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Course Catalog - North Carolina School of Science and Mathematics

Course Catalog - North Carolina School of Science and Mathematics

Course Catalog - North Carolina School of Science and Mathematics

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MATHEMATICSMA480 Vector Functions <strong>and</strong> PartialDerivativesOne trimester (1 unit <strong>of</strong> credit)Prerequisite: MA434 AP Calculus BC (AdvancedTopics III) <strong>and</strong> permission <strong>of</strong> the Dean <strong>of</strong> <strong>Mathematics</strong>.Meeting pattern: 4 periods per weekThis is the first half <strong>of</strong> a university-level course in multivariablecalculus. This course includes the theory <strong>and</strong> application <strong>of</strong>vector functions <strong>and</strong> partial derivatives. Topics include a vectorapproach to regression modeling, the Frenet-Serret equations,continuity <strong>and</strong> differentiability <strong>of</strong> functions <strong>of</strong> several variables,gradients <strong>and</strong> directional derivatives, <strong>and</strong> classic optimizationproblems. Numerical methods such as Newton’s Method forsolving non-linear systems <strong>and</strong> modeling with vector-valuedfunctions <strong>of</strong> scalar <strong>and</strong> scalar-valued functions <strong>of</strong> a vector areincluded.MA482 Multiple Integrals <strong>and</strong> Vector FieldsOne trimester (1 unit <strong>of</strong> credit)Prerequisite: MA480 Vector Functions <strong>and</strong>Partial Derivatives <strong>and</strong> permission <strong>of</strong> the Dean <strong>of</strong><strong>Mathematics</strong>.Meeting pattern: 4 periods per weekThis is the second half <strong>of</strong> a university-level course in multivariablecalculus. This course includes the theory <strong>and</strong> application <strong>of</strong>multiple integrals <strong>and</strong> vector fields. Topics include multipleintegrals, the Jacobian <strong>and</strong> change <strong>of</strong> variables, <strong>and</strong> line <strong>and</strong>surface integrals. Significant time is devoted to consideration <strong>of</strong>Green’s Theorem, Stoke’s Theorem, <strong>and</strong> the Divergence Theorem.Numerical methods such as Simpson’s Rule for volumes under asurface <strong>and</strong> modeling with vector-valued functions <strong>of</strong> a vectorare included.MA490, MA492, AND MA494 AdvancedMathematical TopicsOne trimester each (1 unit <strong>of</strong> credit)Prerequisite: Permission <strong>of</strong> the Dean <strong>of</strong> <strong>Mathematics</strong>.This course <strong>of</strong>fers an opportunity for students with an especiallystrong background in mathematics to pursue a rigorous study <strong>of</strong>a topic outside the st<strong>and</strong>ard curriculum. The topic chosen maybe in mathematics or a mathematical study <strong>of</strong> another field.Students are expected to make formal presentations <strong>and</strong> to writea paper on the topic. This course is intended for students whohave exhausted the other course <strong>of</strong>ferings in mathematics or whowish to do independent research in mathematics.CROSS-LISTED COURSES<strong>Course</strong>s listed below are interdisciplinary courses inmathematics <strong>and</strong> at least one other subject area. Fullcourse descriptions <strong>and</strong> credit information may befound in the areas indicated.EE309* Civil Engineering <strong>and</strong> ArchitectureRead description under Program in Applied <strong>Science</strong>s.IE304* Digital Information Research <strong>and</strong>TechnologyRead description under Interdisciplinary Elective<strong>Course</strong>s.SS354* Great Mathematician-PhilosophersRead description under Humanities/History <strong>and</strong> Social<strong>Science</strong>s.NCSSM 2008-0923COURSE CATALOG

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