Topics include: techniques of integration, an introduction to mathematical modeling with differential equations, infinite sequences and series, Taylor series, parametric and polar curves, and application to mechanics and other engineering problems.

This course covers systems of linear equations and Gaussian elimination, applications; vectors in Rn, independent sets and spanning sets; linear transformations, matrices, inverses; subspaces in Rn, basis and dimension; determinants; eigenvalues and diagonalization; systems of differential equations; dot products and orthogonal sets in Rn; projections and the Gram-Schmidt process; diagonalizing symmetric matrices; least squares approximation. Includes an introduction to numeric computation in a weekly laboratory.

An introduction to complex variables and ordinary differential equations. Topics include: Laplace transforms, ordinary higher-order linear differential equations with constant coefficients; transform methods; complex numbers and the complex plane; complex functions; limits and continuity; derivatives and integrals; analytic functions and the Cauchy-Riemann equations; power series as analytic functions; the logarithmic and exponential functions; Cauchy's integral theorem, Laurent series, residues, Cauchy's integral formula, the Laplace transform as an analytic function. Examples are drawn from electrical systems.

The chain rule for functions of several variables; the gradient, directional derivative, tangent plane and small signal modeling and Jacobians. Multiple integrals; change of variables and Jacobians, line integrals: parametric and explicit representations, the divergence and curl of a vector field, surface integrals; parametric and explicit representations, multi-variable Dirac Delta distribution, superposition of vector fields, Helmholtz decomposition theorem, Divergence theorem and Stokes' theorem and application from electromagnetic fields.

This course on Newtonian mechanics considers the interactions which influence 2-D, curvilinear motion. These interactions are described in terms of the concepts of force, work, momentum and energy. Initially the focus is on the kinematics and kinetics of particles. Then, the kinematics and kinetics of systems of particles and solid bodies are examined. Finally, simple harmonic motion is discussed. The occurrence of dynamic motion in natural systems, such as planetary motion, is emphasized. Applications to engineered systems are also introduced.