MA 231 Calculus for Life and Management Sciences B

Mon-Wed-Fri 9.10 - 10.00

Class-room: 2102 SAS Hall

Instructor: Mette S Olufsen
Office: SAS 3216
Office Hours: By appointment via email.
Phone Number: 515-2678

Course Information

MA231 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 section is an Honors section and emphasis will be put on biological relevance. The course will discuss the calculus concepts in the context on biological problems, and significant focus will be put on the introduction to differential equations and modeling.

Text: Calculus and its applications by Goldstein, Schneider, Lay, Asmar (the same text as for MA231), 12th edition, Prentice-Hall, 2010.

F
ormat: The class will follow a traditional format with material discussed during lectures, combined with discussion of homework problems. Homework will use a combination of web-assign and problems from the book and from other sources. The course will include three tests (30% of grade), a group project (10% of grade), and a comprehensive final (40% of grade).
For each test and the final, students are allowed a calculator, and a sheet of notes.

Evaluation criteria:  The course will be graded based on the work performed in homework (20% of the final grade), the three tests (30% of final grade), a group project (10% of final grade), and a comprehensive final (40% of final grade).

Prerequisites: This course is the second course in the sequence, and thus MA131 is a prerequesite for this course. Since students may have had various versions of MA131, some may have gaps in the material. For students with such gaps, they are expected to read through material missed independently.

Homework:
In general homework will be due every Monday at noon unless otherwise noted.

NOTES

1.    Syllabus
2.    Least squares
3.    Matlab Newton Raphson
4.    Paper Science Sections
5.    Webassign 11.2 problem (4c)
6.    Problem 5.4 13 matlab

Test 1: 2/6 Wednesday [Test Corrections Due 1/18]
Test 2: 3/1 Friday
Test 3: 4/17 Wednesday

HOMEWORK

Homework 1 (Due Monday 1/14)
1.  Review of differentiation and integration
2.  Find 3 examples from biology of functions with 2 or 3 independent variable.
Describe in words of the dependent variable (the variable you observe) change
as a function of your independent variables.

Homework 2 (Due Wednesday 1/23)
1.  Webassign - Sections 7.2 and 7.3
2.  Problems 45-48 page 417 (supplementary exercises chapter 8)

Homework 3 (Due Monday 1/28)
1.  Webassign - Section 7.4
2.  Problems 12 and 23 pages 378-279 (problems section 7.4)

Homework 4 (Due Monday 2/4)
1.  Webassign - Section 7.5

Homework 5 (Due Monday 2/11) - CAN BE DONE IN GROUPS OF 2-3 PEOPLE
1.  Find data from your labs, some system you studied, or the web. Set up a correlation you want to investigate, and discuss that correlation.
Calculate the least squares regression line y = Ax + B, i.e., find A and B. Also calculate the least squares error Etot and discuss if your data
are correlated.

Note, this homework should be typed. It should contain an introduction discussing the data you use, where and how are they collected, and
what do you hypothesize for your correlation. Then the data should be presented in a table and in a graph. After the introduction, show calculations.
Describe what you do in a methods section, and finally include a short discussion reflecting upon your findings.

Homework 6 (Due Wednesday 2/20)
1.    Problems 28 and 30 section 11.1

Homework 7 (Due Friday 3/1)
1.    Problems 1-12 section 11.2
Use Matlab to solve these problems,
A: Give value x for which f(x) = 0
B: Plot the function and show the value of x for which f(x) = 0
C: For two of the problems show evolution with tangent lines (you can draw these on the graphs)

Homework 8 (Due Wednesday 3/20)
1.    Section 5.1  problems 1-4, 15 - 21, 29

2.    Section 5.4  problems 2-5, 9, 10, 13, 14 (for 13 and 14 if solved in Matlab you get extra credit)

Homework 9 (Due Monday 4/1) with Dfield (http://math.rice.edu/~dfield/dfpp.html)
1.    Section 10.1 problems 1, 2, 3 sketch differential equations using slope-fields. Click on one point to sketch a curve and on the graph
write what is the initial condition satisfying that point. In addition solve the problems as stated in the book.
2.    Section 10.1 problems 7-10, solve problems stated in the book using slope-fields.
3.    Section 10.2 (NOT W/ Dfield): Problems 25, 28, 29, 40

Homework 10 (Due Monday 4/8)
1.    Section 10.3 problems 9, 11, 17, 21, 23, 25, 27

Homework 11 (Due Wednesday 4/10)
1.    Section 10.4 problems 17, 18, 19, 20, 26

Homework 12 (Due Monday 4/15)
1.    Section 10.5 problems 11, 21, 29, 34, 37

Homework 13 (Due on Day of Final 5/1) [WORTH 5% OF YOUR GRADE]
EULERCODE

1.    Section 10.7 problems 7, 9,  12,  13, 16
2.    Section 10.6 problems 18,  25 [SOLVE AS DESCRIBED AND WITH EULER'S METHOD]
3.    Section 10 supplementary problems 14, 26 [SOLVE AS DESCRIBED AND WITH EULER'S METHOD]

EXTRA CREDIT

Due Friday 1/25
1.  For the objective function f(x,y) = 48 x + 28 y with the constraint xy = 600. Find values of x and y that maximize f(x,y) using methods from MA131 (sections 2.5 and 2.6).
2.  For the objective function f(x,y) = x^2 + xy - 3y^2 with the constraint g(x,y) = 3x - y - 1. Use Lagrange multiplies (section 7.4) to find values of x and y that maximize or
minimize f(x,y). Check if the point found is a maximum or minimum.

Due Monday 2/4
1.  In the least squares notes (see link above) we calculated the first order derivatives for the error, and found formulas (for our example) predicting A and B. In general
we have A = (N sum xy - sum x sum y) / (N sum x^2 - (sum x)^2) and B = (sum y - A sum x) / N, where N is the number of points. For the example we found
A = ( 3 * 38 - 6 * 17 ) / ( 3 * 14 - 6^2 ) and B = ( 17 - 2 * 6 ) / 3. Compare these equations with those you found that satisfy that dE/dA = 0 and dE/dB = 0.