# South Plains College. MATH 2315 Calculus III

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3 Questions: I invite all your questions except the following: 1. I wasn t able to make it to class. Did I miss anything? (Yes.) 2. Is this going to be on the test? (Perhaps, not directly, but if the ideas were not important, I would not be discussing them in class.) 3. Do you have the tests graded? (I put forth my best effort to have the tests graded so as to return them the next class session. However, there are times due to uncontrollable factors that this may not be possible.) Objectives: Upon completion of this course and obtaining a passing grade, the student will have mastered at least 70% of the course objectives. The course objectives provide that the student be able to: a.) Calculate derivatives of parametric and polar b.) Calculate anti-derivatives of parametric and polar functions; functions; c.) Calculate dot and cross product; d.) Write equations of lines and planes in space using vector analysis; e.) Find maximum, minimum, and level curves of 3 f.) Work with multivariable functions and calculate partial D graphs; derivatives; g.) Perform double and triple integration; h.) Green s Theorem; i.) Find area, volume, arc length, and surface area by use of double and triple integration. Diversity: In this class, the teacher will establish and support an environment that values and nurtures individual and group differences and encourages engagement and interaction. Understanding and respecting multiple experiences and perspectives will serve to challenge and stimulate all of us to learn about others, about the larger world and about ourselves. By promoting diversity and intellectual exchange, we will not only mirror society as it is, but also model society as it should and can be. Disability Statement: Students with disabilities, including but not limited to physical, psychiatric or learning disabilities, who wish to request accommodations in this class should notify the Special Services Office early in the semester so that the appropriate arrangements may be made. In accordance with federal law, a student requesting accommodations must provide acceptable documentation of his/her disability to the Special Services Coordinator. For more information, call or visit the Special Services Office in the Student Services Building, ext Spring 15 Page 3 of 6

4 Week /20, Tues 1/21, Wed 1/22, Thurs 1/26, Mon 1/27, Tues 1/28, Wed 1/29, Thurs 2/2, Mon 2/3, Tues 2/4, Wed 2/5, Thurs 2/9, Mon 2/10, Tues 2/11, Wed 2/12, Thurs 2/16, Mon 2/17, Tues 2/18, Wed 2/19, Thurs 2/23, Mon 2/24, Tues 2/25, Wed 2/26, Thurs 3/2, Mon 3/3, Tues 3/4, Wed 3/5, Thurs 3/9, Mon 3/10, Tues 3/11, Wed 3/12, Thurs Course Outline This schedule is tentative and subjective to change. Changes will be announced in class. Topics and Sections Covered Introduction Relative Extrema (Review) (Student responsibility) Parametric Equations Graphing Introduction Relative Extrema (Review) (Student responsibility) Area & Volume (Review) (Student responsibility) Parametric Equations Graphing (Student responsibility) Parametric Equations Derivatives and Tangents Parametric Equations Derivatives and Tangents Parametric Equations Relative Extrema Area & Volume (Review) (Student responsibility) Parametric Equations Relative Extrema Parametric Equations Area, Arc Length, Volume, & Surface Area Polar Equations Coordinates & Equations Polar Equations Graphing & Intersections Polar Equations Area, Volume, Arc Length, & Surface Area 11.1 Vectors 11.2 Vectors in Space Trigonometric (Polar) Form of Complex Numbers 11.3 Dot Products 11.4 Cross Products Resultant Vectors TEST Lines and Planes in Space (Equation of a Line & Plane and Distance from a point to a Line) 11.5 Lines and Planes in Space contd. (Distance from a point to a Plane, the intersection of lines & planes, and angle between two planes) 12.1 Vector-Valued Functions 12.2 Vector-Valued Functions Calculus 12.3 Velocity & Acceleration 12.4 Tangent & Normal Vectors 12.5 Arc Length only TEST 2 3/16 3/20 Spring Break 3/23, Mon 3/24, Tues 3/25, Wed 3/26, Thurs 3/30, Mon 3/31, Tues 4/1, Wed 4/2, Thurs 12.5 Arc Length contd. & Curvature (Torsion & TNB frame) TEST Cylindrical and Spherical Coordinates 13.1 Functions of Several Variables 13.3 Partial Derivatives 13.5 The Chain Rule: Implicit Differentiation (only) 13.6 Directional Derivatives & Gradients 13.7 Tangent Planes & Normal Lines

5 Week Course Outline This schedule is tentative and subjective to change. Changes will be announced in class. Topics and Sections Covered 4/6, Mon Easter *9.1 Conic Sections and Quadratic Equations (Student 4/7, Tues responsibility) 11.7 Surfaces in Space (Cylinders and Quadric Surfaces) 4/8, Wed 13.8 Extrema of Functions of Several Variables 4/9, Thurs 13.9 Applications of Extrema of Multivariable Functions 4/13, Mon 4/14, Tues Lagrange Multipliers 4/15, Wed 4/16, Thurs 4/20, Mon 4/21, Tues 4/22, Wed 4/23, Thurs 14.1 Area in the Plane (Double Integrals) 14.2 Double Integrals & Volume TEST Polar Coordinates Double Integrals 14.4 Centers of Mass & Moments of Inertia 14.5 Surface Area 4/27, Mon 14.6 Triple Integrals in Rectangular Coordinates 4/28, Tues 14.7 Triple Integrals in Cylindrical and Spherical Coordinates 4/29, Wed 14.8 Jacobian 4/30, Thurs 5/4, Mon 15.1 Vector Fields 5/5, Tues 15.2 Line Integrals 15.3 Conservative Vector Fields & Independence of Path 5/6, Wed 5/7, Thurs 15.4 Green s Theorem Review for Final 5/11, Mon :15 12:15 p FINAL EXAM: 5/12, Tues a Monday class - watch video Spring 15 Page 5 of 6

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