MAT 171 Survey of Calculus for Management and Life Sciences

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Course Description

Functions, linear equations, the derivative and its applications, the integral and its applications, and partial derivatives.

Satisfies the General Education Quantitative Reasoning Requeirement.

Note. Students who have credit in MAT 191 (Calculus I) or its equivalent, or who have credit in a course for which Calculus I is a prerequisite, will not receive credit for MAT 271.

4 units credit.

In recent years MAT 171 has focused almost exclusively on the life sciences and applications that are important in life sciences. MAT 171 aims to give biology and life science students an overview of calculus so that they understand what calculus can do in a life-science context. and read and comprehend life science literature that uses the concepts of calculus. Students learn to use the concepts, symbols, language, and tools of calculus: rates of change, derivatives, differential equations, integration, to solve life-science problems. By the end of the course students should be able to understand life-science literature where calculus is used and communicate productively with mathematicians about life science problems.

Prerequisites

Fulfillment of ELM requirement.

Text

Calculus for the Life Sciences, a Modeling Approach. by James L. Cornette and Ralph A. Ackerman. Available from http://www.maa.org/publications/ebooks/

Course Requirements, Tentative Schedule of Class Meetings and Topics, Readings, Assignments and Due dates, Exams

A schedule of class meetings, topics, assignments, due dates, exam dates, etc. will be provided by instructor. See your class syllabus.

Here is a possible outline for the course. In this version exercises were assigned weekly and due the next week.

• 1st Week
• Modeling bacteria growth using spreadsheet.
• Difference equation for discrete bacteria growth model.
• Difference equation for depletion of light in murky water.
• 2nd Week
• Doubling time and half-life
• Quadratic equation model: mold growth.
• Model of Penicillin clearance.
• 3rd Week
• Quiz
• Algebra: Functions and simple graphs, functional notation.
• Sums, products, quotients, etc. of functions.
• Composition of functions. Inverse functions and their graphs. How to read tables backwards.
• Tangents to a graph. Slopes and rate of change, speed. The idea of the derivative.
• 4th Week
• Introduction to Geogebra http://www.geogebra.org a wonderful free program that produces very nice graphs, computes derivatives and integrals, and all kinds of other things.
• Mathematical models using derivatives.
• Derivatives of polynomials.
• Velocity, falling objects, introduce optimization.
• 5th Week
• Continuity (very lightly). Chain rule. Applications.
• 6th Week
• Test.
• Optimization problems.
• Implicit differentiation (very lightly).
• 7th Week
• Derivatives of exponential functions.
• e and the natural logarithm.
• John Napier 8th Laird of Merchistoun (1550-1617), inventor of logarithms.
• 8th Week
• 9th Week
• Product and quotient rules.
• 10th Week
• More chain rule problems; applications.
• Derivatives of inverse functions.
• Review.
• 11th Week
• Test
• With spreadsheets, modeling the spread of disease: S-I-R model, copied from the textbook Calculus In Context by J. Callahan, K. Hoffman, D Cox, D. O'Shea, H. Pollatsek, L Senechal. Five Colleges, Inc. 2008, pages 1-27.
• Maxima and minima, shape of graph and derivatives.
• 12th Week
• Max-min problems cont.
• Modeling Lotka-Volterra Predator-prey equation with spreadsheets and numerical differential equation solver.
• 13th Week
• Integration: solve the differential equation $$\frac{dg}{dx}=f(x)$$ where $$f$$ is a known function. Elementary interpretation: find position given speed of travel. Connection between this and finding an area.
• Notation for integration $$\int f(x) \,dx$$ and $$\int_a^b f(x) \,dx$$.
• The fundamental theorem of calculus and some applications.
• 14th Week
• Slope fields, another way to visualize differential equations.
• 15th Week
• Review.

The final exam is given at the date and time announced in the Schedule of Classes.

Learning Objectives

After completing MAT 171 the student will be able to

• Model population growth problems using discrete and continuous methods
• Demonstrate understanding of and work with linear, quadratic, exponential and logarithmic functions and use them in applied problems.
• Demonstrate understanding of the meaning of derivatives and compute the derivative of algebraic, exponential and logarithmic functions of one variable.
• Use derivatives to solve problems in population biology, optimization, and related rates.
• Use mathematical notation from calculus to describe problems involving rates of change.
• Solve simple differential equations e.g. y'(t)=ry(t) and y'(t)=f(t) where r is constant and f is given, interpret them in terms of rates of change, and recognize problems in which they arise.
• Approximate solutions of differential equations graphically using slope fields.
• Demonstrate understanding of the meanings of indefinite and definite integrals and fundamental theorem of calculus, use integrals to solve applied problems.
• Use calculators or computers to evaluate complex expressions, use spreadsheets to model dynamic problems where several interrelated things are changing e.g. spread of epidemics.

Computers and Calculators, Computer Literacy

Most instructors encourage the use of machines, calculators computers, phones etc., for analyzing data. The use of machines may be restricted during examinations or at certain other times. Ask your instructor for the policy in your class.

Students are not expected to be programmers or to know any particular computer language before starting this class. Some instructors may expect students to be able to access information on the internet, or to use calculators, or to learn to use particular software with instruction. Basic skill in algebra and the use of mathematical symbols, order of operations etc., and the willingness to read and follow instruction manuals and help files will suffice.

Students' grades are based on homework, class participation, short tests, and scheduled examinations covering students' understanding of the topics covered in this course. The instructor determines the relative weights of these factors and the grading scale. See the syllabus for your particular class.

Location of Class Meetings

Classes meet on the dates and room announced in the official Schedule of Classes. This is a traditional, face-to-face class.

Attendance Requirements

Attendance policy is set by the instructor.

Policy on Due Dates, Make-Up Work, Missed Exams, and Extra-Credit Assignments

Due dates and policy regarding make-up work and missed exams are set by the instructor. Instructors may, or may not, choose to offer extra credit assignments. If extra credit assignments are offered they will be available to all students.

The mathematics department does not tolerate cheating. Students who have questions or concerns about academic integrity should ask their professors or the counselors in the Student Development Office, or refer to the University Catalog for more information. (Look in the index under "academic integrity".)

Accomodations for Students with Disabilities

Cal State Dominguez Hills adheres to all applicable federal, state, and local laws, regulations, and guidelines with respect to providing reasonable accommodations for students with temporary and permanent disabilities. If you have a disability that may adversely affect your work in this class, I encourage you to register with Disabled Student Services (DSS) and to talk with me about how we best can help you. All disclosures of disabilities will be kept strictly confidential. Please note: you must register with DSS to arrange an no accommodation. For information call (310) 243-3660 or send an email message to dss@csudh.edu or visit the DSS website http://www4.csudh.edu/dss/contact-us/index or visit their office WH D-180

Behavioral Expectations

We all are adults so behavior rarely is an issue. Just follow the Golden Rule: "do unto others as you would have them do unto you" then everything will be fine.

The university must maintain a classroom environment that is suitable for learning, so anyone who insists on disrupting that environment will be expelled from the class.

Revision history:

Prepared by C. Chang 3/10/01. Revised 7/7/01, 7/25/06, 1/7/15 (G. Jennings).