Catalog: 2013–2014 Catalog Year

# MATH 283: Calculus III

### General Information

• Name: Calculus III
• Discipline: Mathematics (MATH)
• Units (Credits): 4
• Schedule History: See when this course was offered over the last three years.
• Transfer Information: Courses with numbers 100 to 299: This course is designed to apply toward a WNC degree and/or transfer to other schools within the Nevada System of Higher Education, depending on the degree chosen and other courses completed. It may transfer to colleges and universities outside Nevada. For information about how this course can transfer and apply to your program of study, please contact a counselor.

### Prerequisites and Recommended Courses

• Prerequisites: MATH 182 or equivalent or consent of instructor

### Course Outline

#### I: Catalog Course Description

Covers infinite series, vectors, differential and integral calculus of functions of several variables, and introduction to vector analysis.

#### II: Course Objectives

Continuation of MATH 182; Covers infinite series, vectors, differential and integral calculus of several variables, introduction to vector analysis.

Upon completion of this course, the student should be able to do the following:

• Compute the dot and cross product of two vectors.
• Find the equations of lines and planes in space.
• Convert from rectangular to cylindrical to spherical coordinates.
• Differentiate and integrate vector-valued functions.
• Determine the acceleration, velocity and position functions of an object.
• Find unit tangent and normal vectors.
• Calculate arc length of a space curve and curvature.
• Find partial derivatives, total differentials, directional derivatives, gradients, tangent planes, normal lines, and extrema of functions, using the second derivative test and Lagrange multipliers.
• Apply the chain rule to functions of several variables.
• Use double integrals to find volume, center of mass, surface area.
• Evaluate triple integrals in rectangular, cylindrical and spherical coordinates with applications.
• Evaluate line integrals in rectangular, cylindrical and spherical coordinates, with applications.
• Evaluate line integrals, with and without Green's theorem, and with Stokes's theorem.

Linkage of course to educational program mission and at least one educational program outcome.

General Education Mission: This course addresses the fourth bullet under goal one of the college's mission to, "Provide instruction that contributes to a student's abilities to think critically and solve problems; to reason mathematically and apply computational skills."

Math 283 satisfies the General Education Requirement for any degree or certificate program and addresses the following learning objectives of the General Education Requirement by ensuring that successful students:

• Are able to apply appropriate college-level mathematical skills to real life applications
• Have developed adequate problem solving, creative reasoning, and critical thinking skills.

Educational Objectives for A.A. and A.S. Degrees: Math 283 addresses the following learning objectives of the A.A. and A.S. degree programs by ensuring that successful students:

• Will know the subject matter to a level that is appropriate to the emphasis of the degree program.
• Can succeed at their transfer institutions.

Educational Objectives for A.G.S. Degree: Math 283 addresses the following learning objectives of the A.G.S. degree by ensuring that successful students:

• Will know the subject matter to a level that is appropriate for their desired fields of study.