TEXT: J. Stewart, Calculus, Early Transcendentals, 7th Ed., Ch.12-16, hardcopy or electronic.
Strang et al, Calculus III, Strang, Calculus, Auroux, Multivariable Calculus, Khan, Multivariable Calculus.

COURSE DESCRIPTION:

Many properties of systems studied in applied science are functions of several variables or vector valued functions. This course develops the calculus of such functions. Topics include: vectors and vector valued functions, analytic geometry in space, functions of several variables, partial differentiation, the gradient, maxima and minima, Lagrange multipliers, and multiple integrals, line and surface integrals, Stokes and Divergence theorems.

PREREQUISITES: Calculus II (MAT152 or equivalent).

COURSE OBJECTIVES: The major objective of this course is to introduce multivariate calculus and to illustrate its power with applications.

LEARNING OUTCOMES:
At the end of the semester, students will:

• be fluent with vectors,
• be fluent with vector valued functions and be able to apply them to velocity, acceleration, arclength and curvature,
• be fluent with functions of several variables and be able to calculate directional derivatives, gradients and extrema,
• be able to calculate multiple integrals and apply them to volumes,
• be fluent with vector calculus and be able to calculate curl and divergence and line and surface integrals,
• understand the generalizations of the Fundamental Theorem of Calculus, including the Divergence and Curl Theorems,
• be able to apply multivariate calculus to particles moving along curved trajectories, to temperature distribution around a heat source, to electrostatic potential of a system of charges and to waves traveling through space.

TOPICS:

1. Vectors
   • Dot Product and Cross Product
   • Analytic Geometry in Space - Lines and Planes
   • Cylindrical and Spherical Coordinates
2. Vector Valued Functions
   • Velocity and Acceleration
   • Tangent Vectors and Normal Vectors
   • Arc Length and Curvature
3. Functions of Several Variables
   • Partial Derivatives and Differentials
   • Directional Derivatives, Gradients and Extrema
4. Multiple Integration
   • Double Integrals and Volume
   • Triple integrals and Applications
5. Vector Calculus
   • Vector Fields and Line Integrals
   • Curl and Divergence
   • Surface Integrals
   • Generalizations of Fundamental Theorem of Calculus: Divergence and Curl Theorems
6. Applications to Partial Differential Equations (Time Permitting)

OFFICE HOURS:

T   4-5 PM, DON2275

R   4-5 PM, Learning Center

GRADES:

Portfolio Test (Sept. 19) Test (Oct. 17) Test (Nov. 15) Project (Nov. 29) Final (cumulative)

10 points 20 points 20 points 20 points 20 points 30 points

A+ >= 97 pts A = 93,...,96 pts A- = 90,...,92 pts etc.

The lowest test score will be dropped.

Accommodations for Students with Disabilities

In compliance with the Americans with Disabilities Act of 1990 and Section 504 of the Rehabilitation Act, SUNY Polytechnic Institute is committed to ensuring educational access and accommodations for all registered students seeking access to meet course requirements and fully participate in programs and activities. Students with documented disabilities or medical conditions are encouraged to request these services by registering with the Office of Disability Services. For information related to these services or to schedule an appointment, please contact the Office of Disability Services using the information provided below.

Evelyn Lester, Director
Office of Disability Services
lestere@sunyit.edu
(315) 792-7170
Kunsela Hall, B101