Rose-Hulman - Department of Mathematics - Course Syllabus
MA102 - Differential Calculus - 2010-11
Parts of the web page to be completed or determined by the instructor are in green.
MA101 and MA102 combined are
equivalent to MA111, except that more that usual attention is paid to review
and practice. Depending on the class the amount of MA111 material covered
will vary though it is expected that the italicized Course Goals,
Course Topics, and perfomance standards, given below, will have
been covered and that the MA102 topic to be covered will be seleced from the
non-italicized topics. The instructors for MA101 and MA102 will
collaborate on which set of topics will be covered in each course.
Catalogue Description and Prerequisites
MA 102 Differential Calculus 5R-0L-3C W Pre: MA 101
Covers approximately the second half of MA 111, including the derivative, geometrical
and physical applications of differentiation, and an introduction to integration
and Fundamental Theorem of Calculus. Students who do not transfer to MA 101
in the fall quarter, but do not satisfactorily complete all of MA 111, may
use their midterm grade in MA 111 for credit and grade in MA 101 and enter
MA 102 at the beginning of the winter quarter.
Prerequisite: It is assumed that the student has a mastery of high school algebra, pre-calculus and trigonometry concepts.
Course Goals
- Introduce students to differential calculus topics not covered in MA101
from section 1 below in Topics Covered.
- Iintroduce students to the application of differential
calculus in science and engineering not covered in MA101; see topic 2
below in Topics Covered.
- Develop student mathematical modeling and problem solving skills.
- 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.
- Develop student ability to communicate mathematically.
- Introduce applications of mathematics, especially to science and engineering.
Textbook and other required materials
Textbook: Thomas' Calculus - Early Transcendentals Twelfth Edition - Weir, Hass
Supplement: Just in Time - bundled with text.
Computer Usage: Maple14 must be available on your laptop
Course Topics
- 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.
Time permitting , cover topics from among the following
- Implicit differentiation, parametric curves.
- Approximation by secant and tangent lines, differentials
- Mean value theorem, Rolle's Theorem , Extreme Value Theorem
- 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
- Integration
- Position form 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
The following policies and requirements will apply to all sections:
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
- 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.
- Be able to apply the product, quotient and chain rules for simple, routine differentiation problems.
- Be able to perform implicit differentiation.
- 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), (sec(x))^2, 1/sqrt(1-x^2), 1/(1+x^2) .
These by-hands skills may be tested using in class quizzes.
With regard to basic Maple commands, by the end of
MA 102 every student should be able to
- Use Maple to do arithmetic calculations and function evaluations.
- Use the evalf command correctly and know when this is appropriate.
- Use the expand, simplify, and subs commands
to manipulate algebraic expressions.
- Use the plot command to plot single or multiple functions and parametric
curves, with appropriate scaling.
- Use the solve and fsolve commands.
- 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
Your instructor will determine the following for your class:
- 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*.
*Note that most instructors will enforce some type of grade penalty for students with more than four unexcused absences.
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