# MAT 211 Calculus III

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### Course Description

Multivariable calculus: analytic geometry, scalar and vector products, partial differentiation, multiple integration, change of coordinates, gradient, optimization, line integrals, Green's theorem, elements of vector calculus.

MAT 211 meets for five hours of lecture per week.

### Prerequisites

MAT 193 or equivalent with a grade of "C" or better.

### Objectives

After completing MAT 211 the student should be able to

• Gain an intuitive understanding of functions of several variables via level curves and surfaces, and related concepts of limit, continuity and differentiability.
• Perform partial differentiation and multiple integration of functions of several variables.
• Change from Cartesian co-ordinates to polar, cylindrical or spherical co-ordinates and vice versa, perform differential (partial or ordinary) and integration (multiple or single) in curvilinear co-ordinate systems and effect transformation via the Jacobian..
• Utilize vectors to deal with spatial curves and surfaces, and calculus of several variables
• Understand and use the concepts of vector calculus: gradient, curl, divergence, line and surface integrals, Green's, Stokes' and the divergence theorem.
• Apply calculus of several variables to solve problems of optimization, differential geometry and physics

### Expected outcomes

Students should be able to demonstrate through written assignments, tests, and/or oral presentations, that they have achieved the objectives of MAT 211.

### Method of Evaluating Outcomes

Evaluations are based on homework, class participation, short tests and scheduled examinations covering students' understanding of topics covered in MAT 211.

### Text

• Essential Calculus, by James Stewart. Brooks/Cole 2007. Covers MAT 191, MAT 193, and MAT 211.

#### Course Outline

MAT 211 covers the following material from chapters 10-13 in the text.

10. VECTORS AND THE GEOMETRY OF SPACE

• Three-Dimensional Coordinate Systems
• Vectors
• The Dot Product
• The Cross Product
• Equations of Lines and Planes
• Vector Functions and Space Curves
• Arc Length and Curvature
• Motion in Space: Velocity and Acceleration

11. PARTIAL DERIVATIVES

• Functions of Several Variables
• Limits and Continuity
• Partial Derivatives
• Tangent Planes and Linear Approximations
• The Chain Rule
• Directional Derivatives and the Gradient Vector
• Maximum and Minimum Values
• Lagrange Multipliers

12. MULTIPLE INTEGRALS

• Double Integrals over Rectangles
• Double Integrals over General Regions
• Double Integrals in Polar Coordinates
• Applications of Double Integrals
• Triple Integrals
• Triple Integrals in Cylindrical Coordinates
• Triple Integrals in Spherical Coordinates
• Change of Variables in Multiple Integrals

13. VECTOR CALCULUS

• Vector Fields
• Line Integrals
• The Fundamental Theorem for Line Integrals
• Green's Theorem
• Curl and Divergence
• Parametric Surfaces and Their Areas
• Surface Integrals
• Stokes' Theorem
• The Divergence Theorem

Students' grades are based on homework, class participation, short tests, and scheduled examinations covering students' understanding of the topics covered in MAT 211. The instructor determines the relative weights of these factors.

### Attendance Requirements

Attendance policy is set by the instructor.

### Policy on Due Dates and Make-Up Work

Due dates and policy regarding make-up work are set by the instructor.

### Schedule of Examinations

The instructor sets all test dates except the date of the final exam. The final exam is given at the date and time announced in the Schedule of Classes.