Introduction to mathematical formulations and computational techniques for the modeling and simulation of engineering and other kinds of systems, including electronic, mechanical, biological, biochemical, virtual, abstract and multi-domain dynamical systems. Applications from various engineering disciplines and the sciences. Matrix formulation of equations for linear problems. Formulation of equations for nonlinear problems & linearization. Numerical solution of linear algebraic equations. Gaussian elimination, computations with sparse & structured matrices. Floating point number representation & arithmetic. Numerical conditioning, ill-conditioned problems. Numerical solution of nonlinear algebraic equations. Fixed point iteration & Newton’s method in one dimension. Newton’s method for system of coupled nonlinear algebraic equations. Improving convergence of Newton’s method. Numerical solution of ordinary differential equations. Forward & backward Euler, trapezoidal rule. Multistep methods, accuracy & stability. Implicit vs explicit techniques, region of stability, stiff problems.

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.

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.

Fundamentals of optics and applications of the optical technology: photon and wave nature of light, geometrical optics, optical instruments, electro-magnetic waves, interference and interferometers, fiber optics, diffraction, diffraction gratings, polarization and its applications, multi-layer films, Fresnel equations, and rainbows. Real world applications of course topics.

A series of lectures given by faculty or outside speakers.

Interns will spend four weeks in the Emergency Department. They will take an active role in the initial evaluation and treatment of patients, work alongside senior residents, attendings, and nursing staff, and are exposed to wide variety of patients, medical and surgical emergencies, and procedures. Interns will gain valuable experience, as they will be able to follow patients from presentation, through their workup, and onto their diagnosis and management. Interns will evaluate the patients’ level of urgency, learn and apply triage principles. Learn the basic interventions (such as urinary catheter, N/G gavage, taking blood sample, intubation etc). Interns will participate in daily teaching sessions, weekly departmental conferences, as well as lecture series designed specifically for them. (4 weeks; compulsory on-call nights and weekends)

Interns will spend four weeks in the Emergency Department. They will take an active role in the initial evaluation and treatment of patients, work alongside senior residents, attendings, and nursing staff, and are exposed to wide variety of patients, medical and surgical emergencies, and procedures. Interns will gain valuable experience, as they will be able to follow patients from presentation, through their workup, and onto their diagnosis and management. Interns will evaluate the patients’ level of urgency, learn and apply triage principles. Learn the basic interventions (such as urinary catheter, N/G gavage, taking blood sample, intubation etc). Interns will participate in daily teaching sessions, weekly departmental conferences, as well as lecture series designed specifically for them. (4 weeks; compulsory on-call nights and weekends)

Interns will spend four weeks in the Emergency Department. They will take an active role in the initial evaluation and treatment of patients, work alongside senior residents, attendings, and nursing staff, and are exposed to wide variety of patients, medical and surgical emergencies, and procedures. Interns will gain valuable experience, as they will be able to follow patients from presentation, through their workup, and onto their diagnosis and management. Interns will evaluate the patients’ level of urgency, learn and apply triage principles. Learn the basic interventions (such as urinary catheter, N/G gavage, taking blood sample, intubation etc). Interns will participate in daily teaching sessions, weekly departmental conferences, as well as lecture series designed specifically for them. (4 weeks; compulsory on-call nights and weekends)

Interns will spend four weeks in the Emergency Department. They will take an active role in the initial evaluation and treatment of patients, work alongside senior residents, attendings, and nursing staff, and are exposed to wide variety of patients, medical and surgical emergencies, and procedures. Interns will gain valuable experience, as they will be able to follow patients from presentation, through their workup, and onto their diagnosis and management. Interns will evaluate the patients’ level of urgency, learn and apply triage principles. Learn the basic interventions (such as urinary catheter, N/G gavage, taking blood sample, intubation etc). Interns will participate in daily teaching sessions, weekly departmental conferences, as well as lecture series designed specifically for them. (4 weeks; compulsory on-call nights and weekends)

Interns will spend four weeks in the Emergency Department. They will take an active role in the initial evaluation and treatment of patients, work alongside senior residents, attendings, and nursing staff, and are exposed to wide variety of patients, medical and surgical emergencies, and procedures. Interns will gain valuable experience, as they will be able to follow patients from presentation, through their workup, and onto their diagnosis and management. Interns will evaluate the patients’ level of urgency, learn and apply triage principles. Learn the basic interventions (such as urinary catheter, N/G gavage, taking blood sample, intubation etc). Interns will participate in daily teaching sessions, weekly departmental conferences, as well as lecture series designed specifically for them. (4 weeks; compulsory on-call nights and weekends)

Interns will spend four weeks in the Emergency Department. They will take an active role in the initial evaluation and treatment of patients, work alongside senior residents, attendings, and nursing staff, and are exposed to wide variety of patients, medical and surgical emergencies, and procedures. Interns will gain valuable experience, as they will be able to follow patients from presentation, through their workup, and onto their diagnosis and management. Interns will evaluate the patients’ level of urgency, learn and apply triage principles. Learn the basic interventions (such as urinary catheter, N/G gavage, taking blood sample, intubation etc). Interns will participate in daily teaching sessions, weekly departmental conferences, as well as lecture series designed specifically for them. (4 weeks; compulsory on-call nights and weekends)

Interns will spend four weeks in the Emergency Department. They will take an active role in the initial evaluation and treatment of patients, work alongside senior residents, attendings, and nursing staff, and are exposed to wide variety of patients, medical and surgical emergencies, and procedures. Interns will gain valuable experience, as they will be able to follow patients from presentation, through their workup, and onto their diagnosis and management. Interns will evaluate the patients’ level of urgency, learn and apply triage principles. Learn the basic interventions (such as urinary catheter, N/G gavage, taking blood sample, intubation etc). Interns will participate in daily teaching sessions, weekly departmental conferences, as well as lecture series designed specifically for them. (4 weeks; compulsory on-call nights and weekends)

The following objectives will be met through extensive reading, writing and discussion both in and out of class.Build a solid background in academic discourse, both written and spoken. Improve intensive and extensive critical reading skills. Foster critical and creative thinking. Build fundamental academic writing skills including summary, paraphrase, analysis, synthesis. Master cohesiveness as well as proper academic citation when incorporating the work of others.

The following objectives will be met through extensive reading, writing and discussion both in and out of class.Build a solid background in academic discourse, both written and spoken. Improve intensive and extensive critical reading skills. Foster critical and creative thinking. Build fundamental academic writing skills including summary, paraphrase, analysis, synthesis. Master cohesiveness as well as proper academic citation when incorporating the work of others.

The following objectives will be met through extensive reading, writing and discussion both in and out of class.Build a solid background in academic discourse, both written and spoken. Improve intensive and extensive critical reading skills. Foster critical and creative thinking. Build fundamental academic writing skills including summary, paraphrase, analysis, synthesis. Master cohesiveness as well as proper academic citation when incorporating the work of others.

The following objectives will be met through extensive reading, writing and discussion both in and out of class.Build a solid background in academic discourse, both written and spoken. Improve intensive and extensive critical reading skills. Foster critical and creative thinking. Build fundamental academic writing skills including summary, paraphrase, analysis, synthesis. Master cohesiveness as well as proper academic citation when incorporating the work of others.

The following objectives will be met through extensive reading, writing and discussion both in and out of class.Build a solid background in academic discourse, both written and spoken. Improve intensive and extensive critical reading skills. Foster critical and creative thinking. Build fundamental academic writing skills including summary, paraphrase, analysis, synthesis. Master cohesiveness as well as proper academic citation when incorporating the work of others.

The following objectives will be met through extensive reading, writing and discussion both in and out of class.Build a solid background in academic discourse, both written and spoken. Improve intensive and extensive critical reading skills. Foster critical and creative thinking. Build fundamental academic writing skills including summary, paraphrase, analysis, synthesis. Master cohesiveness as well as proper academic citation when incorporating the work of others.

The following objectives will be met through extensive reading, writing and discussion both in and out of class.Build a solid background in academic discourse, both written and spoken. Improve intensive and extensive critical reading skills. Foster critical and creative thinking. Build fundamental academic writing skills including summary, paraphrase, analysis, synthesis. Master cohesiveness as well as proper academic citation when incorporating the work of others.

The following objectives will be met through extensive reading, writing and discussion both in and out of class.Build a solid background in academic discourse, both written and spoken. Improve intensive and extensive critical reading skills. Foster critical and creative thinking. Build fundamental academic writing skills including summary, paraphrase, analysis, synthesis. Master cohesiveness as well as proper academic citation when incorporating the work of others.

Introduction to probability, sets, conditional probability, total probability theorem and Bayes rule; Independence, counting; Discrete random variables, functions of random variables, expectation, mean and variance; Continuous random variables, probability density functions, and cumulative distribution functions; Multiple random variables; Sums of random variables; Limit theorems; Covariance and correlation; Introduction to Stochastic Processes

Introduction to probability, sets, conditional probability, total probability theorem and Bayes rule; Independence, counting; Discrete random variables, functions of random variables, expectation, mean and variance; Continuous random variables, probability density functions, and cumulative distribution functions; Multiple random variables; Sums of random variables; Limit theorems; Covariance and correlation; Introduction to Stochastic Processes