular calculus classes) working on problems from the book (I repeat – this is on the average – because the need for this extra work is very individual). The best thing about the textbook is the huge number of exercises. In the chapters that wewill cover there are about 2000 exercises. I will give a list of some of these as optional homework, i.e., I will not collect these optional homeworks but you are strongly encouraged to do as many as you can.

Office hours: If the “official” office hours are not convenient for you please contact me to arrange some other time. Don’t be afraid to come and ask. There are no stupid questions.

Disclaimer: This syllabus is subject to modification. The instructor will communicate with students on any changes. The distribution of weeks per chapter is only approximate.

**Expanded Description: **(sections from the textbook we will cover)

**1. Vectors & Geometry of Space **(Chapter 13 – weeks 1-2)

3D Coordinate Systems; Vector and Affine Space (scalar product, norm, vector product;

Lines, planes and quadrics) ; vector fields; Cylindrical and spherical coordinates

**2. Vector Functions **(Chapter 14 – weeks 3-4)

Vector functions and space curves; vector fields; Derivatives and Integrals of Vector

Functions; Arc length and curvature

**3. Partial Derivatives **(Chapter 15 – weeks 5-8 -- midterm)

Functions of Several Variables; Limits and Continuity; Partial Derivatives;

Tangent Planes and Differential; The Chain Rule; Directional Derivatives and the

Gradient Vector; Maximum and Minimum Values – Lagrange Multipliers

**4. Multiple Integrals **(Chapter 16 – weeks 9-14)

Double Integrals over Rectangles; Iterated Integrals; Double Integrals over General

Regions; Double Integrals in Polar Coordinates; Applications of Double Integrals;

Surface Area; Triple Integrals; Triple Integrals in Cylindrical and Spherical Coordinates;

Change of Variables in Multiple Integrals