COURSE OUTLINE MATH 240 Calculus III 4 Semester Hours HOWARD COMMUNITY COLLEGE Description In this course students will develop skills necessary to conclude the Calculus sequence The course includes vector calculus in both two and three dimensional space along with the classical theorems of Green Stokes and Gauss It will also include partial derivatives and multiple integrals along with a number of appropriate applications A graphing calculator and MATLAB a computer algebra system will be integral parts of the course Prerequisite MATH 182 or equivalent a grade of C of higher is recommended 4 hours weekly Statement on General Education and Liberal Learning A liberal education prepares students to lead ethical productive and creative lives and to understand how the pursuit of lifelong learning and critical thinking fosters good citizenship General education courses form the core of a liberal education within the higher education curriculum and provide a coherent intellectual experience for all students by introducing the fundamental concepts and methods of inquiry in the areas of mathematics the physical and natural sciences the social sciences the arts and the humanities and composition This course is part of the general education core experience at Howard Community College Overall Course Objectives Upon completion of this course the student will be able to 1 Evaluate elementary vector arithmetic expressions 2 Evaluate and manipulate the dot and cross products of vectors 3 Formulate parametric equation of lines 4 Formulate the point normal equation of a plane 5 Completely describe the features of any quadric surface 6 Solve classical engineering and physics problems using vector calculus e g velocity and acceleration 7 Understand and use the chain rule for functions of two three variables to solve problems 8 Apply the concepts of multiple integration to solve complex volume area density centroid and moment of inertia problems 9 Understand and apply curls and gradients to solve problems in conservative force fields 10 Solve simple problems using the concepts of Green Strokes Theorem and the Divergence Theorem 11 Use the computer algebra system MATLAB as a means of discovery to reinforce concepts AND as an efficient problem solving tool Major Topics I Revised 1 31 14 Vectors and the Geometry of Space A Vectors in the Plane B Space Coordinates and Vectors in Space C The Dot Product of Two Vectors D The Cross Product of Two Vectors in Space 1 E F G Lines and Planes in Space Surfaces in Space Cylindrical and Spherical Coordinates II Vector Valued Functions A Vector Valued Functions B Differentiation and Integration of Vector Valued Functions C Velocity and Acceleration D Tangent Vectors and Normal Vectors E Arc Length and Curvature III Functions of Several Variables A Introduction to Functions of Several Variables B Limits and Continuity C Partial Derivatives D Differentials E Chain Rules for Functions of Several Variables F Directional Derivatives and Gradients G Tangent Planes and Normal Lines H Extrema of Functions of Two Variables I Applications of Extrema of Functions of Two Variables J Lagrange Multipliers K Change of Variables Jacobians IV Multiple Integration A Iterated Integrals and Area of the Plane B Double Integrals and Volume C Change of Variables Polar Coordinated D Center of Mass and Moments of Inertia E Surface Area F Triple Integrals and Applications G Triple Integrals in Cylindrical and Spherical Coordinates V Vector Analysis A Vector Fields B Line Integrals C Conservative Vector Fields and Independence of Path D Green s Theorem E Surface Integrals F Divergence Theorem G Stokes s Theorem Course Requirements Grading Exams Grading procedures will be determined by the individual faculty member within the guidelines of the Mathematics Division and will include several unit exams projects involving MATLAB and a comprehensive departmental final exam Technology requirements Graphing calculator TI 84 recommended and required course software Other Course Information This course may be used as a Mathematics core course or as an Arts and Science elective Check with your transfer institution concerning transferability for your program Revised 1 31 14 2