SYLLABUS - MATH 275 - CALCULUS III- Joel Cruz - F.pdf -...

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Wenzheng College of Soochow UniversityMATH 275 – ANALYTIC GEOMETRY and CALCULUS IIICourse SyllabusSPRING 2017, 3 credit hoursInstructor:Joel CruzClass Meets:Tues – Frid 13:30 to 16:00 pmOffice:Room 101 Teaching Building #1Email:[email protected]General Course Objectives::This course is an introduction to the calculus of functions of several variables. It begins with studying the basicobjects of multidimensional geometry: vectors and vector operations, lines, planes, cylinders, quadric surfaces,and various coordinate systems. It continues with the elementary differential geometry of vector functions andspace curves. By the end of the course, the student should be able to analyze curves and surfaces in three-space,differentiate and determine any extrema of functions of two or more variables, evaluate double and tripleintegrals in various coordinate systemsCourse Description:Rectangular, cylindrical and spherical coordinates. Vectors, lines, planes, cylinders, quadric surfaces.Vector functions, curves, motion in space. Differential and integral calculus of several variables.Vector fields, line integrals, fundamental theorem for line integrals, Green's theorem. Quantitative.Required Text & Materials:TextbookCalculus Early Transcendentals,7th edition,by Edwards & PennyChapter 11 – Vectors and the Geometry of SpaceThree Dimensional Coordinate SystemVectorsThe Dot ProductThe Cross ProductEquations of Lines and PlanesCylinders and Quadric Surfaces– Vector FunctionsVector Functions and Space CurvesDerivatives and Integrals of Vector FunctionsArc Length and CurvatureMotion in SpaceChapter 12 - Partial DerivativesFunctions of Several VariablesLimits and ContinuityPartial DerivativesTangent Planes and Linear ApproximationsThe Chain RuleDirectional Derivatives and the Gradient VectorMaximum and Minimum ValuesLagrange Multipliers and Constrained Maximum
Chapter 13 – Multiple IntegralsDouble Integrals over RectanglesIterated IntegralsDouble Integrals over General RegionsDouble Integrals in Polar CoordinatesApplications of Double IntegralsTriple IntegralsTriple Integrals in Cylindrical CoordinatesTriple Integrals in Spherical Coordinates

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