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I.Course Title: Calculus IIICourse Number: 2223Catalog Prefix: MATHII.Prerequisites: Math 2222 or Math 222, or the equivalent.III.Credit Hours: 4Lecture Hours: 4Laboratory Hours: 0Observation Hours: 0IV.Course Description:This course concerns multivariable calculus and is a continuation of Math 2222 Calculus II. It includes applications of vectors and vector functions; partial derivatives and their applications, including gradients; multiple integration in rectangular, polar, cylindrical and spherical coordinates; vector fields, line integrals, curl and divergence, and Green’s, Stokes’ and Divergence Theorems.V.Adopted Text:Calculus, 7th edition.James StewartCengage, 2012ISBN # 0-538-49781-5VI.Course Objectives:At the completion of this course the student will be able to:1.Perform and apply vector operations, including the dot and cross product of vectors, in the plane and space. Graph and find equations of lines, planes, cylinders and quadratic surfaces.2.Differentiate and integrate vector-valued functions. For a position vector function of time, interpret these as velocity and acceleration.3.Evaluate limits and determine the continuity and differentiability of functions of several variables.4.Describe graphs, level curves and level surfaces of functions of several variables.5.Find arc length and curvature of space curves, including the use of unit tangents and unit normals; identify and interpret tangential and normal components of acceleration.6.Find partial derivatives, directional derivatives, and gradients and use them to solve applied problems.7.Find differentials of functions of several variables and use them to solve applied problems.8.Find equations of tangent planes and normal lines to surfaces that are given implicitly or parametrically.9.Use the chain rule for functions of several variables (including implicit differentiation).10.For functions of several variables, find critical points using first partials and interpret them as relative extrema/saddle points using the second partials test. Find absolute extrema on a closed region. Apply these techniques to optimization problems.11.Use Lagrange multipliers to solve constrained optimization problems.12.Evaluate multiple integrals in appropriate coordinate systems such as rectangular, polar, cylindrical and spherical coordinates and apply them to solve problems involving volume, surface area, density, moments and centroids.13.Use Jacobians to change variables in multiple integrals.14.Evaluate line and surface integrals. Identify when a line integral is independent of path and use the Fundamental Theorem of Line Integrals to solve applied problems.15.Identify conservative and inverse square fields.16.Find the curl and divergence of a vector field, the work done on an object moving in a vector field, and the flux of a field through a surface. Use these ideas to solve applied problems.17.Introduce and use Green’s Theorem, the Divergence (Gauss’s) Theorem and Stokes’ Theorem.VII.Course Methodology:The course design provides instruction and materials to support the course objectives.? Classes may consist of a variety of means to accomplish this including but not limiting to: lectures, class discussions, small group projects, supplemental materials, and outside assignments.? Practice is an important part of the learning process.? For every one hour of class time, two additional hours of study time should be expected.VIII.GradingGrading will follow the policy in the catalog. The scale is as follows:A: 90 – 100B: 80 – 89C: 70 – 79D: 60 – 69 F: Below 60IX. Course OutlineTAG Summary: This outline covers all Learning Standards in OMT018.Chapter 13Vectors and the Geometry of Space.13.1Three-Dimensional Coordinate Systems. (OMT018 – Standard 1)13.2Vectors.(OMT018 – Standard 1)13.3The Dot Product.(OMT018 – Standard 1)13.4The Cross Product.(OMT018 – Standard 1)13.5Equations of Lines and Planes.(OMT018 – Standard 1)Cylinders and Quadric Surfaces.(OMT018 – Standard 1)Chapter 14Vector Functions.14.1Vector Functions and Space Curves. (OMT018 – Standard 2)14.2Derivatives and Integrals of Vector Functions.(OMT018 – Standard 2)14.3Arc Length and Curvature.(OMT018 – Standard 5)Motion in Space: Velocity and Acceleration.(OMT018 – Standards 2 and 5)Chapter 15Partial Derivatives.15.1Functions of Several Variables. (OMT018 – Standard 4)15.2Limits and Continuity.(OMT018 – Standard 3)15.3Partial Derivatives.(OMT018 – Standard 6)15.4Tangent Planes and Linear Approximations.(OMT018 – Standard 7 and 8)15.5The Chain Rule.(OMT018 – Standard 9)15.6Directional Derivatives and the Gradient Vector.(OMT018 – Standard 6)15.7Maximum and Minimum Values.(OMT018 – Standard 10)15.8Lagrange Multipliers.(OMT018 – Standard 11)Chapter 16Multiple Integrals.16.1Double Integrals over Rectangles. (OMT018 – Standard 12)16.2Iterated Integrals.(OMT018 – Standard 12)16.3Double Integrals over General Regions.(OMT018 – Standard 12)16.4Double Integrals in Polar Coordinates.(OMT018 – Standard 12)16.5Applications of Double Integrals.(OMT018 – Standard 12)16.6Triple Integrals.(OMT018 – Standard 12)16.7Triple Integrals in Cylindrical Coordinates.(OMT018 – Standard 12)16.8Triple Integrals in Spherical Coordinates.(OMT018 – Standard 12)16.9Change of Variables in Multiple Integrals.(OMT018 – Standard 13)Chapter 17Vector Calculus.17.1Vector Fields.(OMT018 – Standard 15)17.2Line Integrals.(OMT018 – Standard 14)17.3The Fundamental Theorem for Line Integrals.(OMT018 – Standards 14 and 15)17.4Green’s Theorem.(OMT018 – Standard 17)17.5Curl and Divergence.(OMT018 – Standard 16)17.6Parametric Surfaces and Their Areas.(OMT018 – Standard 14)17.7Surface Integrals.(OMT018 – Standard 14)17.8Stokes’ Theorem.(OMT018 – Standard 17)17.9The Divergence Theorem.(OMT018 – Standard 17)X.Other Required Books, Software and MaterialsA graphing calculator is required. Symbolic manipulator calculators (e.g., TI–89 or TI–92) are prohibited on tests.XI.EvaluationAssignments will be evaluated according to instructor directives.XII.Specific Management RequirementsSuggested pace for the course, by section numbers:Week 1:13.1, 13.2, 13.3Week 2:13.4, 13.5Week 3:13.5, 13.6, 14.1Week 4:14.2, 14.3Week 5:14.4, 15.1, 15.2Week 6:15.3, 15.4Week 7:15.5, 15.6Week 8:15.7, 15.8Week 9:16.1, 16.2, 16.3Week 10:16.4, 16.5, 16.6Week 11:16.7, 16.8, 16.9Week 12:17.1, 17.2Week 13:17.3, 17.4Week 14:17.5, 17.6, 17.7Week 15:17.8, 17.9Week 16:FinalsXIII.Other Information:FERPA: Students need to understand that your work may be seen by others. Others may see your work when being distributed, during group project work, or if it is chosen for demonstration purposes.Students also need to know that there is a strong possibility that your work may be submitted to other entities for the purpose of plagiarism checks.DISABILITIES: Students with disabilities may contact the Disabilities Service Office, Central Campus, at 800-628-7722 or 937-393-3431. ................
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