Jay A Johnson
Q SCI 291
Introduction to differential calculus, emphasizing development of basic skills. Examples promote understanding of mathematics and applications to modeling and solving biological problems. Topics include optimization and curve analysis. Prerequisite: either MATH 120, Q SCI 190, a minimum score of 2 on advanced placement test, or a score of 153-163 on MPT-AS placement test. Not available for credit to students who have completed MATH 124 with a 2.0 or higher. Offered: AWS.
Course Objectives: 1. Develop an understanding of derivatives and the facility to use them. 2. Develop an appreciation for using differential calculus to solve problems and to gain insight into biologocal and physical phenomena.
Student learning goals
Know how to take derivatives of standard types of formulas encountered in most scientific disciplines.
Know how to find roots of functions using Newton's Method
Know how to locate minimums and maximums of functions
Know how to take partial derivatives
Know how to find the derivative of a relationship that is expessed in terms of parametric equations
Know a little bit about Taylors series expansions of functions
General method of instruction
Lectures and problem solving sessions. I like to use the lectures to show how various formulas, rules or procedures come about and try to provide some kind of tangible meaning to them. Real understanding only comes about as the result of working problems in which these ideas are being used. Consequently, I give out homework problems to do but every so often, I put typical homework type problems up on a screen and have the students do them in class. They can work together to learn how to do them and can ask me for help as I wander around. The point is that they must know how to do the problems to pass the class and how they learn is up to them. Apparently, research has shown that students learn from each other better than from an instructor.
MATH 120 or equivalent. It is assummed, of course, that you have mastered several skills as the result of taking math up to MATH 120 but it seems that some individuals have forgotten some things or did not learn some topics very well in the first place. It is my experience that simple algebraic manuevers and interpretation of symbols cause more difficulties for some students than some of the calculus ideas. Several skills will be required to do well in this course: simplification of expressions, understanding mathematical notation (particularly involving functions), knowing logarithms and trigonometric functions and a few relationships among them to name but a few. Some things will be reveived in the course but the student will be responcible for material that should have been mastered in previous math courses. ---> Mainly, the key to sucess will be putting time into doing the homework and working through the frustration of not seeing the "answer" immediately. You are catching on when you hear yourself say "Oh, I see!" This should happen frequently and more quickly as the course proceeds. (If you have equivalent preparation but have not taken MATH 120, please call Christy Howard at 543-1191 for an entry code.)
Class assignments and grading
Ten homework assignments in the course, one per week, each consisting of ten problems. These will not be corrected but weekly quizes, one half hour duration, will be given to insure that a mastry of the topics has been accomplished. The material in this course builds upon itself. Thus, a midterm exam will cover all material in the first half of the course and the final exam will be comprehensive.
THIS IS AN UNCONVENTIONAL METHOD OF GRADING (STUDY IT THOROUGHLY) Three grade components: Q = quiz average(%), M = midterm(%), and F = final exam(%) A weighted mean is computed as follows: G = 0.40*G1+0.35*G2+0.25*G3 where G1 is largest of (Q,M,F), G2 is middle value and G3 is smallest. In words this means a student gets 40% of the highest grade component, 35% of the next highest and 25% of the lowest -- the student is rewarded for what he does well at! One of the 34 decimal grades (DG) between 4.0 to 0.7 is recorded on the students transcript for this course using the formula: DG = 0.7 + 0.127*(G - 70) for 69 < G < 96 and DG = 4.0 for G > 95 Note: There is no curve and any G below 70 is considered failing, DG = 0.0 (I hear from time to time that this is a severe system, yet the distribution of grades tends to be on the high side. The ideas of calculus are, in fact, deep but the skills that must be mastered in this course are not all that difficult and the grade distribution seems to indicate this. I really do not like "failing" anyone but if the level of performance does not come up to my standards, then I have no alternative but to fill out the 0.0 box on the grade form.)