Instructor: Mette S Olufsen

Office: SAS 3216

Office Hours: By appointment via email.

Phone Number: 515-2678

Email address: msolufse@ncsu.edu

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.

2. Least squares

3. Matlab Newton Raphson

4. Paper Science Sections

5. Webassign 11.2 problem (4c)

6. Problem 5.4 13 matlab

Test 2: 3/1 Friday

Test 3: 4/17 Wednesday

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)

2. Problems 12 and 23 pages 378-279 (problems section 7.4)

Homework 5 (Due Monday 2/11) - CAN BE DONE IN GROUPS OF 2-3 PEOPLE

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.

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)

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

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

EULERCODE

1. Section 10.7 problems 7, 9, 12, 13, 16

2. Section 10.6 problems 18, 25 [SOLVE AS DESCRIBED

3. Section 10 supplementary problems 14, 26 [SOLVE AS DESCRIBED

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.

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.

Homework 20%

Tests 30%

Project 10%

Final 40%