Main Themes for the Spring 2008 Semester
As you can see from the panel of courses on the left, I am teaching 3 classes this Spring Semester — Ordinary Differential Equations (ODE), Honors Precalc/Trig, and Calc 3. But above and beyond the actual subject material of these courses, I want to talk to you about a "tent," so to speak, under which this thing called education takes place. ( "Learning takes place in the pavilion of the mind." ) This tent is held up by a framework of ideas, common to all, which, if properly investigated and developed, will help you to not only tie together and make sense of the subject material within your particular course, but also will provide you with a repertoire of general methods of learning and understanding which will be of life-long benefit to you in all your intellectual pursuits.
So, in addition to the actual subject matter covered in your course, I would like you to keep always in mind the following considerations:
- Your learning style
- What IS my LEARNING STYLE? You must know, or at least have some idea of how you learn. How can you hope to improve your learning process if you don't even know what it is?
- As a matter of fact, just WHAT IS "LEARNING," anyway?
- Ask yourself the question: "Is this material being presented to me in 'my' strongest learning style?"
- Ponder these questions: "After the class is over, after the lecture is over, what do I have to do to really learn the stuff we covered in class? That is, in what manner will I need to further study and review this material in order to gain an adequate understanding of it? How can I wrap my brain around this stuff?"
- And finally: "How do I make the information 'stick' in my mind, so that I won't forget it?"
Here are some links that may help you: — PLEASE NOTE: In none of the
REFERENCES below am I advocating, promoting, or advising you to purchase or sign-up
for anything advertised on those pages. I have, however, found that each link
does provide some relevant, free information.
- The intellectual relationship between Teacher and Learner.
Consider the paradigm of the
"Big T, Little l"
transitioning into the
"Little t, big L"
- T and t stand for the teacher's playing either a greater or lesser role in your education (I am the teacher), and
- L and l stand for the learner's (that's you) playing a greater or lesser role in your education.
- At any stage of your education, there is always the question to be asked and answered "Which of us is the lead-agent in your education?"
- We all start at the T, l level (Big T, little l) with the teacher providing most of the "driving force" in your education,
- And we should progress to the t, L level (Little t, big L) with you, the student-learner, providing most of the "driving force" attendant to your education.
- The question you must constantly ask is "Where am I now on the road from T, l to t, L?
- Consider the paradigm of the "Big T, Little l" transitioning into the "Little t, big L" — where
- The notion of
- Who is telling me this?
- What is she or he trying to "sell" me?
- Should I simply accept what's being said?
- Are we examining all the possibilities?
- What other data or facts are relevant to decision-making with respect to this issue?
- Is the reasoning involved in this issue sound?
- Are the supposed "facts" in this discussion true?
- And, even if I accept the argument, is there a better way to state it?
- On what level of thought is my current thinking taking place,
vis-a-vis Bloom's Taxonomy?
- Just as there are many levels on the learning path discussed above, there are many levels on the thinking path or understanding path, as it might be called.
- These levels are described in BLOOM'S TAXONOMY. I invite you to click on this link, visit the site and study the "triangle."
ODE // MAP 2302 - 55107
Course Title: ORDINARY DIFFERENTIAL EQUATIONS
SCNS Number: MAP 2302
Prepared by: D. Jones
Date: February, 2003
Prerequisite: MAC 2312 with a grade of 'C' or better. Calculus II.
Methods of solutions of ordinary differential equations, linear and non- linear, systems of linear differential equations, boundary value problems. methods include operators undetermined coefficients, variation of parameters. LaPlace transforms, and series solutions. There is also utilization of the CAS (Computer Algebra System) MAPLE. A graphing calculator is required. Lecture 3 hours.
GOALS OF THE COURSE:
Since this is an introductory course, its primary goal is to teach the student how to solve a fairly representative assortment of types of differential equations which will be useful in her/his future course-work and in his/her future profession. A secondary goal, and one which takes longer to achieve, is that of helping the student to see how to construct mathematical models which are fairly faithful translations of specific physical problems, and which, naturally, result in differential equations, or system of differential equations. This secondary goal is really the more important of the two, but it cannot be accomplished within the framework of MAP 2302; it can at most be begun here with its development continued in subsequent courses.
At the end of this course the student should be able to:
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Honors Precalculus Algebra and Trig // MAC 2147 - 55091
Course Description: (5 Semester Hours) OD
Prerequisites: Honors Authorization. This course serves as a prerequisite for MAC2311, Calculus with Analytic Geometry I.
Topics include: properties and graphs of polynomial, rational, exponential, and logarithmic functions; solutions of higher degree polynomial equations; solutions of systems of equations using matrices and determinants; sequences and series; the binomial theorem; an introduction to conic sections; trigonometric functions of angles and real numbers, along with their graphs and inverses; solutions of triangles and other applications; trigonometric identities; conditional trigonometric equations; complex numbers in trigonometric form and DeMoivre’s Theorem; vectors and polar coordinates; and piecewise defined functions. A graphing calculator is required. Please check with your instructor for the most appropriate one for the course. This course may not be taken for credit by any student who already has a grade in MAC2140 or in MAC 2114. Lecture, 5 hours college credit.
Objective of the Course:
To combine Precalculus Algebra and Trigonometry into one 5 semester-hour course in order to allow students with adequate mathematics background to complete the prerequisites for Calculus I in one course instead of two. This would possibly reduce the number of excess hours a student who is majoring in science, engineering, or mathematics may need to take.
Performance Goals of the Course: Upon the completion of this course, the student should be able to:
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Calculus 3 with Analytic Geometry //
MAC 2313 - 55105 MAC2313 Calculus with Analytic Geometry III (4) FA SP
This is a WEB assisted course. A graphing calculator is required. Check with your instructor for the most appropriate one. Lecture 5 hours. Special fee.
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