Math1123                                       Engineering Calculus I                                 

Fall, 2002                 Syllabus                Professor

 

Text:   ThomasŐ Calculus, Early Transcendentals,  10th Edition,  by Finney, Weir

                   and Giordano

 

Class Meetings:

 

My Office:                                               Phone:

                                                                                             or  373-2450 (Department)

Key Number:                                       e-Mail:

 

Office Hours:

 

Calculator:  We require the use of graphing calculators in class. We recommend a calculator at the level of a TI-83, or higher.

 

URL for the course:  http://www.math.neu.edu/undergrad/mth1123/

               Course announcements, hand-outs, answer keys, and practice tests and quizzes can be found here.

 

            This course is a one-quarter introduction to the Differential Calculus and will use this powerful collection of mathematical ideas to model change. We will use the Differential Calculus to describe the rate of change in physical processes. This focus on mathematical modeling of reality will frequently lead us into word problems. The difficulties in word problems involve language and our intuition about reality as much as mathematics. We will work on this area of common concern to students of mathematics, the sciences and engineering. 

 

Prerequisites:             Command of algebra and analytic (Cartesian) geometry, basic knowledge of pre-calculus functions, including trigonometric and logarithmic functions.

 

            The instructor reserves the right to change this syllabus according to the needs which may arise in this class during the passage of the quarter. Students are responsible to be aware of what goes on in the classroom including the announcement of exam dates, material to be covered on exams and any adjustments to this syllabus. If you have any questions that you are not comfortable asking in class please feel free to ask me after class or come to my office hours.

            In addition, if there are problems with the course, you have the options of speaking with the course coordinator,  Professor Maurice Gilmore in room 433 Lake Hall at X5675 and e-mail at gilmore@neu.edu, or with the Vice-Chairman  of the Mathematics Department, Professor Donald King in room 447 Lake Hall at X5679 and e-mail at donking@neu.edu.

 

Course Objectives:

            This course has one all-encompassing goal: to enable students to understand the concept of the derivative and to enable students to display that understanding through a variety of applications.

Specific, measurable, manifestations of your understanding that will be tested during the quarter include your ability to:

 

á             Parameterize curves in the plane and motion along a straight line

á             Describe velocities as rates of change analytically, graphically and numerically.

á             Analyze more general rates of change, including acceleration, from the same three viewpoints as above.

á             Apply the definition of the derivative to algebraically and analytically derive instantaneous rates of change as limits of average rates of change.

á             Visualize and interpret derivatives via slopes of tangent lines to graphs.

á             Derive, memorize, and apply the rules for differentiation to calculate derivatives of given functions, including polynomials, exponential and logarithmic functions, trigonometric and inverse trigonometric functions, and combinations of such functions by using the product rule, the quotient rule, and the chain rule.

á             Sketch graphs of functions by analyzing the first and second derivatives.

á             Model, by using derivatives, physical problems involving rates of change, including velocity and acceleration problems, exponential growth and decay, and simple oscillations.

á             Solve, via derivatives, optimization problems (maximum-minimum problems) which arise in a wide variety of situations involving physics, engineering,  and economics.

á             Calculate the linearization of a function

á             Approximate changes using differentials

á             Estimate roots of equations using NewtonŐs method

 

Grading Policies:        We will get to know one another and will teach each other. There will be activity for you to do on your own and with other students in many class sessions. Mathematics is not a spectator sport. There will be weekly quizzes which will usually be during the first 20 minutes of the class on Thursday. We will have an hour exam on October 31st. Your grade in this course will  be calculated using your quiz average for 30%,  your hour exam for 30% and your 2-hour final exam for 40%. There will be no make-ups and you can drop your lowest quiz score. My usual understanding is that  numerical gades translate into letter grades as follows:

 

    over 92 = A;  90-92 = A-; 87-89 = B+; 83-86 = B; 80-82 = B- ; 77-79 = C+;

    73-76 = C; 70-72 = C-; 67-69 = D+; 63-66 = D; 60-62 = D- and below 60 = F

 

Algebra Proficiency:             A common problem in Calculus courses is that students learn the Calculus material, but have such weak algebra skills that they rarely obtain correct answers to problems. We will require correct algebra work throughout the quarter. Even though this is a calculus course, you will lose points for pre-calculus errors.

 

Algebra and Calculus Help and Tutoring:

            There are many resources for improving your algebra and Calculus skills. The best strategy is to go over any problems with your instructor. Other resources: walk-in tutoring in Cahners Hall and from Engineering tutors in 222 Snell Engineering, tutoring by appointment (sign up in the Media Center in the library), and study aids in the library (SchaumŐs Outlines are great).

 

 

 

Attendance:

            It is essential that you attend class regularly. The easiest way for you to learn the material, and to know what material has been covered, is to come to class each day. Students are responsible for finding out what material has been covered or what announcements have been made on days that they miss class.

 

Excused Absences or Late Work:

            In order to turn in assignments late or to take make-up quizzes and tests, students must bring written proof of some emergency situation; notes from doctors or nurses, documents verifying court appearances, receipts from having a car towed are all examples of valid documentation. Notes from family members are not acceptable. If a situation is of a personal nature, discuss the matter with your academic advisor; an e-mail message from your advisor saying that they believe that you should be allowed to make-up work is acceptable.

 

Cheating Policy:         Cheating will not be tolerated. All incidents of cheating will be reported to the Office of Judicial Affairs. The University's cheating policy and related disciplinary actions are detailed in the Student Handbook. The Handbook also includes a description of what is considered cheating by the University. Cheating in this class includes (but is not limited to): looking at the papers of others during a quiz or test, talking to other students during a quiz or a test, looking at notes during a quiz or a test (unless it is specifically announced that you may), copying other studentsŐ work outside of class, and obtaining help from others on take-home tests.

            In this class, working together on homework or computer laboratory assignments is NOT considered cheating; however, you MUST write up your homework or lab reports individually. When working together on a computer lab, you are allowed to print out and turn in multiple copies of spreadsheets or other computer-generated documents, but copying of each othersŐ written analysis for lab reports IS considered cheating. Please be aware that this policy, about working together outside of class, varies greatly from one course to the next. The policy on what is allowed, that has been described in this paragraph, may well be considered cheating in your other classes.

            The use of advanced calculators is NOT considered cheating in this course. Be aware, however, that other courses may well have a policy barring such calculators. Also, your instructor reserves the right to decide on-the-spot between what constitutes a calculator”and what constitutes a full-fledged computer.

            All incidents of cheating will be reported to the Office of Judicial Affairs.

 

            If you have any questions as to what constitutes cheating, please ask me.

 

            Please note that we will treat you as an adult here. If you must miss a class, be late or leave early, it is expected, as polite behavior, that you will contact the instructor involved ahead of time and reach an agreement. This sort of behavior goes a long way when you have to miss a quiz, for instance. If you do not do this, the ball is in your court to make up work or use the missed quiz as the quiz which you drop.    

        The following page includes a calendar with homework problems to be covered.

They may change as we progress through the course.

 

Schedule of Topics and Assignments

 

Week   Section                     Topic                                              Assignment

 

0: September 19th-20th.

            P.3                   Exponential Functions            1-8, 11-14, 21-2, 29, 31, 35 and 40.

Week   Section                     Topic                                              Assignment

 

1: September 23rd-27th.

            P.4                   Inverse Functions & Logs      1-4, 7, 8, 11-3, 17, 20, 31-33, 37-8,

                                                                                    39a, 41, 43 and 57.

            P.5                   Trig Functions & their Inverses   1, 2, 5, 7, 8, 10, 13, 19, 21-24, 27,

                                                                                          39 and 44.

            P.6                   Parametric Equations              1-3, 7, 8, 10, 17, 19, 21-23.

 

2: September 1st-October 4th.

            1.1                   Rates of Change & Limits      1, 2, 5, 7, 9, 11, 13-4, 17, 19, 23, 41

            1.2                   Finding Limits & One-Sided Limits   1, 2 and 6.

            1.3                   Limits Involving Infinity        1, 2, 7, 8, 11, 21, 25-6, 33 and 63.

            1.4                   Continuity                               1-5, 26, 26a and 28.

 

3: October 7th-11th.

            1.5                   Tangent Lines                         1, 3, 5-7, 13, 15, 19, 21, 23, 24, 29,

                                                                                    30, 33a&b, 35 and 42.

            2.1                   Derivatives as a Functions      1-3, 6-8, 13, 15-18, 24-26, 33, 34.

            2.2                   Derivatives as Rates of Change   1-7, 13, 18, 22, 23 and 25.

 

            Friday, October 11th.   LAST DAY TO DROP WITHOUT A W GRADE.

                                                                                               

4: October 15th-18th. October 14th is  Columbus Day. The University is closed.

            2.3                   Derivatives of Products, Quotients &    1-5, 7, 11-13, 19, 21

                                    Negative Powers.                                            and 29.

            2.4                   Derivatives of Trig Functions    1-5, 8, 13, 14, 27, 31, 37 and 39.

 

5: October 21st-25th.

            2.5                   Chain Rule & Parametric Equations   1, 3, 6, 9, 11-13,  16, 21-2,

                                                                        26,  27, 33, 37, 39, 41, 44, 45, 51, 59 and 65.

            2.6                   Implicit Differentiation           1, 2, 7, 13, 19, 20, 27, 37, 39 and 61.

 

6: October 28th-November 1st.

            2.7                   Related Rates                          1-3, 5, 10, 11, 13, 15, 30, 31, 33, 35.

            2.8                   Derivatives of Inv. Trig. Functions   1, 3, 5, 8, 11, 18-20, 22, 31-2.

 

Hour Exam.   October 31st,  in week 6.

 

7:   November 4th-8th.

            2.9                   Derivatives of Exp. & Log Functions   1-3, 7, 11, 15-21(odd), 22,

                                                                                          29, 31-33, 39, 41, 43, 47 and 49.

            3.1                   Extreme Values of Functions   1-6, 10-14, 16-7, 21, 24, 25, 31, 33,

                                                                                                 36-7, 39, 47, 53 and 54.

 

8:   November 12th-15th.  November 11th is VeteranŐs Day. The University is closed.

            3.2                   The Mean Value Theorem &   9, 12-14, 17, 19, 20, 22-3, 25

                                    Differential Equations                                    and 29

            3.3                   Shapes of Graphs                    5-8, 13-19(odd), 20, 23, 27, 43, 45,

                                                                                                47 and 59.

 

9: November 18th-22nd.

            3.5                   Modeling & Optimization      1, 7, 14-16, 22, 32-3.

            3.6                   Linearization & Differentials 1-3, 6, 7, 15, 17, 21, 25-6, 33 and 36.

Thanksgiving on Nov. 28,  no classes from 1:30, Wed. Nov. 27, through Fri. Nov. 29

 

10: November 25th-27th

            3.7                   NewtonŐs Method.                  1, 2, 5 and 10

 

11: December 2nd & 3rd.  Review and Evaluations.

 

Reading days on Dec. 4th & 5th

 

Friday, December 6th through Thursday December 12th: FINAL EXAMS

 

 Note :  The dates indicated for exams and quizzes are only recommendations. They are subject to change within reason. You are responsible to keep informed about such date changes on your own.