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# Calculus III MA1 MAT 203

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This 2 page Class Notes was uploaded by Stephanie Batz on Monday October 12, 2015. The Class Notes belongs to MAT 203 at Front Range Community College taught by Staff in Fall. Since its upload, it has received 23 views. For similar materials see /class/221865/mat-203-front-range-community-college in Math at Front Range Community College.

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Date Created: 10/12/15

MAT 203 CALCULUS III Learning Outcomes Vectors The student should a Perform vector operations and interpret the results geometrically b Understand the threedimensional rectangular coordinate system and analyze vectors in space c Use the dot product of two vectors to nd the angle between two vectors direction cosines and projection of one vector onto another d Find the cross product of two vectors in space and the triple scalar product e Find parametric equations for lines in space f Sketch planes given by linear equations g Recognize and write equations for cylindrical surfaces quadratic surfaces and surfaces of revolution h Use spherical and cylindrical coordinates to represent surfaces in space Vectorvalued Functions The student should a Sketch analyze and apply limits to vectorvalued functions Differentiate and integrate vectorvalued functions Use vectorvalued functions to describe projectile motion velocity and acceleration Determine a unit tangent vector at a point on a space curve Find arc length and curvature of a space curve 9519 Functions of Several Variables The student should Sketch level curves and level surfaces for a function Apply the concept of continuity to a function with either two or three variables Find and use partial derivatives Understand and use differentials of a function in two variables Apply the Chain rule to functions of several variables Find directional derivatives and the gradient and use these values in applications Find equations of tangent planes and normal lines to surfaces Determine absolute and relative extrema of a function of two variables and solve optimization problems PWWQPQFquot Multiple Integration The student should a Evaluate an iterated integral and use it to find the area of a plane region Use a double integral to represent the volume of a solid region Write and evaluate double integrals in polar coordinates Locate the center of mass and moments of inertia Evaluate the area of a surface Use triple integrals to nd volume of a solid region Evaluate triple integrals using cylindrical and spherical coordinates CEO 1090 Vector Analysis The student should Determine if a vector field is conservative Find the curl and divergence of a vector field Write and evaluate a line integral Use the Fundamental Theorem of Line Integrals Understand the concepts of independence of path and conservation of energy Apply Green s Theorem to evaluate a line integral Wop99 FQ39r39P QO Find parametric equations to represent a surface Find a normal vector and tangent plane to a parametric surface Evaluate a surface integral as a double integral Understand and apply the divergence theorem to calculate ux Understand and apply Stokes s Theorem General Education The student should a b c Demonstrate the ability to select and apply contemporary forms of technology to solve problems or compile information in the study of math Read analyze and apply to new situations written material related to the study of math Write and speak clearly and logically in presentations and essays about the topics related to math All written reports are expected to demonstrate the following competencies Identify the problem to be discussed and state a position or hypothesis Select research material appropriate to topic Critically compare and defend a personal point of view as well as alternate views Research interpret and convey the topic using suitable resources and technologies including the intemet as a resource tool Use correct vocabulary formats and documentation of sources

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