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

2. 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

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

4. 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 www.nhlbi.nih.gov Figure from Stewart’s Calculus: Concepts and Contexts, 4e

5. Assignments

6. Calculus II Project: Applying Integrals Calculus Figure from Stewart’s Calculus: Concepts and Contexts, 4e

7. Calculus II Project: Applying Integral Calculus

8. Calculus III Project: Modeling Tumors using Bumpy and Wrinkled Spheres www.valstarsolution.com/images/turb.jpg

9. 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.

10. 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

11. 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