! ROCHESTER INSTITUTE OF TECHNOLOGY COURSE OUTLINE FORM COLLEGE OF SCIENCE School of Mathematical Sciences New Revised COURSE: COS-MATH-221 Multivariable and Vector Calculus 1.0 Course designations and approvals: Required Course Approvals: Approval Approval Request Date Grant Date Academic Unit Curriculum Committee 4-08-10 5-12-10 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: Multivariable and Vector Calculus Credit Hours: 4 Prerequisite(s): C or better in COS-MATH-182 or -182a or -173 Co-requisite(s): None Course proposed by: School of Mathematical Sciences Effective date: Fall 2013 Contact Hours Maximum Students/section Classroom 4 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: 1016-305 and parts of 1016-328 and 1016-410 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) Second-year Electrical Engineering, Imaging Science, and Mathematics majors Students who might elect to take the course: Chemistry, Engineering Technology, Business Administration, and Information Technology majors as well as others who want to continue the study of calculus 3.0 Goals of the course: (including rationale for the course, when appropriate) 3.1 To develop an understanding and ability to work with the topics of the calculus of functions of more than one variable and vector-valued functions. 3.2 To provide knowledge and appreciation of calculus as a tool in solving applied physical problems. 3.3 To provide a background in mathematics which can be used for the study of science and engineering. 3.4 To examine the major theorems of vector calculus. 4.0 Course description: (as it will appear in the RIT Catalog, including pre- and co-requisites, semesters offered) COS-MATH-221 Multivariable and Vector Calculus This course is principally a study of the calculus of functions of two or more variables, but also includes a study of vectors, vector-valued functions and their derivatives. The course covers limits, partial derivatives, multiple integrals, Stokes Theorem, Green s Theorem, the Divergence Theorem, and applications in physics. Credit cannot be granted for both this course and COS-MATH-219. (C or better in COS-MATH-182 or -182a or -173) Class 4, Credit 4 (F, S, Su) 5.0 Possible resources: (texts, references, computer packages, etc.) 5.1 M. Weir and J. Hass, Thomas Calculus Early Transcendentals, Addison-Wesley, Reading, MA. 5.2 Schey, H. M., Div, Grad, Curl, and All That, Norton, New York, NY. 5.3 Hubbard, J. H. and Hubbard, B. B., Vector Calculus, Linear Algebra, and Differential Forms: A Unified Approach, Prentice Hall, Upper Saddle River, NJ. 5.4 Davis, H. F. and Snider, A. D., Introduction to Vector Analysis, Allyn & Bacon, Boston, MA. 6.0 Topics: (outline) Topics with an asterisk(*) are at the instructor s discretion, as time permits 6.1 Vectors and the Geometry of Space 6.1.1 Three-dimensional coordinate systems 6.1.2 Vectors 6.1.3 The dot product 6.1.4 The cross product Page 2 of 5
6.1.5 Parametric and symmetric equations of lines in space 6.1.6 Equations of planes in space 6.2 Vector-valued Functions 6.2.1 Vector functions and curves in space 6.2.2 Derivatives and integrals of vector functions 6.2.3 Arclength, curvature, and normal vectors of curves in space* 6.2.4 Tangential and normal components of acceleration* 6.3 Partial Derivatives 6.3.1 Functions of several variables 6.3.2 Limits and continuity 6.3.3 Partial derivatives 6.3.4 The chain rule 6.3.5 Directional derivatives and the gradient vector 6.3.6 Tangent planes and linear approximations 6.3.7 Extremal values and saddle points 6.3.8 Lagrange multipliers* 6.4 Multiple Integrals 6.4.1 Double integrals over rectangles 6.4.2 Iterated integrals 6.4.3 Double integrals over general regions 6.4.4 Double integrals in polar coordinates 6.4.5 Applications of double integrals* 6.4.6 Triple integrals in rectangular, cylindrical and spherical coordinates 6.5 Vector Calculus and Integral Theorems 6.5.1 Divergence 6.5.2 Curl 6.5.3 Line integrals 6.5.4 Work, circulation, and flux via line integrals 6.5.5 Potentials, conservative fields, and path independence 6.5.6 Green s theorem in the plane 6.5.7 Surfaces, area and surface integrals 6.5.8 Stokes theorem 6.5.9 The Divergence theorem 7.0 Intended learning outcomes and associated assessment methods of those outcomes: Page 3 of 5
Assessment Methods Learning Outcomes 7.1 Use the basic definitions, concepts, rules, vocabulary, and mathematical notation of multivariable and vector calculus 7.2 Demonstrate the necessary manipulative skills required to solve problems in multivariable and vector calculus 7.3 Use differentiation and integration techniques for algebraic and transcendental multivariable functions 7.4 Apply multivariable calculus and vector calculus as tools to solve physical problems 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. 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 Page 4 of 5
Assessment Methods General Education Learning Outcomes 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 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.) Smart classroom Page 5 of 5