! ROCHESTER INSTITUTE OF TECHNOLOGY COURSE OUTLINE FORM COLLEGE OF SCIENCE School of Mathematical Sciences New Revised COURSE: COS-MATH-186 Mathematics of Graphical Simulation II 1.0 Course designations and approvals: Required Course Approvals: Approval Approval Request Date Grant Date Academic Unit Curriculum Committee 10-20-10 10-27-10 College Curriculum Committee 11-01-10 11-17-10 Optional Course Designations: Yes No General Education Writing Intensive Honors Approval Request Date Approval Grant Date 2.0 Course information: Course Title: Mathematics of Graphical Simulation II Credit Hours: 3 Prerequisite(s): COS-MATH-185 or equivalent Co-requisite(s): None Course proposed by: School of Mathematical Sciences Effective date: Fall 2013 Contact Hours Maximum Students/section Classroom 3 35 Lab Workshop Other (specify) 2.1 Course conversion designation: (Please check which applies to this course) Semester Equivalent (SE) to: Semester Replacement (SR) to: New 2.2 Semester(s) offered: Fall Spring Summer Offered every other year only Other Page 1 of 5
2.3 Student requirements: Students required to take this course: (by program and year, as appropriate) First-year Game Design and Development majors Students who might elect to take the course: Information Technology majors 3.0 Goals of the course: (including rationale for the course, when appropriate) 3.1 To learn the basic definitions, concepts, rules, vocabulary, and mathematical notation of analytic geometry and calculus. 3.2 To practice the necessary manipulative skills required for solving problems in analytic geometry and calculus. 3.3 To provide the background necessary to study Game Design and Development. 4.0 Course description: (as it will appear in the RIT Catalog, including pre- and co-requisites, semesters offered) COS-MATH-186 Mathematics of Graphical Simulation II This is the second part of a two-course sequence that aims at providing the mathematical tools needed to manipulate graphical objects and to model and simulate the physical properties of these objects. Topics from linear algebra, primarily in two and three dimensional space, analytic geometry, and calculus will be presented. The emphasis is on analytic geometry and calculus, as applied to geometric and physical simulations. (COS-MATH-185) Class 3, Credit 3 (F) 5.0 Possible resources: (texts, references, computer packages, etc.) 5.1 Douglas F. Riddle, Analytic Geometry, PWS Publishing Company, Pacific Grove, CA. 5.2 James M. Van Berth and Lars M. Bishop, Essential Mathematics for Games and Interactive Applications: A Programmers Guide, Morgan Kaufmann, San Francisco, CA. 5.3 David Eberly, Game Physics, Morgan Kaufmann, San Francisco, CA. 5.4 M. Weir and J. Hass, Thomas Calculus: Early Transcendentals, Addison-Wesley, Reading, MA. 5.5 Steven G. Krantz, Calculus Demystified, McGraw-Hill, Columbus, OH. 6.0 Topics: (outline) Topics with an asterisk(*) are at the instructor s discretion, as time permits 6.1 Analytic Geometry and Coordinate Systems 6.1.1 Curves and conic sections in the plane 6.1.2 Translation and rotation of curves and regions 6.1.3 Parametric equations 6.1.4 Polar coordinates 6.1.5 Curves and surfaces in space 6.1.6 Cylindrical and spherical coordinates 6.1.7 Barycentric coordinates Page 2 of 5
6.2 Derivatives of Functions 6.2.1 Limits 6.2.2 Rules of differentiation 6.2.3 Tangent lines 6.2.4 Higher order derivatives 6.2.5 Implicit differentiation 6.3 Derivatives of Vector Valued Functions 6.3.1 Rates of change of functions and vectors 6.3.2 Motion: velocity and acceleration 6.3.3 The derivative as it relates to the shape of curves 6.3.4 Tangent and normal vectors of curves in R 3 6.4 The Integral and its Applications 6.4.1 Definition of the integral and computation of areas 6.4.2 Motion: distance traveled 6.4.3 Work 6.5 Functions of Several Variables 6.5.1 Limits 6.5.2 Partial derivatives 6.5.3 Directional derivatives and the gradient vector 6.5.4 Tangent planes 7.0 Intended learning outcomes and associated assessment methods of those outcomes: Assessment Methods Learning Outcomes 7.1 Acquire the basic definitions, concepts, rules, vocabulary, and mathematical notation of analytic geometry and calculus 7.2 Demonstrate the skills needed to apply calculus to graphical objects and physical simulation 8.0 Program goals supported by this course: 8.1 To develop an understanding of the mathematical framework that supports engineering, science, and mathematics. 8.2 To develop critical and analytical thinking. Page 3 of 5
8.3 To develop an appropriate level of mathematical literacy and competency. 8.4 To provide an acquaintance with mathematical notation used to express physical and natural laws. 9.0 General education learning outcomes and/or goals supported by this course: Assessment Methods General Education Learning Outcomes 9.1 Communication Express themselves effectively in common college-level written forms using standard American English Revise and improve written and visual content Express themselves effectively in presentations, either in spoken standard American English or sign language (American Sign Language or English-based Signing) Comprehend information accessed through reading and discussion 9.2 Intellectual Inquiry Review, assess, and draw conclusions about hypotheses and theories Analyze arguments, in relation to their premises, assumptions, contexts, and conclusions Construct logical and reasonable arguments that include anticipation of counterarguments Use relevant evidence gathered through accepted scholarly methods and properly acknowledge sources of information 9.3 Ethical, Social and Global Awareness Analyze similarities and differences in human experiences and consequent perspectives Examine connections among the world s populations Identify contemporary ethical questions and relevant stakeholder positions 9.4 Scientific, Mathematical and Technological Literacy Explain basic principles and concepts of one of the natural sciences Apply methods of scientific inquiry and problem solving to contemporary issues Comprehend and evaluate mathematical and statistical information Page 4 of 5
Assessment Methods General Education Learning Outcomes Perform college-level mathematical operations on quantitative data Describe the potential and the limitations of technology Use appropriate technology to achieve desired outcomes 9.5 Creativity, Innovation and Artistic Literacy Demonstrate creative/innovative approaches to coursebased assignments or projects Interpret and evaluate artistic expression considering the cultural context in which it was created 10.0 Other relevant information: (such as special classroom, studio, or lab needs, special scheduling, media requirements, etc.) None Page 5 of 5