This course will be taught from an applied mathematics perspective and is intended towards senior undergraduates and graduate students of Mathematics, sciences, engineering, and business students interested in operational research. The second part of the course will be devoted to constrained optimization problems, linear programming, interior-point methods, quadrative programming, and sequential quadratic programs. Familiarity with basic calculus and linear algebra is necessary. Mathematical Modeling and Optimization Differential equation models of wide variety of physical, social, and biological phenomena presented.
Qualitative analysis is introduced and used to investigate models.
Optimal criteria are incorporated to convert models to optimal control problems. Pontriagin's maximal principle is used to find analytic solutions. Numerical solutions to optimal control problems are also treated. Intro to Numerical Analysis Iterative methods for solving non-linear equations, polynomial interpolation and approximations, numerical differentiation and integration, numerical solution of differential equations and error analysis are covered in this course. Stability, error estimates, applications to engineering problems.