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Viewing: MA 231 : Calculus for Life and Management Sciences B

Last approved: Thu, 07 Sep 2017 08:01:51 GMT

Last edit: Thu, 07 Sep 2017 08:01:51 GMT

Change Type
Major
MA (Mathematics)
231
013665
Dual-Level Course
Cross-listed Course
No
Calculus for Life and Management Sciences B
Calc Life Manag B
College of Sciences
Mathematics (17MA)
Term Offering
Fall, Spring and Summer
Offered Every Year
Fall 2017
Previously taught as Special Topics?
No
 
Course Delivery
Face-to-Face (On Campus)
Distance Education (DELTA)
Hybrid (Online/Face to Face)

Grading Method
Graded with S/U option
3
16
Contact Hours
(Per Week)
Component TypeContact Hours
Lecture3.0
Course Attribute(s)
GEP (Gen Ed)

If your course includes any of the following competencies, check all that apply.
University Competencies

Course Is Repeatable for Credit
No
 
 
Molly Fenn
Teaching Associate Professor

Open when course_delivery = campus OR course_delivery = blended OR course_delivery = flip
Enrollment ComponentPer SemesterPer SectionMultiple Sections?Comments
Lecture30030YesN/A
Open when course_delivery = distance OR course_delivery = online OR course_delivery = remote
Delivery FormatPer SemesterPer SectionMultiple Sections?Comments
LEC3030NoN/A
Prerequisite: MA 131 or MA 141; Credit is not allowed for both MA 231 and MA 241.
Is the course required or an elective for a Curriculum?
Yes
SIS Program CodeProgram TitleRequired or Elective?
see attachedsee attachmentRequired
see attachedsee attachmentElective
Functions of several variables - partial derivatives, optimization, least squares, Lagrange multiplier method; differential equations - population growth, finance and investment models, systems, numerical methods; MA 121 is not an accepted prerequisite for MA 231.

Removed: chain rule, flow processes, multiple integrals, gradient, Taylor polynomials and series.


Changed some ordering, grammar, and punctuation.


No

Is this a GEP Course?
Yes
GEP Categories
Mathematical Sciences
Humanities Open when gep_category = HUM
Each course in the Humanities category of the General Education Program will provide instruction and guidance that help students to:
 
 

 
 

 
 

 
 

 
 

 
 

Mathematical Sciences Open when gep_category = MATH
Each course in the Mathematial Sciences category of the General Education Program will provide instruction and guidance that help students to:
 
 
Outcome 1: Use the techniques of partial differentiation to explore the properties of a function of two or more variables


Outcome 6: Carry out numerical simulations and mathematical analyses of a model
 
 
Outcome 1 will be assessed through WebAssign homework, in class work, and exam questions similar to those below.
Example 1: The volume V (measured in cubic metres) of a certain amount of gas is determined by the temperature T (measured in Kelvin) and the pressure P (measured in megapascals) by the formula V = 0.08(T/P). Calculate the values and units of dV/dP and dV/dT when P = 0.5 MPa and T= 300 K. (Give exact answers.) Then give an interpretation of these values in the context of the problem.
Example 2: U.S. postal rules require that the length plus the girth of a package cannot exceed 84 inches in order to be mailed. Find the exact dimensions of the rectangular package of greatest volume that can be mailed.
Example 3: In economics, substitute goods are two products that are similar or comparable to each other, think iPhones and Nexus phones. On the other hand, complementary goods are products that go together, think iPhones and Apple Watches.
1. Suppose we have two products that are substitute goods where product 1 costs $x
per unit and product 2 costs $y per unit. If f(x,y) is a function that models the number
of units of product 1 that are sold, what would the signs of df/dx and df/dy be? Why?
2. Now suppose instead that out two products are complementary goods with x, y, and f(x,y) defined exactly as above. What would the signs of df/dx and df/dy be now? Why?

Outcome 6 will be assessed through WebAssign homework, in class work, and exam questions similar to those below.
Example 1: (a) Given the initial value problem y' = 10 − y, y(0) = 1, use Euler's method with h=1/3 to estimate the value of y(1). (Give your answer correct to at least three decimal places.)
(b) Using separation of variables, solve the initial value problem
y' = 10 − y, y(0) = 1.Use this solution to find the exact value of y(1). (Give your answer correct to at least three decimal places.)
(c) Compare the two answers.
Example 2: A certain hormone is produced by an endocrine gland, causing its concentration to increase at a constant rate of A mg/L. The hormone is metabolized by the liver, with the rate of elimination being proportional to the concentration of the hormone. The constant of proportionality in this relationship is given by the (positive) constant k. The concentration of the hormone at time t is written as y(t). At time t = 0, a patient comes off a drug treatment that had blocked production of the hormone. (So, at that time, they do not have any of the hormone in their body.) Their doctor finds that the initial rate of increase of their hormone concentration is 0.625 mg/L/hour and that, in the long run, the concentration approaches 4.25 mg/L. After how long would the patient's hormone concentration have reached half of its long-term level? At what rate would the level of hormone be increasing at that time?
 
 
Outcome 2: Set up and solve optimization problems in various contexts

Outcome 5: Create a mathematical model that describes a given problem from biology, economics, or business

Outcome 6: Carry out numerical simulations and mathematical analyses of a model
 
 
Outcome 2 will be assessed through WebAssign homework, in class work, and exam questions similar to those below.
Example 1: A monopolist manufactures and sells two competing products, call them I and II, that cost $43 and $32 per unit, respectively, to produce. The revenue from marketing x units of product I and y units of product II is R(x, y) = 111x + 124y − 0.04xy − 0.1x2 − 0.2y2. Find the exact values of x and y that maximize the monopolist's profits and the maximum profit she would earn. Justify why this is a maximum and not a minimum.
Example 2: The amount of space required by a particular firm is given below, where x and y are, respectively, the number of units of labor and capital utilized.
f(x, y) = 1000sqrt(6x^2+y^2). Suppose that labor costs $480 per unit and capital costs $40 per unit and that the firm has $4000 to spend. Determine the amounts of labor and capital that should be utilized in order to minimize the amount of space required.

Outcome 5 will be assessed through WebAssign homework, in class work, and exam questions similar to those below.
Example 1: A student must learn M unfamiliar words for an upcoming test. The rate at which the student learns is proportional to the number of items remaining to be learned, with constant of proportionality equal to k. Initially, the student knows none of the words. Let y(t) stand for the number of the words that the student knows at time t.
(a) Write down the right hand side of the differential equation satisfied by y.
(b) What is the initial value of y?
Example 2: A certain drug is administered intravenously to a patient at the continuous rate of 5 mg per hour. The patient's body removes the drug from the body at a rate that is proportional to the amount of drug in the blood. Write the amount of drug in the blood as y and let the positive constant of proportionality for the removal rate be k. Write a differential equation that is satisfied by the amount of drug in the blood.

Outcome 6 will be assessed through WebAssign homework, in class work, and exam questions similar to those below.
Example 1: The population of a city is growing exponentially. At the start of the year 2000, it had 7 million inhabitants and was growing at a rate of 200 thousand people per year.
(a) During which year will the population size reach 10 million people?
(b) At what rate will the population be growing at that time?
Example 2: A student must learn M unfamiliar words for an upcoming test. The rate at which the student learns is proportional to the number of items remaining to be learned, with constant of proportionality equal to k. Initially, the student knows none of the words. Let y(t) stand for the number of the words that the student knows at time t.
Suppose that there are 150 words to be learned and that k = 0.5 per hour for this student. Recall that the solution to
y' = k(M − y) with y(0) = 0 is given by y(t) = M(1 − e^{−kt}).
How many hours would it take the student to learn the first 22 percent of the words?
How long would it take to learn the next 22 percent of the words?
Natural Sciences Open when gep_category = NATSCI
Each course in the Natural Sciences category of the General Education Program will provide instruction and guidance that help students to:
 
 

 
 

 
 

 
 

Social Sciences Open when gep_category = SOCSCI
Each course in the Social Sciences category of the General Education Program will provide instruction and guidance that help students to:
 
 

 
 

 
 

 
 

 
 

 
 

Interdisciplinary Perspectives Open when gep_category = INTERDISC
Each course in the Interdisciplinary Perspectives category of the General Education Program will provide instruction and guidance that help students to:
 
 

 
 

 
 

 
 

 
 

 
 

 
 

 
 

Visual & Performing Arts Open when gep_category = VPA
Each course in the Visual and Performing Arts category of the General Education Program will provide instruction and guidance that help students to:
 
 

 
 

 
 

 
 

 
 

 
 

Health and Exercise Studies Open when gep_category = HES
Each course in the Health and Exercise Studies category of the General Education Program will provide instruction and guidance that help students to:
 
 

 
 

 
 

 
 

 
&
 

 
 

 
 

 
 

Global Knowledge Open when gep_category = GLOBAL
Each course in the Global Knowledge category of the General Education Program will provide instruction and guidance that help students to achieve objective #1 plus at least one of objectives 2, 3, and 4:
 
 

 
 

 
Please complete at least 1 of the following student objectives.
 

 
 

 
 

 
 

 
 

 
 

US Diversity Open when gep_category = USDIV
Each course in the US Diversity category of the General Education Program will provide instruction and guidance that help students to achieve at least 2 of the following objectives:
Please complete at least 2 of the following student objectives.
 
 

 
 

 
 

 
 

 
 

 
 

 
 

 
 

Requisites and Scheduling
100%
 
a. If seats are restricted, describe the restrictions being applied.
 
N/A
 
b. Is this restriction listed in the course catalog description for the course?
 
N/A
 
List all course pre-requisites, co-requisites, and restrictive statements (ex: Jr standing; Chemistry majors only). If none, state none.
 
P: MA 131 or MA 141
R: Credit is not allowed for both MA 231 and MA 241.
 
List any discipline specific background or skills that a student is expected to have prior to taking this course. If none, state none. (ex: ability to analyze historical text; prepare a lesson plan)
 
none
Additional Information
Complete the following 3 questions or attach a syllabus that includes this information. If a 400-level or dual level course, a syllabus is required.
 
Title and author of any required text or publications.
 

 
Major topics to be covered and required readings including laboratory and studio topics.
 

 
List any required field trips, out of class activities, and/or guest speakers.
 

All traditional sections of this course will be taught by one instructor with TA support dependent upon enrollment. All hybrid sections of this course will be run by one faculty member who will be responsible for online material and who will act as coordinator of all TAs running face-to-face classes. No additional resources will be needed.

MA 231 is the second course of a two-semester sequence in calculus, designed for students who require a brief overview of the basic concepts, including modeling and differential equations. This course has a heavy emphasis on concepts and ideas, less on manipulations and proofs. The students are in fields (textiles, forestry, economics, biological sciences) where multivariate techniques and modeling using differential equations are important tools. These form the central coverage of MA 231.


Student Learning Outcomes

After successfully completing this course, students will be able to:



  1. Use the techniques of partial differentiation to explore the properties of a function of two or more variables

  2. Set up and solve optimization problems in various contexts

  3. Use least squares to fit linear and nonlinear functions to a given data set

  4. Give examples of how and why different disciplines use differential equations and mathematical models

  5. Create a mathematical model that describes a given problem from biology, economics, or business

  6. Carry out numerical simulations and mathematical analyses of a model


Evaluation MethodWeighting/Points for EachDetails
Homework15%Before class homework will be done through WebAssign. An assignment corresponding to the online lesson will be due each week before the weekly class meeting time.
Other15%During class students will be actively working with their peers on applying the concepts learned in the online lessons to more detailed problems. Many assignments will be done through WebAssign and some may be turned in on paper. Assignments will be due after the weekly class meeting.
Participation5%The online participation score is the percent of lessons submitted. It does not take into account how many self-check questions were answered correctly.
Multiple exams40%There will be two 60 minute midterm tests.
Final Exam25%The comprehensive final exam will be 180 minutes.
TopicTime Devoted to Each TopicActivity
N/AN/AN/A

Key: 3443