Business Calculus II

Math 1476: Business Calculus II

Fall 2003


Please make sure you have the necessary prerequisites for this course. That means you need a C or better in Business Calculus I (or an equivalent course) or an acceptable grade on placement tests. If I  feel you are not prepared for this course, I may choose to withdraw you. If you have any questions about your preparation for the course, please come and talk to me about it.


There will be 4 exams.  There will be no comprehensive final. There will also be several computer labs that will together count as a single exam grade. The 4 exams plus the 1 total computer lab grade will all count equally and together will comprise 90% of your grade. The remaining 10% will come from your homework assignments.

You may earn bonus points on each test, except for the final test, by correcting all errors and turning them in by the announced deadline. If you take any test late for any reason, there will be a penalty of 10 points off your test grade. However, no late tests will be allowed after the graded tests are handed back in class.

If you miss a test, you must try to take it during this ?late? period. If you miss this deadline as well, I  may consider allowing you to make-up the test, but only in the case of serious illness or emergency.  No make-ups will be given for tests administered in the Testing Center or for the final for any reason and make-ups of any sort are solely at my discretion. Otherwise, you will receive a 0 on the test. All tests and assignments must be turned in on or before the last class meeting.

Grades will be assigned as follows:


90% or better


60% - 69%


80% - 89%


below 60%


70% - 79%



Withdrawn by student or instructor prior to last withdrawal date on school calendar


Incomplete grades (I) will be given only in very rare circumstances. Generally, to receive a grade of "I", a student must have taken all tests, be passing, and after the last date to withdraw, have a personal tragedy occur which prevents course completion.


You should bring your homework to class every day.  It will be collected regularly and graded.  There may also be in-class assignments collected for a grade (as part of your homework grade). There will be a penalty on late homework. Homework that is more than two weeks late might not receive any credit.

Other Important Stuff


It is the student's responsibility to initiate all withdrawals in this course.  The instructor may withdraw students for excessive absences (4) but makes no commitment to do this for the student. (If you decide to stop coming, you had best make sure that you drop the course. While I MIGHT do this, it is YOUR responsibility. If you fail to do so, you could receive an F on your permanent record.) After the withdrawal deadline, neither the student nor the instructor may initiate a withdrawal. If you are withdrawn by mistake, I will only consider reinstating you if you have taken all necessary tests, are current in your homework, and have not missed an excessive number of classes.

The withdrawal deadline for Fall 2003 is November 20, 2003.


Attendance is required in this course.  It is extremely important for you to attend class regularly. Although I may not take regular attendance, I MAY drop you from the course for excessive absences, although I make no commitment to do so.

Classroom behavior:

Classroom behavior should support and enhance learning. Behavior that disrupts the learning process will be dealt with appropriately, which may include having the student leave class for the rest of that day. In serious cases, disruptive behavior may lead to a student being withdrawn from the class. ACC's policy on student discipline can be found in the Student Handbook page 32 or on the web at:

Class participation:

All students are expected to actively participate in this class. This can include asking relevant questions in class, participating in class discussions and other in-class activities, helping other students, coming to office hours with questions, and doing other things that contribute to the class.

Keeping up:

Please, try to keep up with the homework and with the lecture in class. There just isn't much time to catch up. This means you have to be sure to allow yourself plenty of time to do the homework and to study.

Ask questions:

Please, please, please, if you don't understand something, or you aren't clear about something, or if you think I (or the book) have made a mistake (it has been known to happen), or if you have any other questions, please ask. Don't let confusion accumulate. If you don't want to ask in class, come to my office hours (or call me) and ask. It is much easier to ask a question now than to miss it on the test.  I expect all students to participate in class discussions and other activities. Trust me, you will get much more out of the class if you become actively involved in it.

Always show your work:

It is much more important that you understand the processes involved in solving problems than that you just give me the right answer. If I see from your work that you understand what you are doing, I will usually give partial credit for a problem, even if you made a mistake somewhere along the line. If you don't show your work (unless I believe you could reasonably do it in your head), I may not give you full credit, even if the answer is right. If you can really do something in your head, that's great, but when in doubt, write it down.  It is also very important that you write what you mean. I will correct your notation the first few times, but I will start counting it wrong if you continue to write things incorrectly. In addition, please write clearly and legibly. If I can't read it, I won't grade it.

Scholastic Dishonesty:

Acts prohibited by the college for which discipline may be administered include scholastic dishonesty, including but not limited to, cheating on an exam or quiz, plagiarizing, and unauthorized collaboration with another in preparing outside work.  Academic work submitted by students shall be the result of their thought, work, research or self-expression.  Academic work is defined as, but not limited to, tests, quizzes, whether taken electronically or on paper; projects, either individual or group; classroom presentations; and homework.

Students who violate the rules concerning scholastic dishonesty will be assessed an academic penalty which the instructor determines is in keeping with the seriousness of the offense. This academic penalty may range from a grade penalty on the particular assignment to an overall grade penalty in the course, including possibly an F in the course. ACC's policy can be found in the Student Handbook page 33 or on the web at: 

MATH 1476
Business Calculus II
Information for Students: 

Text: Applied Calculus with Linear Programming A Special Edition by Barnett & Ziegler, Pearson Custom Publishing. (An errata sheet is available. Ask your instructor.)

Calculator: Students need either a scientific or business calculator. If you cannot purchase one, they are available from the library. Graphing calculators are fine, but their use may be restricted on the graphing test.


MATH 1476 BUSINESS CALCULUS AND APPLICATIONS II (4-4-0). A course treating multivariable calculus and its applications for business students, as well as selected other business applications. Topics include functions of several variables and their derivatives, partial differentiation, optimization problems and LaGrange multipliers, special methods of integration, differential equations, probability and calculus, Taylor polynomials and infinite series, and topics in matrix theory and linear programming. Prerequisites: MATH 1425 or MATH 2413 or the equivalent. (MTH 1684)

INSTRUCTIONAL METHODOLOGY:  This course is taught in the classroom primarily as a lecture/discussion course. This class will also have a computer lab component

Syllabus/Calendar/Suggested Testing Schedule:
Please note:  schedule changes may occur during the semester. Any changes will be announced in class


16-Week Semester




Review, 9.1


Review, 9.2


5.4, (5.5), 3.6, 5.6


7.1, 7.2, 7.3, Test


 7.4, 9.3


6.1, 6.2


6.3, 6.4, 6.5


6.5, 6.6, 6.7, Test


8.1, 8.2


(8.3, 8.4), 10.1


10.2, 10.3


10.4, 10.5, Test


10.6, 10.7


11.1, 11.2


11.3, 11.4




1. Business applications will be emphasized throughout the course.

2. Instructors may introduce supplemental materials as needed to enhance and clarify topics covered in the text.

3. Incomplete grades (I) will be given only in very rare circumstances. Generally, to receive a grade of I, a student must have taken all examinations, be passing, and have a personal tragedy occur after the last date to withdraw which prevents course completion.

.COURSE RATIONALE:  This is the second course in a two-course business calculus sequence. The course covers more multivariable calculus, differential equations, probability, numerical techniques and linear programming. The course stresses applications in business and economics, and is intended to give students the appropriate conceptual and computational mathematical background for future study in business.

TESTING CENTER POLICY:  ACC Testing Center policies can be found at:  Deadlines for all tests will be announced in class.  Any tests taken after the announced deadline are considered late.

STUDENT SERVICES:  The web address for student services is: The ACC student handbook can be found at:

INSTRUCTIONAL SERVICES:  The web address is: , then click on ?Campus Based Student Support Overview?.

Course-Specific Support Services

Sometimes sections of MATH 0163(1-0-2) are offered. The lab is designed for students currently registered in Business Calculus and Applications I, MATH 1425. It offers individualized and group setting to provide additional practice and explanation. This course is not for college-level credit. Repeatable up to two credit hours. Students should check the course schedule for possible offerings of the lab class.

ACC main campuses have Learning Labs which offer free first-come first-serve tutoring in mathematics courses, but not all tutors can help with this class. Check in advance . The locations, contact information and hours of availability of the Learning Labs are posted at:

Statement on Students with Disabilities

Each ACC campus offers support services for students with documented physical or psychological disabilities.  Students with disabilities must request reasonable accommodations through the Office of Students with Disabilities on the campus where they expect to take the majority of their classes.  Students are encouraged to do this three weeks before the start of the semester.

Students who are requesting accommodation must provide the instructor with a letter of accommodation from the Office of Students with Disabilities (OSD) at the beginning of the semester.   Accommodations can only be made after the instructor receives the letter of accommodation from OSD.

Statement on Academic Freedom:  Institutions of higher education are conducted for the common good.  The common good depends upon a search for truth and upon free expression.  In this course the professor and students shall strive to protect free inquiry and the open exchange of facts, ideas, and opinions.  Students are free to take exception to views offered in this course and to reserve judgment about debatable issues. Grades will not be affected by personal views.  With this freedom comes the responsibility of civility and a respect for a diversity of ideas and opinions.  This means that students must take turns speaking, listen to others speak without interruption, and refrain from name-calling or other personal attacks.

Time required and outside help: To do homework and study requires two or three times as much time outside of class as the time you spend in class in order to succeed in this course. Free tutoring is available in the Learning Labs (see above) and your instructor has office hours and can give some extra help, of course.

Additional information about ACC's mathematics curriculum and faculty is available on the Internet at

Errata in Business Calculus text, updated 5/15/00

p. 8,  example 5, middle of the page, the third limit should read , instead of   .

p.8, same example, bottom of the page, should read f(1)= 5 instead of f(-1)=5.

p.88, In the blue box, the marginal average cost and the marginal average revenue should have bars over the C and R.  The marginal average profit is ok.

p. 88, in the green box, there should be bars over the C's in the Marginal Average Cost Equation and there should be bars over the R's in the Marginal Average Revenue Equation.

page 112, the first derivative test graphic: The second sentence should read "Construct a sign chart for  f'(x) .".

p. 133, #43, change the -4x^3 term to +4x^3 if you'd like the answer in the back and the solution in the Student Solutions Manual to be correspond correctly,   f(x) = -x4 + 4x3+ 3x + 7  instead of  f(x) = -x4 - 4x3+ 3x + 7

p 172, example 20 part (B).  Find...    instead  of  .

p.173, near the middle of the page it says, " times  y = f(x + x) - f(x)."  Huh?  It should say simply " ."

p. 243  Step 2 in Solution   In denominator at end of line, should be    not 

p. 246, Example 31, the numerator should be .

page 342, Problem 67.the exponent on "e" should be -0.1 not  -.01 the answer key has problem worked with exponent  -0.1

page 357, Example 2, the shading in the graph (green) should include the sliver on the lower left.

page 373, five lines below Problem 10, the word "equilibrium" is misspelled in text

Page 497 #10     Chapter Six Review:  The answer in the back of the book assumes a FOURTH point which is not given in the problem, namely, (8,3) .

page 538   example 13,  third line of equations     exponent on e should be "0.08" , not  "0.008",  you will note exponent is correct everywhere else in the problem

There are a number of errors in Chapter 8, Sections 1 and 2, on Taylor polynomials and series, one bad one in the green box on p. 581 (should  be an "a" not a "0" in derivative.  Also on p. 594, the Problem 6 title is one line too high, which is confusing.  And the calculations in the  third line of Example 7, p. 595,  are all messed up.

page 736, green box, line with integral, should be  F(x)  where the type is blotched

page 743, x  0,  not 5 in problem 47.

page 756.  On the top of the page, in a green box entitled "Uniform Probability Density Function" under the heading "cumulative probability distribution" it reads  F(x) = 0  if  x<b.  It should read  F(x) = 0 if x<a.

p 847, tableau at very top of page the third row should begin with basic variable   not with  [a pivot has already taken place from the first tableau on the previous page and the basic variable has to change; it is correct in the third tableau on the top of page 847

Pg 850, Exercise 21, Second constraint equation (one with "less than 3"), First variable should be "x-sub-two".

p. 922, 15.  Solution is  y' = 3x^2y/(1+y)

p. 923, 1(A)  Delete "finger" at end of line (Who knows where that came from???)

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It was last updated on January 22, 2016 .