MATH/PHYS 191 – Math & Physics for Games I

Syllabus

Credit Hours: 4.0
Lecture: MWF 2:00 to 2:50 in RC 380
Lab: M 3:00 to 4:50 in RC 380

Instructors:

  • Rob Grondahl, CLB 202 (By the Coffee Shop), 469-8500 x2802, email: ude.cccj|lhadnorgr#ude.cccj|lhadnorgr.
  • J. Douglas Patterson, CLB 302, 469-8500 x4268, e-mail: ude.cccj|rettapd#ude.cccj|rettapd.

Office Hours:

  • Grondahl: MTWRF 12:00-12:50pm;
  • JDP: MWF 1-2pm; TR 8am-9pm

Course Description:
This introductory course focuses on the mathematics and physics concepts needed to program a variety of video game scenarios. Students will learn to use vectors and matrix transformations to model the motion of physical objects in two and three dimensions. Students will also learn various computer programming methods in order to model these mathematical and physical concepts.

Prerequisites:
MATH 171 (College Algebra) or MATH 173 (Precalculus) with grade of ‘C’ or higher or appropriate score on the math assessment test. GAME 121 (Programming Algorithms Using C# or C++) or equivalent programming experience.

Text: You're looking at it! This wiki will be the location for all of the textbook and laboratory material.

Supplies: Calculator with trigonometric functions, your brain.

Course Objectives: Upon successful completion of this course, the student should be able to:

  1. Use coordinates and vectors to describe objects and space in two and three dimensions.
  2. Use matrices to transform between coordinate systems.
  3. Model particle and rigid body kinetics.
  4. Use the principles of physics to model the motion and collision of objects.
  5. Create programs which simulate the motion and collision of objects.

Course Competencies:
A. Basic Math

  1. Write the equations of circles, lines, planes and spheres.
  2. Determine if two circles or two spheres are intersecting.
  3. Use trigonometry to determine the components of a vector and the angle produced by a vector.
  4. Analyze a trigonometric function for amplitude and period.
  5. Convert between polar and rectangular coordinates.
  6. Convert units of measurement.
  7. Construct code that will detect collisions between circles, lines, planes and spheres.

B. Vectors

  1. Compare the concepts of scalar and vector.
  2. Add and subtract vectors.
  3. Multiply vectors by scalars.
  4. Normalize vectors.
  5. Find dot products and cross products of vectors.
  6. Find the angle between two vectors.
  7. Find the normal vector to a surface.
  8. Construct code that will perform vector arithmetic and normalization.

C. Matrices

  1. Add, subtract, and multiply matrices.
  2. Multiply matrices by scalars.
  3. Describe translations using matrices and homogeneous coordinates.
  4. Describe scaling using matrices and homogeneous coordinates.
  5. Describe rotations using matrices and homogeneous coordinates.
  6. Construct code that will perform scaling, rotation, and translations on vectors and geometric objects.

D. Linear Motion

  1. Compute distance, displacement, velocity, speed, and acceleration for one-dimensional motion.
  2. Use vectors to describe displacements, velocities, and accelerations in two and three dimensions.
  3. Write equations which model the motion of projectiles.
  4. Use Newton's Laws to determine the effect of forces on the motion of an object.
  5. Solve for the motion of an object
  6. Calculate the work done by a force on an object.
  7. Calculate the kinetic energy, potential energy, and momentum of an object.
  8. Use conservation of energy and conservation of momentum to model the collision of objects.
  9. Construct code that can simulate the motion of a projectile.
  10. Construct code that can simulate the motion of an object according to Newton’s Laws of Motion.
  11. Construct code that can simulate the collision between two objects.

E. Rotational Motion

  1. Compute angular displacement, angular velocity, and angular acceleration.
  2. Determine the angular motion caused by a torque on an object.
  3. Find the kinetic energy and angular momentum of a rotating object.
  4. Construct code that can model the three-dimentional motion of a rigid body incorporating the concepts of the conservation of energy and momentum, and Newton’s Laws of Motion.

Course Requirements:
Lectures:
The lecture will consist of traditional instructive lectures, class discussions, video material, and laboratory demonstrations. Not all material in the lecture will appear in the text and not all material in the text will be discussed in the lecture. Students are responsible for material covered in lecture as well as in the text.

Homework:
Homework will be assigned and collected daily. Doing the homework problems is just as essential to success in this course as daily practice is in sports. No late homework will be accepted.

Labs:
There will be 12 weekly laboratory assignments. A written lab report will be due at the beginning of the next lab session. No late lab reports will be accepted. There will be no make-up labs during the semester except if the lab was missed because of an excused absence as described in the Student Handbook.

Tests:
There will be four unit tests and a final exam. Unit tests will cover material from lecture, homework, lab, and the text. The final exam will be comprehensive.

Grading Standards:
Grades will be based upon the following:

Assignment Points Possible
Homework 160 pts.
Lab Reports 12 x 20 240 pts.
Unit Tests, 4 x 100 400 pts.
Final Exam 200 pts.
Total 1000 pts.

Letter grades will be assigned as follows:

  • 90 - 100% = A
  • 80 - 89% = B
  • 70 - 79% = C
  • 60 - 69% = D
  • below 60% = F

CAVEATS:
The majority of mathematics and physics courses are sequential. Students must earn a grade of C or higher in a prerequisite course to progress to its subsequent course.

In accordance with the assertion made on your billing statement, during the first two weeks of the semester, if a student is found not to have successfully fulfilled the prerequisite(s) for this course, the student will be dropped from the course. He/she will be allowed to enroll in the appropriate lower level course on a space available basis with an even exchange of tuition. After the first two weeks, students who have not met the prerequisite(s) will be dropped from the course with no refund of tuition.
Computer Literacy Expectations:
Students will need basic word processing and Internet searching skills for the completion of some papers, exercises and projects.

Academic Dishonesty Policy Statement:
Academic dishonesty will not be tolerated and will be subject to the appropriate penalties. Please make every effort to avoid the appearance of dishonesty in all course activities. All cases of academic dishonesty will be brought to the attention of the Program Director for the Division.

Disability Statement:
JCCC provides a range of services to allow persons with disabilities to participate in educational programs and activities. If you are a student with a disability and if you are in need of accommodations or services, it is your responsibility to contact Access Services and make a formal request. To schedule an appointment with an Access Advisor or for additional information, you can contact Access Services at (913) 469-3521 or ude.cccj|secivresssecca#ude.cccj|secivresssecca. Access Services office is located in the Success Center on the second floor of the Student Center.

Math and Science Resource Centers:
There are resource centers for both math and science help with free tutoring available on demand. The Math Resource Center is located in CLB 212, and the Science Resource Center is located in CLB 112. These resource centers are not free, you've ALREADY PAID FOR THEM! Be sure to get your money's worth!

Tentative Course Schedule
The tentative schedule of lecture topics, lab assignments, and exam dates can be found on the schedule page.

Building Emergency Plan
http://www.jccc.edu/about/campus/maps/buildings/rc.html

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