ࡱ> npmg bjbjhh F7|\|\tt#####$$$88$<t$D$ @H$$$$$%%%???????$QAD?#%%%%%?##$$?M*M*M*%j#$#$?M*%?M*M*n`<\>$`:݋c%4h= t??0 @=D1&,D@\>D#\>%%M*%%%%%??](%%% @%%%%D%%%%%%%%%t> ":  GROSSMONT COLLEGE Official Course Outline MATHEMATICS 281 MULTIVARIABLE CALCULUS Course Number Course Title Semester Units Semester Hours MATH 281 Multivariable Calculus 4 4 hours lecture: 64-72 hours 128-144 outside-of-class hours 192-216 total hours Course Prerequisites A C grade or higher or Pass in MATH 280 or equivalent. Corequisite None Recommended Preparation None. Catalog Description Math 281 is the third of a three-course sequence in calculus. Topics include vector valued functions, calculus of functions of more than one variable, partial derivatives, multiple integration, Greens Theorem, Stokes Theorem, divergence theorem. Course Objectives The student will: Perform vector operations. Determine equations of lines and planes. Find the limit of a function at a point. Evaluate derivatives. Write the equation of a tangent plane at a point. Determine differentiability. Find local extrema and test for saddle points. Solve constraint problems using Lagrange multipliers. Compute arc length. Find the divergence and curl of a vector field. Evaluate two and three dimensional integrals. Apply Greens, Stokes, and divergence theorems. Instructional Facilities a. Standard classroom equipped with: 1) Whiteboards (ample board space is essential for the calculus sequence) 2) Overhead projector/document camera 3) SmartCart Special Materials Required of Student Graphing calculator. MATHEMATICS 281 MULTIVARIABLE CALCULUS page 2 Course Content Vectors and vector operations in two and three dimensions. Vector and parametric equations of lines and planes; rectangular equation of a plane. Dot, cross, and triple products and projections. Differentiability and differentiation including partial derivatives, chain rule, higher-order derivatives, directional derivatives, and the gradient. Arc length and curvature; tangent, normal, binormal vectors. Vector-valued functions and their derivatives and integrals; finding velocity and acceleration. Real-valued functions of several variables, level curves and surfaces. Limits, continuity, and properties of limits and continuity. Local and global maxima and minima extrema, saddle points, and Lagrange multipliers. Vector fields including the gradient vector field and conservative fields. Double and triple integrals. Applications of multiple integration such as area, volume, center of mass, or moments of inertia. Change of variables theorem. Integrals in polar, cylindrical, and spherical coordinates. Line and surface integrals including parametrically defined surface. Integrals of real-valued functions over surfaces. Divergence and curl. Greens, Stokes, and divergence theorems. Method of Instruction a. Lecture and problem analysis. b. Collaborative learning and group work Methods of Evaluating Student Performance a. Homework/Problem Sets b. Quizzes c. Exams b. In-class comprehensive final exam Outside Class Assignments Homework. Problems sets. Online assignments. Texts Required Text(s): Stewart, James. Multivariable Calculus, Belmont, CA: Brooks/Cole, 7th edition, 2012. Supplementary texts and workbooks: Student Solution Manual Addendum: Student Learning Outcomes Upon completion of this course, our students will be able to do the following: Use rectangular, polar, parametric, cylindrical and spherical coordinates to solve a variety of integrals and associated application problems. Analyze, graph and solve equations related to multi-variable functions. Evaluate, interpret and apply higher order partial derivatives. Analyze and interpret physical examples of vector fields and vector functions. 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