Multivariable and Vector Calculus for Engineers ((4))

Catalog description

Topics include: 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, and 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 surfaces; Integrals of real-valued functions over surfaces; Divergence and curl; Green's, Stokes, and divergence theorems. Course makes use of a Computer Algebra System, and includes problem solving with a focus on engineering applications. Note: Not open to students with credit in MATH 2020 .