## Mathematics 213

### Calculus III

Length of Course: 14 weeks

Classroom Hours per Week: 4 hours of lecture and 1 hour of tutorial

Number of Credits: 3

Prerequisite: Mathematics 114 and 12 credits.

### Course Description

An introduction to calculus of several variables, treating limits and continuity, partial derivatives, extrema, the chain rule, double, triple and path integrals.

### Course Outline

Length Description

Week 1

Parametric Equations; Tangent Lines and Arc Length for Parametric Curves, Polar Coordinates, Tangent Lines, Arc Length, Area for Polar Curves

Week 2

Conic Sections, Rotation of Axes, Conic Sections in Polar Coordinates

Week 3

Rectangular Coordinates in 3-Space, Spheres, Cylindrical Surfaces

Vectors, Dot Product, Projections

Week 4

Cross Product, Parametric Equations of Lines, Planes in 3-Space

Week 5

Quadric Surfaces, Cylindrical and Spherical Coordinates

Week 6

Functions of Two or More Variables

Limits and Continuity

Partial Derivatives

Week 7

Differentiability, Differentials, Local Linearity

The Chain Rule

Week 8

Tangent Plane and Normal Vector

Maxima and Minima of Functions of Two Variables

Lagrange Multipliers

Week 9

Double Integral

Double Integrals over Nonrectangular Regions

Double Integrals in Polar Coordinates

Week 10

Surface Area: Parametric Surfaces

Triple Integrals

Triple Integrals in Cylindrical and Spherical Coordinates

Week 11

Change of Variables in Multiple Integrals; Jacobians

Vector Valued Functions

Week 12

Vector Fields, Line Integrals, Green’s Theorem

Week 13

Review

Week 14

Final Exam

### Textbook

Calculus: Early Transcendentals, 10th edition by Anton, Bivens, and Davis

### Course Evaluation

10-20% Quizzes and Homework Midterm Exam(s) Final Exam

Arman Ahmadieh B.Sc., M.Sc. (Sharif University of Technology)
Hayri Ardal, B.Sc.(Bogazici), Ph.D.(Simon Fraser)
Kim Peu Chew, B.Sc. (Nanjing), M.A., Ph.D. (British Columbia)