* To review the basic tools of linear algebra. * To introduce the student to the laws of physics in vector form. * To give the student a solid grounding in vector analysis.

[Vectorial Mechanics:] rotation of axes, index notation, review of vector and scalar algebra (scalar vector and triple scalar products); vector functions of a real variable, functions of time; differentiation of vectors, derivative of dot and cross products, tangent to a curve, arclength, smoothness, curvature, applications in mechanics. [Fields:] scalar and vector fields; functions of several variables, maxima/minima,contour maps, directional derivative and gradient vector of scalar fields; divergence and curl of vector field; applications in electromagnetism and fluid mechanics; vector identities; cylindrical and spherical coordinates. [Line, surface and volume integrals] line integrals and work; conservation of energy and potential function; applications to planetary dynamics, area, surface and volume integrals; Gauss's GreenÆs and Stoke's theorems. Multiple integrals in radial, cylindrical and spherical coordinates, scalar and vector potentials, HelmholtzÆs theorem. [Tensor Algebra and Calculus:] Review of matrix algebra introducing suffix notation; definition of determinant; evaluation of determinants by row and column expansions; eigenvalues and eigenvectors, introduction to Cartesian tensors.

1. Be able to manipulate scalars, vectors and matrices fluently. Have grasp of and give examples of scalar vs vector fields. 2. Compute arc-length and curvature of a differentiable curve in 2D and 3D. 3. Be able to apply the standard vector calculus identities in applications in physics, engineering and chemistry. 4.Be able to compute partial derivatives of multi-variate functions. In particular be able to compute the gradient, divergence and curl (where appropriate). 5. Be able to compute line, surface (area) and volume integrals using the Divergence, Stokes and GreenÆs theorems. 6. Understand when it is appropriate to switch to a more suitable coordinate system, such as polar, cylindrical, etc in order to carry out computations more efficiently. 7. Have a basic understanding of tenors both from an index point and index/coordinate-free point of view. Be able to give examples of tensors (generally from mathematical physics).

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Weekly lectures. Homework (not for credit). Mid-term exam and final exam.