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Analytic Geometry The coordinate plane The graph of a function The graph of a function or an equation involving x and y is the set of points whose coordinates ( x y ) satisfy the equation or the rule of correspondence. If the function is explicit , any line parallel to the y -axis will not intersect the graph in more than one point. If it is implicit , the lines may intersect it in more than one point. Intercepts The values of x at which the curve (or the line) intersects the x -axis are called the x -intercepts of the graph. The values of y at which the curve (or the line) intersects the y -axis are called the y -intercepts of the graph. m The slope of a line The slope of a line equals the tangent of the angle between the line and the positive direction of the x -axis (the angle of inclination). To determine the slope m of the line passing through we can use the formula: Slopes of parallel and perpendicular lines Suppose we have two lines with slopes and , but neither is vertical. If the two lines are parallel, then If the two lines are perpendicular, then

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27. Analytic Geometry Note that the information below is valid for the course given in Spring 2001. Schedule. Lecture Wednesday 10001200, Orenstein 103. Targil http://www.tau.ac.il/~biranp/Teaching/Analytic_Geometry.html

Analytic Geometry Paul Biran General Information Recommended books Video Announcements Information on the course. Note that the information below is valid for the course given in Spring 2001 Schedule: Lecture: Wednesday 10:00-12:00, Orenstein 103. Targil: Group 1: Tuesday 17.00-18.00, Kaplun 118. Group 2: Thursday 19.00-20.00, Kaplun 118. Lecturer: Paul Biran (biran@math.tau.ac.il). Office Hours: Wednesday 12:10-13:10, Schreiber 208, (Phone 5362). Course Assitant: David Erschler (erschler@post.tau.ac.il). Office Hours: Tuesday 15.00-16.00 research authority shed room 3 ("tzrifim near rashut ha'mehkar"). Prerequisites: Linear Algebra 1, Calculus 1 (hedva 1 or infi 1). Very recommended to take linear algebra 2 in parallel. Homework: You will normally get a homework assingment once a week (in the "tirgul" class). Turning homework in is NOT mandatory, however it is strongly recommended as a necessary condition for succeeding in the course. Syllabus: This is an introductory course in geometry. The name Analytic Geometry is to a great extent misleading since the course has very little to do with what is commonly called in highschools analytic geometry.

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34. Dersin Adı Course Name. Code. Regular. Semester. ECTS Credits. Group No. Credits. Lecture. 2. Application. 2. Analytic Geometry. 0521032 http://www.mtm.yildiz.edu.tr/english/courses/Analytic_geometry.htm

Mathematical Engineering Department Course Name Code Regular Semester ECTS Credits Group No Credits Lecture Application Analytic Geometry Laboratory (Hour/Week) Course Language Turkish Compulsory or Elective Compulsory Instructor Course Contents Afine ,Projective and Euclidean Geometry: Fundemantal prenciple of Analytic Geometry, Orthonormalty and inner Product. Transformations in the coordinates systems : Rotation and Translation Coordinate systems of vertical and oblique :Base vectors,Linear independed and linear depended. Vectoral calcules in oblique system Analytic geometry in plane:Lines in 2-spaces, Family of curves and Envelopes Analytic geometry in space and surfaces: Lines and plane in 3-space. Basis about conics: Circle.Ellipse,Hyperbola and Parabola : Quadratic surfaces: Ellipsoid , Hyperbolaid and parabolaid Course Objectives Students are achieved basic geometrical concepts which are necessary in all engineering disiplines Illustrating geometric forms with algebraic equations and writing geometrical relations with anaytical formulas Course Outcomes (The knowledge and the skills that the student will gain at the end of the course) Devoloping of geometric thought ability and writing geometric relations with algebraic language Understanding the strong relation between mathematics and engineering by teaching basic knowledge in engineering science Achieving the ability of analytical thinking Textbook 1.H.Hilmi

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