Linear algebra: Vector and inner product spaces, linear operators, eigenvalue problems; Vector calculus: Review of differential and integral calculus, divergence and Stokes' theorems. Ordinary differential equations: Linear equations, Sturm-Liouville theory and orthogonal functions, system of linear equations; Methods of mathematics for science and engineering students.

Provides hands-on teaching experience to graduate students in undergraduate courses. Reinforces students' understanding of basic concepts and allows them to communicate and apply their knowledge of the subject matter.

Advanced nanostructured materials used in energy conversion and production, membrane electrode assemblies for fuel cells, photovoltaic devices, nanoporous materials for acoustic and thermal insulation, energy storage devices such as lithium ion batteries.

Advanced level thermodynamics, entropy, free energy, physical conversion of pure Materials and mixtures, phase rules and phase diagrams, chemical equilibrium, electrochemistry, chemical reaction rate, complex reaction kinetics, molecular reaction Dynamics, statistical thermodynamics, molecular structures.

This advanced course will help students to understand fundamental methods used for materials characterization. Students will learn principles and applications of detectors and amplifiers, optical spectroscopy, electron and scanning probe microscopy, X-ray diffraction, fluorescence and spectroscopic methods, surface analysis techniques. Students will be able to use the knowledge in the broad area of materials research. By the end of the course, the students will be able to choose appropriate methods for characterizing each specific type of materials and to treat and analyze the data obtained by such techniques.

Non-covalent interactions; molecular recognition; self-assembly; fluorescence and molecular devices; the chemistry, properties and application areas of major anion, cation or neutral molecule hosts such as crown ethers, cryptands, cucurbiturils, calixarenes and cyclodextrins; examples of artificial, self-assembled systems that are mimicking the important biological processes as well as some related studies from current literature.

Crystal structures, Synthesis methods, determination of crystal structures; imperfections, defects in metals and ceramics, vacancies, substitutional and interstitial impurities, dislocation defects in ionic solids, Phase diagrams.

SELECTED TOPICS IN CHEMISTRY

Chemical transformations and reactions at surfaces. Metal and oxide surfaces; introduction of experimental techniques for surface characterization; dynamics, thermodynamics, and kinetics of processes at gas/solid interface; liquid-solid interactions; fundamentals of heterogenous catalysis; surface growth and epitaxy.

SEMINAR

Review of electromagnetism; geometrical optics, analysis of optical systems; wave properties of light, Gaussian beams, beam optics; interaction of light with matter, spontaneous and stimulated emission, optical amplification, theory and applications of lasers, optical interactions in semiconductors, light emitting diodes and diode lasers; detectors, noise in detection systems; light propagation in anisotropic crystals, Pockels and Kerr effect, light modulators; nonlinear optics, second harmonic generation, phase matching, nonlinear optical materials.

Introduction to Microsystems, MEMS and its integration with optics; Microfabrication and process integration; MEMS Modeling and design; Actuator and sensor design; Mechanical structure design; Optical system design basics; Packaging; Optical MEMS application case studies; Scanning systems (Retinal Scanning Displays, Barcode scanners); Projection display systems (DMD and GLV); Infrared imaging cameras; Optical switching for telecommunications.

Survey of the properties and applications of photonic materials and devices; semiconductors; photon detectors, light emitting diodes, noise in light detection systems; light propagation in anisotropic media, Pockels and Kerr effects, light modulators, electromagnetic wave propagation in dielectric waveguides, waveguide dispersion; nonlinear optical materials, second harmonic generation, Raman converters.

Nomenclature, tacticity, molecular weight, physical state: amorphous/crystalline, properties & applications: elastomers, fibers, plastics; Synthesis of polymers: step growth polymerization, chain growth polymerization; Special materials: supramolecular structures, liquid crystalline materials.

Differences between the small molecules and macromolecules, different groups of polymers under addition and condensation polymers; thermosets and thermoplastics, basic structural features and the related properties: backbone , pendant group, intermolecular interactions, intramolecular interactions, diluents, crosslinking, block copolymers. Also discusses supramolecular structures, blends, composites and IPNs; free volume, packing, energy of mixing, crystallization, Flory-Huggins, Flory-Fox equation.

Quantum mechanical description of the molecular structure; exact solution of simple systems, approximate solutions to molecular problems; variational solutions, molecular orbital theory, Hückel approximation, self-consistent-field theory, semiempirical and ab-initio methods, and electron correlation. Properties such as interaction potential functions, electrostatic potential maps and population analysis will be analyzed using MOPAC, GAUSSIAN 94 and MOLCAD.

Molecular symmetry, group theory, reducible and irreducible representation, character tables, introduction to vibrational spectroscopy, Raman effect, infrared absorption, selection rules, pure rotational spectroscopy, normal modes, prediction and interpretation of the vibrational spectra of polyatomic species.

Microscopy methods and application development for health sciences, optics for advanced image acquisition methods, live-cell imaging, fluorescence, confocal and two-photon microscopy, introduction to optogenetics and neuroimaging applications, optical spectroscopy, fluorescence resonance energy transfer (FRET) methods and biosensors, single molecule imaging, sub-diffraction limit high resolution imaging, Brownian motion, diffusion and transport mechanism, image and video analysis methods in biology, image processing algorithms, principal component analysis and statistics for systems biology.

Materials behavior using phenomenological and microstructure-based approaches. Topics include

Statistical mechanics of the single chain, configurational averages, polymer solution statistics and thermodynamics, dilute and concentrated polymer solutions, the bulk state of polymers, critical phenomena and phase equilibria; numerical techniques for polymeric systems.

Classical theories of rubber elasticity, elasticity of the single chain, intermolecular effects, effects of entanglements, relationships between stress and strain, swelling of networks, critical phenomena and phase transitions in gels, thermoelastic behavior of elastomers, computational aspects.

Block copolymers, polymer blends and composites; design, preparation, properties and applications of multicomponent polymeric materials; phase separation in polymeric systems; structure-property relations in multicomponent polymers.

Intermolecular forces which govern self-organization of biological and synthetic nanostructures. Thermodynamic aspects of strong (covalent and coulomb interactions) and weak forces (dipolar, hydrogen bonding). Self-assembling systems: micelles, bilayers, and biological membranes. Computer simulations for ôhands-onö experience with nanostructures.

Interaction forces in interfacial systems; fluid interfaces; colloids; amphiphilic systems; interfaces in polymeric systems & polymer composites; liquid coating processes.