MULTIVARIABLE CALCULUSThis course extends the limit, differentiation, and integration concepts of first year calculus to functions of more than one independent variable. Some topics covered are the geometry of space, vector-valued functions, tangential and normal components of acceleration, cylindrical coordinates, spherical coordinates, curvature, Kepler's Laws, functions of several variables, increments and differentials, directional derivatives, partial derivatives, Lagrange multipliers, multiple integrals, surface area, vector calculus, line integrals, Green's theorem, curl and divergence, surface integrals, The divergence theorem, Stoke's theorem. Students will solve problems by methods of traditional analysis and through the use of 2D and 3D web based graphers. Some applications include proving theorems from Euclidean geometry using vectors, analysis of Magnus forces, Cobb-Douglas production function, static equilibrium, analysis of sags in beams used in construction. The applications of the concepts are made as visual as possible through the use of technology.
Prerequisite: AP Calculus AB (MCS21XA) or Corequisite: AP Calculus BC (MCS21XB). Now accredited by SUNY Albany
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LINEAR ALGEBRAStudents will gain experience using linear algebra to explore various applications such as Network Analysis, Electric Circuits, Chemical Equations, and Polynomial Interpolation. Students will be taught to solve systems of linear equations using matrices leading to the development of vector spaces. Theorems involving matrices, determinants, finite dimensional vector spaces, linear transformations and Euclidean spaces will be developed. Finding real and complex eigenvalues and corresponding eigenvectors will lead to students solving systems of differential equations by means of diagonalization. Analytic methods as well as interactive computer software and graphing calculators will explore solutions to first and second order differential equations. The Gram-Schmidt Process, QR-Decomposition, and LU-Decomposition will also be featured.
Prerequisite or corequisite: AP Calculus AB (MCS21XA) or AP Calculus BC (MCS21XB). Now accredited by SUNY Albany
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