STEM Program Department 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 Mathematics Engineering/Physics Computer Science Math 281: Honors Seminar

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

Calculus I Project: Rates of Change Calculus I Project: Rates of Change Purpose: Apply Differential Calculus to Authentic Problems Theme: Blood Flow in Human Body Figure from Stewart’s Calculus: Concepts and Contexts, 4e

Assignments

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

Student Work Zach Richardson Math 253 Project Fall 2012 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. 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 Work 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. As b grows larger, the space between the bumps, the valleys, becomes more pronounced and seems to cut deeper into the sphere. Zach Richardson Math 253 Project Fall 2012

Student Work Assignment 5 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 Richardson Math 253 Project Fall 2012