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MAT 308



I. TITLE:  Calculus and Analytic Geometry II

II. CATALOG DESCRIPTION: A continuation of MAT 250.

III. PURPOSE:
The purpose of this course is to promote students’ continued mathematical and intellectual development.  More specifically, participation in small group projects, and class discussions will develop students’ ability to think independently and communicate effectively with their peers.  Moreover, these activities will develop students’ problem-solving and mathematical reasoning skills and help them learn to construct logical arguments which proceed from hypothesis to conclusion.  Finally, computer related activities will provide students insight into the uses of technology as a problem solving tool.  Students will use the computer to search for patterns, experiment, and attack open-ended problems.

IV. COURSE OBJECTIVES:
Students will be introduced to the concept of studying mathematics problems from different points of view: numerically, graphically, and symbolically.  Students will also be introduced to open-ended problems and will learn how to make onjectures based on partial solutions to such problems.
  Students will study integration techniques and their applications to various disciplines, including science, industry and technology, and business.
  Students will study approximation techniques in the context of a broader concept: a difficult problem can be approached by studying a sequence of related, simpler problems.
  Students will develop a level of mathematical maturity and a core of mathematical knowledge necessary to succeed in upper level mathematics, science, and engineering courses.
  Students will develop their critical thinking or problem solving skills; that is, the ability to analyze problems, determine what solution techniques are appropriate, determine what information in needed, what information is given, and what information is extraneous.  Also, students will learn to interpret solutions to problems in the context of a real-world setting.

V. CONTENT OUTLINE:
Finding Antiderivatives

a)  Substitution techniques
b)  Use of a computer algebra system
Numerical Integration
a)  Left and right rectangular sums, error and first derivatives
b)  Trapezoid and midpoint sums, error and second derivatives
c)  Simpson's rule
Applications of the Definite Integral
a)  Volume and arclength
b)  Work and other applications from physics
c)  Present value and other applications from economics
d)  Fourier polynomials
Antidifferentiation Techniques
a)  Integration by parts
b)  Miscellaneous techniques
Improper Integrals
a)  Convergence
b)  Applications to probability
c)  l'Hopital's rule, comparing growth rates
Infinite Series
a)  Sequences and limits
b)  Convergence and divergence of series
c)  Power series
d)  Power series as functions
VI. INSTRUCTIONAL ACTIVITIES:
Each day students should come to class having already read that day’s topic in the text and having attempted to solve previously assigned problems.  The instructor will summarize and supplement the assigned reading, and outline subsequent material, but will not “lecture” in a traditional sense.  Some days the class will discuss an example or a problem from the book.  Other days the class will work in small groups on some particular problem or problems.  The class will meet regularly in the computer lab; students will use computers frequently both during and outside of class.  Emphasis will be placed on using the computer to experiment and answer “what if ...” questions.  Through computer lab “write-ups” and project reports, attention will be given to the development of students' writing skills.
  Group work (lab “write-ups” and project reports) will be graded by the instructor and evaluated on the basis of mathematical accuracy (75 to 85%) and clarity of exposition and grammatical correctness (15 to 25%).

VII. FIELD AND CLINICAL EXPERIENCES:  none

VIII. RESOURCES:
Students will need a scientific or graphing calculator.  Students will use the Mathematics Department computer laboratory.

IX. GRADING PROCEDURES:
There will be three 100 point exams and a 100 point comprehensive final.  These exams will have an in-class component and a take-home component.  Exam material will be derived from material covered in class discussions, topics discussed in lectures, and topics assigned for reading.  Also, computer lab assignments will be given regularly throughout the semester.  These lab assignments collectively will count as one test.  Critical thinking (problem solving skills) and writing will be evaluated on each exam and computer lab assignment. Grading will be based on the usual 90 - 80 - 70 - 60 scale.  In determining your course grade, exams will count as 60% of your grade, computer labs as 20%,  and the final exam as 20%.  This distribution of points will yield the following (approximate) weights based on instructional activities:  class discussions - 40%, reading - 30%, group work - 20%, and lectures - 10%.

X. ATTENDANCE POLICY:
Attendance will be taken daily.  If you miss no more that two classes during the semester, two percentage points will be added to your final class average.  If you miss seven or more classes during the semester and don't discuss the situation with your instructor, your final grade may be reduced by one letter.

XI. ACADEMIC HONESTY POLICY:
Any instance of academic dishonesty, as determined by the instructor (in compliance with Board of Regents policy on  Academic Integrity - Feb. 1975) will result in zero points for the assignment and possibly a grade of “E” for the course.

XII. TEXT AND REFERENCES:  Current

XIII. PREREQUISITES:  MAT 250

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Last updated February 14, 2000. Designed and maintained by Kyosung Koo