STEM Program Department of Math and Computer Science Lansing Community College Prof. Jing Wang, Ph. D.
Dec 18, 2015
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