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