## Rose-Hulman - Department of Mathematics - Course Syllabus MA FTC - Fast Track Calculus - 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 FTC Fast-Track Calculus 15L-0R-15C

A 5-week fast paced course equivalent to Calculus I, II and III.  Taught in the summer only to incoming freshmen. Review of differential calculus.  Introduction to integration and the Fundamental Theorem of Calculus.  Techniques of integration, numerical integration, applications of integration. L’Hopital’s rule (and improper integrals). Separable first order differential equations, applications of separable first order differential equation. Series of constants, power series, Taylor polynomials, Taylor and McLaurin series.  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: At least one year of high school Calculus, at least a 700 Math Score on the SAT (or equivalent), and approval by the Fast Track Selection Committee.

### Course Goals

1. Review with students differential calculus (including anti-derivatives) and vectors.
2. Review with students the application of differential calculus and vectors in science and engineering.
3. Introduce students to integral calculus (including elementary first order differential equations).
4. Introduce students to the application of the integral calculus and differential equations in science and engineering.
5. Introduce students to series of constants and functions, and the notions of approximation and convergence.
6. Introduce students to multivariable differential and integral calculus, and more vector techniques, especially in three dimensions
7. Introduce students to the application of multivariable calculus and in science and engineering.
8. Develop student mathematical modeling and problem solving skills.
9. 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 below in Performance Standards below.
10. Develop student ability to communicate mathematically.

### Textbook and other required materials

Textbook:
Computer Usage:  Maple13   must be available on your laptop

### Course Topics

Course topics can be found here MAFTCTopics.pdf.

### 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. Be able to perform elementary vector computations, e.g., vector addition, dot products, and cross products.
2. Be able to compute the derivative of a function using chain rule, product rule, and quotient rule.
3. Be able to compute elementary partial derivatives, gradients, and directional derivative.
4. Be able to evaluate simple single, 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 Fast Track Calculus every student should be able to:

1. Use Maple to do arithmetic calculations and function .evaluations
2. Use the evalf command correctly and know when this is appropriate.
3. Use the expand, simplify, and subs commands to manipulate algebraic expressions.
4. Use the plot command to plot single or multiple functions and parametric curves, with appropriate scaling.
5. Use the solve and fsolve commands.
6. Use the diff command for computing derivatives.
7. Use the int command to compute anti-derivatives and definite integrals.
8. Use evalf with the Int command to approximate integrals numerically.
9. Perform basic vector computations including dot products and cross products.
10. Extend plots to cover space curves and surfaces.
11. Extend solve and fsolve to systems of several variables.
12. Extend diff, Int and int to differentiation and integration of functions of several variables.