## Rose-Hulman - Department of Mathematics - Course Syllabus MA113 - Calculus III - 2010-11

 Description & Prerequisites Course Goals Texts and Other Materials Course Topics Course Policies Links last posted to site: 08/19/10

Parts of the web page to be completed or determined by the instructor are in green.

### Catalogue Description and Prerequisites

MA 113 Calculus III 5R-0L-5C F,W,S Pre: MA 112
Vectors and parametric equations in three dimensions. Functions of several variables, partial derivatives, maxima and minima of functions of several variables, multiple integrals, and other coordinate systems. Applications of partial derivatives and multiple integrals.

Prerequisite: All of the topics in MA112 will be assumed.

### Course Goals

1. Introduce students to multivariable differential and integral calculus, and more vector techniques, especially in three dimensions; see topics 1, 2 and 3 below in Topics Covered below for specific topics.
2. Introduce students to the application of multivariable calculus and in science and engineering; see topics 2 and 3 below in Topics Covered.
3. Develop student mathematical modeling and problem solving skills.
4. Develop student ability to use a computer algebra system (CAS) to aid in the analysis of quantitative problems.  This includes (but is certainly not limited to) mastery of the commands listed in Performance Standards below.
5. Develop student ability to communicate mathematically.
6. Introduce applications of mathematics, especially to science and engineering.

### Textbook and other required materials

Text: Thomas's Thomas' Calculus - Early Transcendentals Twelfth Edition - Weir, Hass
Supplement: Just in Time - bundled with text.
Other supplements: Normal and tangential components of accelertion problems from Angel.
Computer Usage:  Maple14 must be available on your laptop

### Course Topics

1. Vectors in Three Dimensions, Vector-valued functions
• Space coordinates and vectors in space
• Dot product and projection
• Cross products
• Lines and planes in space
• Vector-valued functions
• Differentiation/Integration of vector-valued functions
• Curvature, arc length, unit tangent and normal vectors, components of acceleration

•
2. Multivariable Differential Calculus
• Functions of several variables
• Partial derivatives
• Chain rule
• Tangent planes and normal lines
• Unconstrained extrema
• Lagrange multipliers

•
3. Multivariable Integral Calculus
• Double integrals, evaluation
• Polar coordinates, change of coordinates
• Triple integrals, evaluation
• Cylindrical and spherical coordinates, integration in these coordinate systems

•
4. Applications
• Velocity and acceleration problems, projectile motion
• Unconstrained and constrained multivariable max/min problems
• Volume, surface area
• Mass, moments, moment of inertia

### Course Requirements and Policies

The following policies and requirements will apply to all sections and classes:

#### Computer Policy

A summary of the computer policy page:

Students will be expected to demonstrate a minimal level of competency with a relevant computer algebra system. The computer algebra system will be an integral part of the course and will be used regularly in class work, in homework assignments and during quizzes/exams. Students will also be expected to demonstrate the ability to perform certain elementary computations by hand. (See Performance Standards below.)

#### Performance Standards

With regard to be "by hands" computational skills, each student should

1. Retain the skills developed in MA 111 and MA 112.
2. Be able to perform elementary vector computations, e.g., vector addition, dot products, and cross products.
3. Be able to compute elementary partial derivatives, gradients, and directional derivative.
4. Be able to evaluate simple double and triple integrals by iterated integration.
5. Know and be able to apply the equations for describing lines and planes in three-dimensional space.

These by-hands skills may be tested using in class quizzes.

With regard to basic Maple commands, by the end of MA 113 every student should be able to:

1. Items from MA111 and MA112.
2. Perform basic vector computations including dot products and cross products.
3. Extend plots to cover space curves and surfaces.
4. Extend solve and fsolve to systems of several variables.
5. Extend diff, Int and int to several variables.

#### Final Exam Policy

The following is an extract from the final exam policy page. Consult the policy page for complete details.

The final exam will consist of two parts. The first part will be "by hands" (paper, pencil). No computing devices (calculators/computers) will be allowed during the first part of the final exam. This part of the exam will cover both computational fundamentals as well as some conceptual interpretation, though the level of difficulty and depth of conceptual interpretation must take into account that this part of the exam will be shorter than the second part of the exam.  The laptop, starting with a blank Maple work sheet, and a calculator, may be used during the second part of the exam. No "cheat sheets", prepared Maple worksheets or prepared program on the calculator may be used. The second part of the exams will cover all skills: concepts, calculation, modeling, problem solving, and interpretation.