Syllabus for MTH1123/MTH1140 - Northeastern …



Fall 2001 Syllabus for MTH1223

Instructor/office/contact info/office hours:

Professor Chris King, 437 Lake Hall

Email: king@neu.edu

Office Hours: M, Tu, Th 10:30 – 11:30 am

Prerequisites:

MTH1125 or MTH1725

Required Materials:

Text: Thomas’ Calculus, Part 2, by Finney, Weir, and Giordano

Calculator: scientific, graphing calculator (recommend TI83 or higher)

Course Web Page:

Go to math.neu.edu/undergrad/syllabi.html

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

Course Objectives:

To have students understand the concepts of vectors, vector functions, and functions of more than one variable, and their derivatives and integrals, 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:

• algebraically and graphically manipulate vectors, find their components, and determine length and direction

• calculate dot products, projections, and angles between vectors

• solve physics problems, involving velocity, acceleration, force, and work, by using vectors

• differentiate and integrate vector functions

• differentiate the position vector function to obtain the tangent, velocity, and acceleration vectors

• integrate the acceleration and velocity vector functions to obtain the position vector function

• calculate the position, velocity, and acceleration vector functions of a projectile

• calculate polar coordinates given Cartesian coordinates, and vice-versa, and draw graphs of polar equations

• calculate the cross product of two vectors in 3-dimensional space to find normal vectors to planes

• apply the cross product to calculate areas of triangles and parallelograms, and to find the torque vector

• produce equations of lines and planes in 3-dimensional space

• sketch cylinders and quadric surfaces, and recognize their equations

• differentiate dot products and cross products of vector functions

• identify the domain of a function of several variables, and produce a rough sketch of the graph

• sketch the level curves of a function of several variables

• match functions of several variables with their level curves and graphs

• calculate partial derivatives of functions of several variables

• calculate partial derivatives via the multivariable chain rule

• calculate the gradient vector of a function of several variables at a point

• calculate the directional derivatives of a function of several variables, and determine the directions of most and least rapid increase of the function, and the directions in which the function remains constant

• produce equations of the tangent plane to the graph of a function of several variables at a point

• approximate changes in the function by using the tangent plane, the local linearization, and the differential

• determine the critical points of a function of several variables, and determine whether they correspond to local maxima, local minima, saddle points, or none of these

• sketch the graph and level curves of a function of several variables near local maxima, local minima, and saddle points

• determine absolute extreme values on closed, bounded regions

• approximate double integrals by using partitions

• calculate indefinite and definite double integrals

• reverse the order of integration to calculate double integrals

• use double integrals to calculate the volume beneath surfaces

• calculate areas, masses, moments, and centers of mass using double integrals

• calculate double integrals in polar coordinates

• calculate triple integrals in rectangular coordinates

• calculate the average value of a function of several variables

• use triple integrals to calculate volumes, masses, moments, and centers of mass

Calculus Help and Tutoring:

There are many resources for improving your Calculus skills. The best one 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 (Schaum’s 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/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.

Homework and quizzes:

HOMEWORKS: There will be a weekly homework assignment, due in class on Thursday. The homework will be graded and returned on the following Monday. The problems will be assigned each week in class.

QUIZZES: There will be bi-weekly (10 minute) quizzes on Thursdays, the first one being on October 4.

TESTS: In addition to the final exam, there will be two midterm exams (dates to be announced).

Grading:

The course grade will be determined as follows:

Final exam 40%

Midterm Exams 40%

Quizzes and Homework 20%

Values of letter grades: A 85 – 100; B 70 – 85; C 55 – 70; D 40 – 55

Cheating Policy:

Cheating is an insult to honest students – it will not be tolerated. 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/test, looking at notes during a quiz/test (unless it is specifically announced that you may), copying other students’ work outside of class, and obtaining help from others on take-home tests.

In this class, working together on homework is NOT considered cheating; however, you MUST write up your homework. Please be aware that this policy on 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.

Additional Contacts:

If you have concerns/ problems in the course, and are not comfortable discussing them with your instructor, please contact either of the following:

Course Coordinator: Prof. David Massey, dmassey@neu.edu, 529 NI, 373-5527

Vice-chairman of Mathematics: Prof. Donald King, donking@neu.edu, 447 LA, 373-5679

Timetable

Week 0: Sept. 20-21

§9.1 Vectors in the plane

Week 1: Sept. 24-28

§9.2 Dot products

§9.3 Vector-valued functions

§9.4 Modeling projectile motion

Week 2: Oct. 1-5

§9.5 Polar coordinates and graphs

§10.1 Cartesian (rectangular) coordinates and vectors in space

§10.2 Dot and cross products

Monday, October 8, COLUMBUS DAY, UNIVERSITY CLOSED

Week 3: Oct. 9-12

§10.3 Lines and planes in space

§10.4 Cylinders and quadric surfaces

Friday, October 12, LAST DAY TO DROP WITHOUT A W GRADE

Week 4: Oct. 15-19

§10.5 Vector-valued functions and space curves

§11.1 Functions of several variables

§11.2 Limits and continuity in higher dimensions

Week 5: Oct. 22-26

§11.3 Partial derivatives

§11.4 The chain rule

Week 6: Oct. 29-Nov. 2

§11.5 Directional derivatives, gradient vectors, and tangent planes

§11.6 Linearization and differentials

Week 7: Nov. 5-9

§11.7 Extreme values and saddle points

§12.1 Double integrals

Monday, November 12, VETERAN’S DAY, UNIVERSITY CLOSED

Week 8: Nov. 13-16

§12.2 Areas, moments, and centers of mass

Friday, November 16, LAST DAY TO DROP WITH A W GRADE

Week 9: Nov. 19 – 20 and Nov. 21 until 1:30pm

§12.3 Double integrals in polar form

Wed., November 21, from 1:30pm thru Fri., Nov. 23, THANKSGIVING BREAK

Week 10: Nov. 26-30

§12.4 Triple integrals in rectangular coordinates

§12.5 Masses and moments in three dimensions

Week 10.5: Dec. 3-4

Review and evaluations

December 5 & 6, Wednesday and Thursday, READING DAYS

Friday, December 7 – Thursday, December 13, FINAL EXAMS

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