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)

Distance Education (DELTA)

Hybrid (Online/Face to Face)

Grading Method

Graded with S/U option

3

16

Contact Hours

(Per Week)

(Per Week)

Component Type | Contact Hours |
---|---|

Lecture | 3.0 |

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 Component | Per Semester | Per Section | Multiple Sections? | Comments |
---|---|---|---|---|

Lecture | 300 | 30 | Yes | N/A |

Delivery Format | Per Semester | Per Section | Multiple Sections? | Comments |
---|---|---|---|---|

LEC | 30 | 30 | No | N/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 Code | Program Title | Required or Elective? |
---|---|---|

see attached | see attachment | Required |

see attached | see attachment | Elective |

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

Each course in the Humanities category of the General Education Program will provide instruction and guidance that help students to:

Obj. 1) Engage the human experience through the interpretation of culture.

Obj. 2): Become aware of the act of interpretation itself as a critical form of knowing in the humanities.

Obj. 3) Make academic arguments about the human experience using reasons and evidence for supporting those reasons that are appropriate to the humanities.

Each course in the Mathematial Sciences category
of the General Education Program will provide instruction and
guidance that help students to:

Obj. 1) Improve and refine mathematical problem-solving abilities.

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 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?

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?

Obj. 2) Develop logical reasoning skills.

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 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?

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?

Each course in the Natural Sciences category
of the General Education Program will provide instruction and
guidance that help students to:

Obj.O 1) Use the methods and processes of science in testing hypotheses, solving problems and making decisions

Obj. 2) Make inferences from and articulate, scientific concepts, principles, laws, and theories, and apply this knowledge to problem solving.

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

Obj. 1) Examine at least one of the following: human behavior, culture, mental processes, organizational processes, or institutional processes.

Obj. 2) Demonstrate how social scientific methods may be applied to the study of human behavior, culture, mental processes, organizational processes, or institutional processes.

Obj. 3) Use theories or concepts of the social sciences to analyze and explain theoretical and or real-world problems, including the underlying origins of such problems.

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

Obj. 1) Distinguish between the distinct approaches of two or more disciplines.

Obj. 2) Identify and apply authentic connections between two or more disciplines.

Obj. 3) Explore and synthesize the approaches or views of two or more disciplines.

1. Which disciplines will be synthesized, connected, and/or considered in this course?

Each course in the Visual and Performing Arts category of the General Education Program will provide instruction and guidance that help students to:

Obj. 1) Deepen their understanding of aesthetic, cultural, and historical dimensions of artistic traditions.

Obj. 2) Strengthen their ability to interpret and make critical judgements about the arts through the analysis of structure, form, and style of specific works.

Obj. 3) Strengthen their ability to create, recreate, or evaluate art based upon techniques and standards appropriate to the genre.

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

Obj. 1) Acquire the fundamentals of health-related fitness, encompassing cardio-respiratory and cardiovascular endurance, muscular strength and endurance, muscular flexibility and body composition.

Obj. 2) Apply knowledge of the fundamentals of health-related fitness toward developing, maintaining, and sustaining an active and healthy lifestyle.

Obj. 3) Acquire or enhance the basic motor skills and skill-related competencies, concepts, and strategies used in physical activities and sport.

Obj. 4) Gain a thorough working knowledge, appreciation, and understanding of the spirit and rules, history, safety, and etiquette of physical activities and sport.

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:

Obj. 1) Identify and examine distinguishing characteristics, including ideas, values, images, cultural artifacts, economic structures, technological or scientific developments, and/or attitudes of people in a society or culture outside the United States.

Obj. 2) Compare these distinguishing characteristics between the non-U.S. society and at least one other society.

Obj. 3) Explain how these distinguishing characteristics relate to their cultural and/or historical contexts in the non-U.S. society.

Obj. 4) Explain how these disinguishing characteristics change in response to internal and external pressures on the non-U.S. society.

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:

Obj. 1) Analyze how religious, gender, ethnic, racial, class, sexual orientation, disability, and/or age identities are shaped by cultural and societal influences.

Obj. 2) Categorize and compare historical, social, political, and/or economic processes producing diversity, equality, and structured inequalities in the U.S.

Obj. 3) Interpret and evaluate social actions by religious, gender, ethnic, racial, class, sexual orientation, disability, and/or age groups affecting equality and social justice in the U.S.

Obj. 4) Examine interactions between people from different religious, gender, ethnic, racial, class, sexual orientation, disability, and/or age groups in the U.S.

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.

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

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:

- Use the techniques of partial differentiation to explore the properties of a function of two or more variables
- Set up and solve optimization problems in various contexts
- Use least squares to fit linear and nonlinear functions to a given data set
- Give examples of how and why different disciplines use differential equations and mathematical models
- Create a mathematical model that describes a given problem from biology, economics, or business
- Carry out numerical simulations and mathematical analyses of a model

Evaluation Method | Weighting/Points for Each | Details |
---|---|---|

Homework | 15% | 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. |

Other | 15% | 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. |

Participation | 5% | 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 exams | 40% | There will be two 60 minute midterm tests. |

Final Exam | 25% | The comprehensive final exam will be 180 minutes. |

Topic | Time Devoted to Each Topic | Activity |
---|---|---|

N/A | N/A | N/A |

Key: 3443