Calculus II - MA112-01
Winter 2002-03 - S. Allen Broughton
Course Guide and Syllabus
Course Information
Course Goals
- Introduce students to integral calculus (including elementary first order
differential equations); see topics 1, 2 and 3 below in Topics Covered below
for specific topics.
- Introduce students to the application of the integral calculus and differential
equations in science and engineering; see topics 2 and 3 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 below in Performance Standards
below.
- Develop student ability to communicate mathematically.
Major Topics Studied
- Integration---Basic Theory and Techniques
- Integral as a sum or accumulation, approximation by Riemann sums.
- Fundamental Theorem of Calculus
- Anti-derivatives for xn, exp(x), 1/x,
sin(x), cos(x), 1/(x2+1), 1/sqrt(1-x2)
- Integration by parts
- Integration by partial fraction decomposition
- Integration by substitution
- Improper integrals
- Numerical approximation using trapezoidal and Simpson's rule
- Applications of Integration
- Area
- Mass from density
- Volumes of revolution (disk/shells)
- Arc length, surface area of revolution
- Work
- If time permits, hydrostatic pressure, line integrals/flux.
- Differential Equations
- Definition, order, linearity
- Separation of Variables for separable first order equations.
- Application to exponential growth and decay, population growth (logistic
equation), Newton's law of cooling, salt tank problems, falling bodies (with
and without air resistance.)
- Direction fields and simple qualitative analysis.
Course Policies
Grading: The course grade will be based on four in-class tests, a final
examination, assigned work, occasional quizzes, worksheets, some routine exercises
from the text, and projects.
Exams: The tentative dates for the in-class tests
are (you will have a one-week warning):
- Test 1: Thursday, Dec 19
- Test 2: Thursday, Jan 16
- Test 3: Thursday, Jan 30
- Test 4: Thursday, Feb 13
The time and place for the final examination will be announced during the quarter.
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:
Tests (100 points each) |
400 |
Final Examination |
200 |
Homework, Worksheets, Quizzes and Projects |
200 |
------------------------------------------------ |
---- |
Total |
800 |
Group Work: Some class work and all of the projects will be done
in teams.
-
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.
Attendance: You are to be in class and to be there on time. Following Rose�s
policy on attendance, after 4 unexcused absences you will lose 5% for each additional
unexcused absence.
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 basic Maple commands, by the end of MA 112 every student should
be able to:
- Use all Maple commands expected in MA 111.
- Use Maple to do arithmetic calculations.
- 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 evalf command correctly and know when this is appropriate.
- Use the solve command.
- Use the diff command.
- Use relevant vector commands from the linalg package.
- Use the int command to compute anti-derivatives.
- Use evalf with the Int command to approximate integrals numerically.
With regard to "by hands" computational skills, each student should
- Know all rules listed in the MA 111 document.
- Differentiate polynomials, exp(x), ln(x), sin(x),
and cos(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 perform elementary vector computations, e.g., addition, scalar
multiplication, and dot products.
- Know anti-derivatives for xn, exp(x), 1/x, sin(x),
cos(x), tan(x), 1/(x2+1), 1/sqrt(1-x2),
cosh(x), and sinh(x) with respect to x, and linear
combinations of these functions.
- Be able to use integration by parts, u-substitution, and partial fraction
decomposition to evaluate simple integrals.
- Be able to solve simple separable first order ODE's.
- Stability diagrams.
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.
Last Update 21 Nov 02