stem program department of math and computer science lansing community college prof. jing wang, ph....

STEM ProgramDepartment of Math and Computer Science

Lansing Community College

Prof. Jing Wang, Ph. D.

MATH after 112 STEM Programs

Calculus Sequence:

MATH 151: Calculus I

MATH 161: Honors Calculus I

Math 152: Calculus II

Math 162: Honors Calculus II

Math 253: Calculus III

MATH 126

Accelerated Precalculus

MATH 112

Intermediate 

Algebra

or

High School Graduates

MATH 122

Precalculus II

MATH 121

Precalculus I

Math 254: Diff Equation

Math 260: Linear Algebra

Computer Science

CPSC 131: MATLAB

CPSC 230: C++

CPSC 231: Data Structures

CPSC 260: Computer Science Structures

Degree/Curriculum

MathematicsEngineering/PhysicsComputer Science

Math 281: Honors Seminar

Calculus Projects

Problems adapted from Stewart’s Calculus: Concepts and Contexts, 4e

Calculus I Project: Rates of ChangePurpose: Apply Differential Calculus to Authentic Problems Theme: Blood Flow in Human Body

www.nhlbi.nih.gov

Figure from Stewart’s Calculus: Concepts and Contexts, 4e

Assignments

Figure from Stewart’s Calculus: Concepts and Contexts, 4e

Figure from Stewart’s Calculus: Concepts and Contexts, 4e

Calculus II Project: Applying Integrals

Calculus

Figure from Stewart’s Calculus: Concepts and Contexts, 4e

Calculus II Project: Applying Integral

Calculus

Calculus III Project: Modeling Tumors using Bumpy

and Wrinkled Spheres

www.valstarsolution.com/images/turb.jpg

Student WorkZach RichardsonMath 253 ProjectFall 2012 Assignment 1

n = 10 n = 25 n=5

As n grows larger, more wedges protrude from the service of the sphere. The number of wedges appears to be equal to the value of n.

Assignment 2

m = 3 m = 7 m = 30

The value of m seems to shift horizontal sections of the sphere alternately so that they appear “off center”. As m grows larger, there are more such shifted sections.

Student WorkAssignment 3

(2,3) (8,4) (6,5)

Rather than dividing the sphere vertically or horizontally, when both n and m vary the sphere becomes deformed by bumps which could be caused by the two types of wedges intersecting. The number of bumps appears to be dependent on the product of n and m so if you know their values you can predict how many bumps there will be.

Assignment 4

b = .4 b = .6 b = .8 b = 1

As b grows larger, the space between the bumps, the valleys, becomes more pronounced and seems to cut deeper into the sphere.

Zach RichardsonMath 253 ProjectFall 2012

Student WorkAssignment 5

a = .5 a = 5 a = 50 a = 500

As a grows larger, the valleys grow less noticeable and soon appear to disappear altogether. Also, as a increases so does the radius of the sphere. When a > 5b the valleys are either gone or extremely shallow. When 5b > a the valleys become more noticeable as the difference between the two increases.

Result from doing this project:Students should realize the importance of spherical coordinates. Gain experience analyzing a family of functions. Appreciate the power of computer software programs such as mathematica .

Zach RichardsonMath 253 ProjectFall 2012