MATH 3041 DIFFERENTIAL GEOMETRY - kisi.deu.edu. ?· MATH 3041 DIFFERENTIAL GEOMETRY 4+0 ... Elementary…

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<ul><li><p>MATH 3041 </p><p>DIFFERENTIAL GEOMETRY </p><p>4+0 </p><p>Prerequisites: None </p><p>Text book: Differential Geometry of Curves and Surfaces, M. P. Do Carmo. Elementary </p><p>Differential Geometry, A. Pressley. </p><p>Reference Books: Theory and Problems of Differential Geometry, M. M. Lipschutz, </p><p>Elementary Differential Geometry, B. ONeill. </p><p>Course Objectives: The course is aim to introduce the differential geometry of curves and surfaces both in their local and global aspects. The prerequisites for understanding this course </p><p>are linear algebra and calculus. Especially, students are expected to be familiar with calculus </p><p>of several variables including the statement of the implicit function theorem and the inverse </p><p>function theorem. </p><p>Course Outline: </p><p>1. Curves (5 weeks) </p><p>Parametrized curves, Regular curves, Arc length, Reparametrization, the vector product in </p><p>R^3, The local theory of curves parametrized by arc length, The local canonical form, </p><p>Arbitrary speed curves, Global properties of plane curves. </p><p>2. Continuity and Differentiability (1 week) </p><p>3. Regular Surfaces (3 weeks) </p><p>Inverse images of Regular Values, change of Parameters, The Tangent Plane. </p><p>4. The First Fundamental Form, Area (1 week) </p><p>5. Orientation of Surfaces (2 weeks) </p><p>A characterization of Compact Orientable Surfaces </p><p>GRADING: </p><p>There may be some presentations which will be given by students. The presentations will </p><p>affect the grading 15%. For the mid-term exam, there will be a written assignment. It will </p><p>count for 35% of the grading. The final exam will be 50% of the grading. </p></li></ul>

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