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
Email address: msolufse@ncsu.edu
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.
Format: 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
TESTS (30% of final grade)
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.
GRADES
Homework 20%
Tests 30%
Project 10%
Final 40%
This page was last modified January 4th 2013.