Calculus I - MA111-01 & MA111-11

Fall 2003-04 - S. Allen Broughton

Course Guide and Syllabus

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Course Information

• Instructor:
• Professor S. Allen Broughton,
• Office: G205-A,
• Phone x8179
• Email: allen.broughton@rose-hulman.edu
• Schedule
• Time & Place: MA111-01 Period 4 MTWRF in G221, MA111-11 Period 3 MTWRF in G221
• Office hours: 5'th hour or by appointment (may be changed after first class meeting)
• Class Webpage: http://www.rose-hulman.edu/class/ma/broughton/courses/ma111/
• Text: Larson, Hostetler and Edwards- 3'rd edition

Course Goals

1. Introduce students to differential calculus (including anti-derivatives) and vectors; see topics 1, 2, and 3 below in Topics Covered below for specific topics.
2. Introduce students to the application of differential calculus and vectors in science and engineering; see topic 4 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 below in Performance Standards below.
5. Develop student ability to communicate mathematically.
   

Major Topics Studied

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/logarithmic functions, and relevant inverse functions.
   • Parametric equations: physical interpretation as motion of a body
     
2. Vectors
   • Definition of vectors, analytical and graphical interpretation of elementary operations (addition, scalar multiplication).
   • Distance formula and magnitude/direction of vectors.
   • Dot product and angle between vectors.
   • Vector projection.
     
3. Limits and Continuity
   • Limits.
   • Continuity
   • Intermediate value theorem
     
4. Differentiation
• Average rate of change.
• Instantaneous rate of change and definition of the derivative.
• Formulas for elementary derivatives (linearity, powers of x, sin(x), cos(x), exp(x), ln(x), arcsin(x), arctan(x), cosh(x), sinh(x).)
• 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
   
5. Curve sketching and Applications
• 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
  
6. Integration
   • Position form velocity, area under a curve
   • Riemann sums
   • Fundamental Theorem, anti-derivative

Course Policies

Exams: The tentative dates for the in-class tests are (you will have a one-week warning):

• Test 1: Wednesday, September 24
• Test 2: Wednesday, October 8
• Test 3: Wednesday, October 22
• Test 4: Wednesday, November 5

Projects: Some challenge problems and projects, to develop your ability in application, modeling and problem solving with the material in the course, will be given. These problems will be done as group work. Project rules will be given out with the first project. There are  1-2 projects of about one week's duration.

Final Grades: Various components of the course will contribute to the course point total as follows:
 

• Be aware of the Rose-Hulman Honor Code and that honesty and integrity in one's work is of the utmost importance. Inappropriate sharing of work and information, including electronic sharing, will not be tolerated

• Note, however that you are encouraged to collaborate with others on homework, and in class you may be directed to work in groups. If you are in doubt about what is or is not appropriate just ask me. If you consult others in your submitted work you must acknowledge their contributions in writing on the assignments. You will not be penalized for honest collaboration, but don't just copy.

Computer Policy: 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 "by hands" computational skills, each student should be able to

1. Differentiate polynomials, exp(x), ln(x), sin(x), and cos(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 perform elementary vector computations, e.g., addition, scalar multiplication, and dot products.

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

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 evalautions.
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 command.
6. Use the diff and int command.
7. Use relevant vector commands,.

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

Final Exam Policy: The final exam will consist of two parts. The first part will "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, interpretation.