MA/BMA 574 Syllabus

MA/BMA 574 Syllabus Mathematical Modeling of Physical and Biological Processes II Spring 2017

R&R Description: Model development, using Newtonian and Hamiltonian principles, for acoustic and fluid applications, and structural systems including membranes, rods, beams, and shells. Fundamental aspects of electromagnetic theory. Analytic and numerical solution techniques and experimental validation of models.

Instructor: Dr. Mansoor Haider, SAS 3280, 515-3100, [email protected]

Time/Place: 11:45-12:35 MWF, Gardner 3214

Office Hours: Wednesdays 9:30-10:30, Thursdays 1:00-2:00, or by appointment

Prerequisites: MA/BMA 573

Textbook: Mathematical and Experimental Modeling of Physical and Biological Processes by H.T. Banks and H.T. Tran, CRC Press, 2009 [optional]

Grade: Homework & Projects (60%) Mid-term Exam (15%) Final Exam (25%)

Mid-term: The Mid-term exam date will be finalized prior to the end of January, in consultation with students enrolled in the class.

Final Exam: Thursday May 4th, 8:00-11:00am

Topics: I) Fundamentals & Conservation Laws  Conservation of mass  Conservation of momentum  Control volumes and Reynolds Transport Theorem  Extensions to 2D/3D II) Acoustics & Wave Phenomena  Equation of state  Linearized models & acoustic wave equations  Potential form  Finite difference numerical solutions III) Introduction to Continuum Mechanics of Fluids & Solids  Strain and deformation  Rate of deformation  Cauchy’s principle and the Cauchy stress tensor  Stress equilibrium  Inviscid & Newtonian viscous fluids  Navier-Stokes equations  Burger’s equation  Energy conservation  Bernoulli’s Principle IV) String/Membrane Models & Variational Methods  Elastic string model  Energy and variational form  Galerkin (finite element) numerical solutions  Membrane model V) Rod & Beam Models  Magnetic materials  Uniform and nonuniform inputs  Thin beam models  Weak formulations and Galerkin solutions

Evaluations: Schedule: Online class evaluations will be available for students to complete during the last 2 weeks of the semester then become unavailable at 8am on the first day of finals for the full semester. Students will receive an email message directing them to a website where they can login using their Unity ID and complete evaluations. All evaluations are confidential; instructors will not know how any one student responded to any question, and students will not know the ratings for any instructors.

Evaluation website: http://go.ncsu.edu/cesurvey

Student help desk: [email protected]

Academic Integrity and Disabilities Information: Please review the following NCSU policies: https://policies.ncsu.edu/policy/pol-11-35-01 https://policies.ncsu.edu/regulation/reg-02-20-01