Use double, triple and line integrals in applications, including Green's Theorem, Stokes' Theorem, Divergence Theorem and Fundamental theorem of line integrals. Textbook: Thomas Calculus, Early Transcendentals by Thomas, Weir and Hass (13th. Synthesize the key concepts differential, integral and multivariate calculus.Įvaluate double integrals in Cartesian and polar coordinates evaluate triple integrals in rectangular, cylindrical, and spherical coordinates and calculate areas and volumes using multiple integrals. Graphically and analytically synthesize and apply multivariable and vector-valued functions and their derivatives, using correct notation and mathematical precision. Perform vector operations, determine equations of lines and planes, parametrize 2D & 3D curves. Upon completion of this course, students should be able to: Recognize and apply Fundamental theorem of line integrals, Green’s theorem, Divergence Theorem, and Stokes’ theorem correctly. Set up and evaluate double and triple integrals using a variety of coordinate systems Įvaluate integrals through scalar or vector fields and explain some physical interpretation of these integrals View MultiVariable Calculus Final Exam.pdf from BCS MTH105 at COMSATS Institute of Information Technology, Wah. (10 points) Find the equation of the plane that contains both the point ( 1 1 2) and the line given by x 1 t y 1 + 2t z 2 3t: Solutions: A point on the line is (1 1 2) and a vector parallel to the line is h 1 2 3i. (a) In what direction, starting at (0, /2), is f changing the. Math 211, Multivariable Calculus, Fall 2011 Final Exam Solutions 1.
#MULTIVARIABLE CALCULUS FINAL EXAM SERIES#
Recognize and apply the algebraic and geometric properties of vectors and vector functions in two and three dimensions Ĭompute dot products and cross products and interpret their geometric meaning Ĭompute partial derivatives of functions of several variables and explain their meaning Ĭompute directional derivatives and gradients of scalar functions and explain their meaning Ĭompute and classify the critical points Some even take multivariable calculus and linear algebra, both college sophomore-level subjects, before graduating high school. Sequences, Series and Multivariable Calculus: Multivariable Calculus: Advanced Calculus II: Elementary Statistics: Teaching: Discrete Mathematics: Number Theory: Differential Equations and Linear Algebra. Vector Calculus Solutions to Sample Final Examination 1. Recognize and sketch surfaces in three-dimensional space
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