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. 3 hrs. lecture and 2 hrs. lab/wk.

Associated Costs: These are additional (out-of-pocket) expense considerations that students should expect in addition to the course tuition, fees, and textbooks. $0 to $100.

Supplies: Refer to the instructor’s course syllabus for details about any supplies that may be required.

Textbook(s): For information see - http://bookstore.jccc.net

Course Fees: NONE

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.

Content Outline & Competencies:

I. Basic Math
   A. Write the equations of circles, lines, planes and spheres.
   B. Determine if two circles or two spheres are intersecting.
   C. Use trigonometry to determine the components of a vector and the
angle produced by a vector.
   D. Analyze a trigonometric function for amplitude and period.
   E. Convert between polar and rectangular coordinates.
   F. Convert units of measurement.
   G. Construct code that will detect collisions between circles, lines,
planes and spheres.
 
II. Vectors
   A. Compare the concepts of scalar and vector.
   B. Add and subtract vectors.
   C. Multiply vectors by scalars.
   D. Normalize vectors.
   E. Find dot products and cross products of vectors.
   F. Find the angle between two vectors.
   G. Find the normal vector to a surface.
   H. Construct code that will perform vector arithmetic and
normalization.
 
III. Matrices
   A. Add, subtract, and multiply matrices.
   B. Multiply matrices by scalars.
   C. Describe translations using matrices and homogeneous coordinates.
   D. Describe scalings using matrices and homogeneous coordinates.
   E. Describe rotations using matrices and homogeneous coordinates.
   F. Construct code that will perform scaling, rotation, and translations
on vectors and geometric objects.
 
IV. Linear Motion
   A. Compute distance, displacement, velocity, speed, and acceleration
for one-dimensional motion.
   B. Use vectors to describe displacements, velocities, and accelerations
in two and three dimensions.
   C. Write equations which model the motion of projectiles.
   D. Use Newton's Laws to determine the effect of forces on the motion of
an object.
   E. Solve for the motion of an object 
   F. Calculate the work done by a force on an object.
   G. Calculate the kinetic energy, potential energy, and momentum of an
object.
   H. Use conservation of energy and conservation of momentum to model the
collision of objects.
   I. Construct code that can simulate the motion of a projectile.
   J. Construct code that can simulate the motion of an object according
to Newton’s Laws of Motion.
   K. Construct code that can simulate the collision between two objects.
 
V. Rotational Motion
   A. Compute angular displacement, angular velocity, and angular
acceleration.
   B. Determine the angular motion caused by a torque on an object.
   C. Find the kinetic energy and angular momentum of a rotating object.
   D. 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.

Methods of Evaluation of Competencies:

Evaluation of student mastery of course competencies will be accomplished using the following methods:

40-80% Unit Exams, Unit Papers, and/or Unit Projects
10-50% Homework, Quizzes, and/or Small Projects
10-40% Final Exam

The final exam must count at least as much as any unit exam, unit paper or
unit project. In any course where unit exams are not proctored, the
instructor may require that the student score at least a 70% on the final
exam to earn a ‘C’ for the course. At the instructor's discretion, the
grade on all or any part of the final exam may replace any lower test
score. No student may be exempt from the final exam.  Any student not
taking the final exam will receive a score of zero for the final
exam.

Caveats:

1. The majority of mathematics courses are sequential. Students must earn a grade of C or higher in a prerequisite mathematics course to progress to its subsequent mathematics course.
2. Computer Literacy Expectations: Students will need basic word processing, Internet searching, and C++ coding skills for the completion of some papers, exercises and projects.
3. 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.

Disabilities:

If you are a student with a disability, and if you will be requesting accommodations, it is your responsibility to contact Access Services. Access Services will recommend any appropriate accommodations to your professor and his/her director. The professor and director will identify for you which accommodations will be arranged.

JCCC provides a range of services to allow persons with disabilities to participate in educational programs and activities. If you desire support services, contact the office of Access Services for Students With Disabilities (913) 469-8500, ext. 3521 or TDD (913) 469-3885. The Access Services office is located in the Success Center on the second floor of the Student Center.