Use double, triple and line integrals in applications, including Green's Theorem, Stokes' Theorem, Divergence Theorem and Fundamental theorem of line integrals. 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. Vectors are mathematical constructs that have both length and direction. In Einstein notation, the vector field has curl given by: where ☑ or 0 is the Levi-Civita parity symbol. And who doesn’t want that Physical Intuition Think of flux as the amount of something crossing a surface. 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 Syllabus - What you will learn from this course Vectors. Your vector calculus math life will be so much better once you understand flux. 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 Vector Calculus 4th Edition ISBN: 9780321780652 Susan J. ![]() Recognize and sketch surfaces in three-dimensional space Perform vector operations, determine equations of lines and planes, parametrize 2D & 3D curves. ![]() Div F = ∇ ⋅ F = ( ∂ ∂ x, ∂ ∂ y, ∂ ∂ z ) ⋅ ( F x, F y, F z ) = ∂ F x ∂ x + ∂ F y ∂ y + ∂ F z ∂ z. Now, assume that P (x,y,z) P ( x, y, z) is any point in the plane.
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