Department of Mathematics Generic Syllabus
Boise State University Updated August 15, 2006
MATH 175
Calculus II
4 semester credits
Catalog Description
MATH 175 CALCULUS II (4-0-4)(Area III)
A continuation of MATH 170. Applications of the integral, symbolic and
numerical techniques of integration. Sequences and series, with an emphasis
on power series and approximations, convergence and error bounds. Separable
differential equations. Parametric equations in the plane and polar
coordinates. Includes use of mathematical software such as Maple of
Mathematica. PREREQ: MATH 170
Prerequisites
MATH 175 is the second term in our 3-term calculus sequence. Students
should complete MATH 170, the first term,
before enrolling in the second.
A few students who have taken a year of calculus in high school begin
their BSU calculus experience with this course. If they find they are
in over their heads, they can then drop back to MATH 170.
Jurisdiction
This course is controlled by a departmental committee, whose members
may or may not be teaching the course. All sections use the same
text, which is chosen by the committee. The committee also writes a
syllabus detailing which sections should be covered and how much time
should be allotted to each.
Learning Objectives
Upon completion of this course, students should:
- Be adept at finding antiderivatives in the easy cases.
- Be able to use tables to find antiderivatives for more difficult
cases.
- Set up as definite integrals those common application problems
involving volumes of rotation, arc length, surface area, work.
- Have an intuitive understanding of the definitions of limit of a
sequence and sum of an infinite series.
- Be able to find intervals of convergence of power series using
ratio, root, comparison, and integral tests.
- Have an understanding of separable differential equations.
- Have an understanding of polar coordinates and the calculus of
functions described in those coordinates.
1 Assessment of Learning Objectives
Students will be assessed by evaluating their ability to do problems
based on the learning objectives. The problems will occur in several
contexts;
- Periodic problem sets for homework serve both as learning and
assessment tools. Classroom activities may vary depending on students'
performances on homework assignments.
- Problems given on in-class examinations are designed to give
students the opportunity to demonstrate their ability to apply rules
and formulae to the solution of simpler problems.
- Instructor optional take-home examinations designed to evaluate
the students ability to solve more complicated and time consuming
problems. These problems give students the opportunity to demonstrate
their ability to use technology to solve problems that are not
amenable to simple analytic techniques.
Core Outcomes
After successfully completing MATH 175, students will be able to
demonstrate the following competencies in order to fulfill specific
requirements set by the Core Philosophy and Goals Statement:
- Critical Thinking/Problem Solving Skills
Clearly identify and analyze a problem, identify possible
solutions and give the rationale for a preferred solution
Students will identify in homework and on tests their abilities in
applying calculus theory and concepts to problems.
- Communication Skills
Write clearly
Students are expected to provide interpretations and explanations of
their solutions to problems that are posed to them in class and on
homework. Their grammar, sentence structure, punctuation and spelling
are considered in the evaluation of their work.
- Cultural Perspective
Mathematics is a culturally
independent discipline which is studied and advanced by people of
all cultures, races, and nationalities.
- Breadth of Knowledge and Intellectual Perspective
Articulate relevant basic assumptions, concepts, theoretical
constructs, and factual information.
Throughout the course, students are expected to explain their
assumptions and interpret their results in the theoretical framework
of calculus.
Understand and apply relevant discipline-specific methodologies
and strategies of inquiry.
Students will demonstrate their facility in applying techniques of
calculus to problems designed to test their understanding of the
concepts.
Topics and Approximate Timeline
The following table is based on a typical semester schedule - 60
class meetings of 50 minutes each. The actual time will vary from
semester to semester and instructor to instructor.
|
| MATH 175 Calculus II |
| Topic |
|
| Applications of integration | 13
|
| Techniques of integration | 9
|
| Numeric Integration | 2
|
| Separable differential equations | 2
|
| Parametric and Polar equations | 5
|
| Conic sections | 2
|
| Sequences and series | 15
|
Text
The current text is University Calculus by Joel Hass, Maurice Weir and George Thomas, Addison-Wesley (2007). Other texts in recent years are Calculus, Concepts and Contexts, James Stewart, Brooks/Cole and Calculus from Graphical, Numerical and Symbolic Points of View, Ostebee and Zorn, Saunders Publishing Company.
Format, Student Activities, and Grades
Class meetings involve a
combination of lecture, questions and discussion, and sometimes small
group activity; the instructor chooses the appropriate mix. The
laboratories are an integral portion of the course and are used to
assist the students intuition into the value and power of calculus.
Grades are determined by the individual instructor. Homework is an
important part of the course; some exercises may involve extensions of
ideas in the text to new situations, rather than just routine
applications. Some examinations may be partially take-home. The
instructor chooses the exact grading scheme, but a typical
distribution might be
|
|
| Homework | 14%
|
| 4 examinations | 56%
|
| Final Examination | 30%
|
| Total | 100%
|
Letter grades are based on a scale in which 90% of the total possible
points guarantees and A, 80% a B, 70% a C and 60% a D, with the
instructor having the discretion to lower these cut-offs if warranted
File translated from TEX by TTH, version 1.56.