Rose-Hulman - Department of Mathematics - Course Syllabus
MA111 - Calculus I - 2010-11

Catalogue Description and Prerequisites

MA 111 Calculus I 5R-0L-5C F Calculus and analytic geometry in the plane. Algebraic and transcendental functions. Limits and continuity. Differentiation, geometric and physical interpretations of the derivative, Newton's method. Introduction to integration and the Fundamental Theorem of Calculus.

Prerequisite: It is assumed that the student has a mastery of high school algebra, pre-calculus and trigonometry concepts.

Course Goals

1. Introduce students to differential calculus and beginning integration, including anti-derivatives and the Fundamental Theorem of Calculus; see topics 1, 2, 3, and 5 below in Topics Covered below for specific topics.
2. Introduce students to the application of differential calculus and beginning integration in science and engineering; see topics 4 and 5 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

Course Topics

1. Functions and Pre-Calculus review
• Graph of a function y=f(x), domain/range.
• Properties of functions and graphs, e.g., increasing/decreasing intervals, local max/min.
• Definition and properties of polynomial, trigonometric, exponential and logarithmic functions, and relevant inverse functions.
• Parametric equations: physical interpretation as motion of a body
  
  
2. Limits and Continuity
   • Limits.
   • Continuity
   • Intermediate value theorem


3. Differentiation
• Average rate of change.
• Instantaneous rate of change and definition of the derivative.
• Formulas for elementary derivatives (polynomials, powers of x, sin(x), cos(x), tan(x), sec(x) , exp(x), ln(x), arcsin(x), arctan(x)
• Linearity, product, quotient, and chain rules.
• Implicit differentiation, parametric curves.
• Approximation by secant and tangent lines, differentials
• Mean value theorem, Rolle's Theorem , Extreme Value Theorem
   
4. Applications of Derivatives
• limits at infinity
• Graphical/physical interpretation of first and second derivatives
• Derivatives as velocity and acceleration, motion problems (including motion described by parametric equations.)
• Optimization problems.
• Related-rate problems.
• Newton's method
  
  
5. Integration
   • Position from velocity, area under a curve
   • Riemann sums
   • Fundamental Theorem, anti-derivatives and properties, specifically linearity, polynomials, powers of x, 1/x, sin(x), cos(x), (sec(x))^2, exp(x), 1/sqrt(1-x^2), 1/(1+x^2).

Course Requirements and Policies

Computer Usage

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/Final Exam Policy

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

1. Differentiate polynomials, exp(x), ln(x), sin(x), cos(x), tan(x), sec(x), arcsin(x), and arctan(x) with respect to x, and linear combinations of these functions.
2. Be able to apply the product, quotient and chain rules for simple, routine differentiation problems.
3. Be able to perform implicit differentiation.
4. Be able to compute simple anti-derivatives and definite integrals applying linearity and involving polynomials, powers of x, 1/x, exp(x), sin(x), cos(x), sec²(x) 1/sqrt(1-x²), 1/(1+x²) .

These by-hands skills may be tested using in class quizzes. In particular, a Precalculus Gateway exam must be passed for successful completion of the course.

With regard to basic Maple commands, by the end of MA 111 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 and int commands.

Final Exam Policies

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.

Individual Instructor Policies

• the grading scheme, based on the various course components.
• the number and format of hour exams, quizzes, homework assignments, in class assignments, and projects,
• the policies governing the work items above, e.g.,
• all policies for classroom procedure, including group work, class participation, laptop use and attendance*.

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