General Information: Fall 2017
Course title and number: Math 203 Calculus III
Required Text: Calculus, (10th ed.) Larson, Hostetler, Edwards
Instructor's name: Donald P. Robinson , Professor
Office Location/Hours: Via Skype and by appointment
Office Phone: 304-947-7970††††††
EMail: drobinson@allegany.eduFax: 301 784 5060 Skype odonata5237
Class meeting time: Web class
*Please note: Under extenuating circumstances, the instructor has the right to change any course provisions or requirements during the semester.


A. Catalog description

This course includes a study of vectors in n-space and their applications, partial derivatives, multiple integrals and line integrals. A graphing calculator is required. TI-83 is strongly recommended. Approximate cost is between $80 and $110 at the bookstore.

Prerequisite: Mathematics 202 (Calculus II)

B. Course objectives:

Learn about operations with vectors in two and three dimensions and applications of vectors to physics and engineering.

Learn about three dimensional analytical geometry and surfaces.

Learn about vector valued functions and applications.

Study functions of several variables and partial derivatives and applications.

Learn about multiple integral and applications of multiple integrals.

Introduction to vector analysis, line integrals, Greenís theorem, and divergence.


† C.††††† The following General Education Goals are covered in the course:

†††††††††††††††††††††††1.†††††† Scientific and Quantitative Reasoning.

†††††††††††††††††††††††2.†††††† Critical Analysis and Reasoning .




A. Attendance

Units should be studied, listened to, watched and homework should be completed according to the posted schedule of events. Exams must be taken by the required dates, so getting behind can be a serious problem. There is no class to attend, but at least weekly, have contact with the instructor by email or messenger to discuss your questions and progress in the lessons.

B. Try to get into a routine of checking out the lectures during a regular basis, say every evening after dinner, or every morning when you get up. Probably 'best practice' is to do the assigned problems right after examining the lecture material and examples. Of course, study for exams by doing or redoing more problems. It is crucial for you to help me do a better job by asking questions (via email) about the problems you don't understand. I have a way of answering via email with videos that will surprise you, I hope.

C. Grades:

There will likely be five regular exams, one at the completion of each unit (see IV A for units), and possibly a weighted comprehensive exam. The scale will be no more difficult than:

90 - 100 = A

80 - 89 = B

70 - 79 = C

60 - 69 = D

under 59 = F

There will be no other grades.

D. Extra credit: is not given in this course.

E. Tutoring may be available, but is not likely.  You must contact the office controlling this in your own school. AC students may use the math study lab in H-66 (free!).

ACCOMMODATING DISABILITIES In compliance with federal 504/ADA requirements, Allegany College of Maryland supports the belief that all "otherwise qualified" citizens should have access to higher education and that individuals should not be excluded from this pursuit solely by reason of handicap. The college is committed to the integration of students with disabilities into all areas of college life and offers support services intended to maximize the independence and participation of all students. The College complies with applicable state and federal laws and regulations prohibiting discrimination in the admission and treatment of students. Any student who wishes to receive accommodations must register with the Disabilities Services Office, providing documentation of the declared disability. Once documentation is received, the Director will establish eligibility for specific accommodations based on the student's documented functional limitations and the essential functions required within specific courses. Any student who wishes to declare a disability should contact Wilma Kerns or June Bracken at 301-784-5234, TDD 301-784-5001, or to obtain information and assistance.

If you are at a distant site, I donít know what to tell you. See your local version of the AC Instructional Assistance Center.

F. Assignments are for your benefit. You really canít learn or retain mathematics without doing mathematics. If conditions warrant, the assignments will be collected and the grading will be approximately equal to another exam grade to be averaged in. I will accept MathCad assignments, scans of written assignments, snail mail, or faxes (if done in black pen only!). This is your responsibility. Assignments should be neat and legible. Also, assignments must be submitted when required.

G. Assignments are to be prepared for submission when due. Late assignments will not be accepted.

H. Cheating will not be tolerated. The AC Student Handbook describes the policy in regard to this matter. You should make yourself familiar with this. Other schools have similar policies, and I will try to abide by them as cases occur.

I. Make up exams will not be given. If you are unable to attend the scheduled exam, and you have a sound reason for absence, then you must contact the instructor before the exam date.


Course outline

Vectors and the geometry of space
    vectors in R2
    vectors and coordinate systems in R3
    dot product of vectors
    cross product of vectors
    lines and planes in R3
    surfaces in R3
    Cylindrical and spherical coordinates

Vector-valued functions
   Vector Valued Functions
    Differentiation and integration of vector valued functions
    Velocity and acceleration
    Tangent and normal vectors
    Arc length and curvature

Functions of several variables
    Introduction to functions of several variables
    Limits and continuity
    Partial derivatives
    Chain rules for functions of several variables
    Directional derivatives and gradients
    Tangent planes and normal lines
    Extrema of functions of two variables
    Applications of extrema of functions of two variables
    Lagrange multipliers

Multiple integrals

    Iterated integrals and area in R2
    Double integrals and volume
    Change of variables, polar coordinates
    Center of mass, moment of inertia
    Surface area
    Triple integrals and applications
    Triple integrals in cylindrical and spherical coordinates
    Change of variables: Jacobians

Vector analysis
    Vector fields
    Line integrals
    Conservative vector fields and independence of path
    Greenís theorem
    Parametric surfaces
    Surface integrals
    Divergence theorem
    Stokeís theorem

B. Assignments: made as each lesson is completed. Note that I will 'color code' the assignments so the eighth edition of the text may also be used.

C. Required Reading: Textbook, website

D. Recommended Reading Assignments: try to read the next section or two ahead before reviewing the web lesson. You may not understand it much but it will make the web lesson easier to understand.

E. Supplemental Learning Resources: MathCad software might be useful to you, as I have that also and files with questions or homework can be emailed to me in that format. Please save back to MathCad 2000 for me to read it. If you wish to use other software, make sure you can 'save as' a .doc, .rtf, .pdf or something universally readable. The catalog description needs a fix, as the TI-89 is a better choice of calculator than the one listed there (TI-83), but really software (like MathCad) is better than that. If what you have is Maple, Matlab, or Mathematica (or anything else), let me know, and I will try to get a reader to open your files so you can use what you are familiar with.

Title IX statement Allegany College of Maryland does not discriminate against any individual for reasons of race, ethnicity, color, sex, religion or creed, sexual orientation, gender identity or expression, national origin, age, genetic information, familial status, disability or veteran status in the admission and treatment of students, educational programs and activities, scholarship and loan programs, or to terms and conditions of employment, including but not limited to, hiring, placement, promotion, termination, layoff, recall, transfer, leave of absence, compensation and training. Allegany College of Maryland complies with applicable state and federal laws and regulations prohibiting discrimination and Maryland prohibits retaliation in any form against any person who reports discrimination or who participates in an investigation. Non-Discrimination Statement Allegany College of Maryland prohibits sexual misconduct and sex discrimination by or against all students, employees, and campus guests. If you have any questions or concerns or if you need to make a complaint, contact ACM's Title IX Coordinator, Dr. Renee Conner in CC-152, by email at , or by phone at (301) 784-5206. For detailed information about policy, procedures, and prevention education, see .