Engineering

This course covers the following topics: sets and mappings, complete induction; number representations, real numbers, complex numbers; number sequences, convergence, infinite series, power series, limits and continuity of functions; elementary rational and transcendental functions; differentiation, extreme values, mean value theorem and consequences; higher derivatives, Taylor polynomial and series; applications of differentiation; definite and indefinite integral, integration of rational and complex functions, improper integrals, Fourier series; matrices, linear systems of equations, Gauss algorithm; vectors and vector spaces; linear mappings; dimension and linear independence; matrix algebra; vector geometry; determinants, eigenvalues; linear differential equations.
 

This course provides individual research training for students in the Junior Year Engineering Program through the experience of belonging to a specific laboratory at Tohoku University. Students are assigned to a laboratory with the consent of the faculty member in charge. They participate in various group activities, including seminars, for the purposes of training in research methods and developing teamwork skills. The specific topic studied depends on the instructor in charge of the laboratory to which each student is assigned. The methods of assessment vary with the student's project and laboratory instructor. Students submit an abstract concerning the results of their individual research each semester and present the results near the end of this program.

This course includes practical application of data science theory and methodology to real world issues. Students complete a data science project with the following content: data collection and pre-processing; development of a technical solution based on data science; analysis of legal and ethical aspects; analysis of economic feasibility of the proposed solution.

This course emphasizes the use of stochastic dynamic optimization methods in theory and practice. General knowledge of probability theory and stochastic processes is assumed. Applications considered include revenue management, queueing systems and supply chain systems. The topics discussed also have wide applications to financial, economic, and engineering systems. 

Required Prerequisites: A background in college level mathematical analysis, probability theory, and stochastic processes is required. In addition, homework and term projects will include developing computer codes for algorithms presented in class. These computer codes could be applied to solve stochastic dynamic decision problems in practice. 

This course provides a comprehensive exploration of the principles and applications of building energy systems. The course is for students in engineering and architecture, focusing on the intersection of energy efficiency, electrical systems, and building design. Topics include building energy analysis, psychrometrics, steady state and seasonal analysis, electricity supply system, electrical services in buildings, lightning protection.

Stochastic processes find applications in a wide variety of fields and offer a refined and powerful framework to examine and analyze time series. This course presents the basics for the treatment of stochastic signals and time series. Topics covered include models for stochastic dependence; concepts of description of stationary stochastic processes in the time domain including expectation, covariance, and cross-covariance functions; concepts of description of stationary stochastic processes in the frequency domain including effect spectrum and cross-spectrum; Gaussian process, Wiener process, white noise, and Gaussian fields in time and space; Stochastic processes in linear filters including relationships between in- and out-signals, autoregression and moving average (AR, MA, ARMA), and derivation and integration of stochastic processes; the basics in statistical signal processing, estimation of expectations, covariance function, and spectrum; and application of linear filters: frequency analysis and optimal filters.

This course introduces the concepts behind the analysis of renewable energy systems. Choice awareness of energy systems are considered in the uptake of renewable energy systems. The fundamentals of generation, cogeneration, and tri-generation are explored for low-carbon/renewable energy systems. Methods and tools for hybrid energy systems integration and optimization to provide specified service loads (electricity, heating, and cooling) are applied considering energy flows, energy systems integration, and bases for sustainable energy systems. Design and analyses of renewables is based on special purpose computer tools with capability for integration of renewable energy resources and/or conversion technologies for multiple energy systems/sectors including energy demand and supply modelling.

This course offers a study of the theory of automata and formal languages. Topics include: automata theory; finite automata; languages and formal grammars; regular languages; pushdown automata; Turing machine; computational complexity.

Mechanics of Materials utilizes models that drastically simplify the geometry of structures/components to be designed and the loading modes acting on them, while retaining their essential feature. Based on the simplified models the fundamental and necessary knowledge of their mechanical responses is derived and therefore provides the design of the structures/components. This course is intended as an introduction to mechanics of solids to engineering students. It presents the underlying theories and formulations for the description of stress/strain and deformations under various types of loading.
 

Mechanics of Materials II discusses the loading mode of bending in addition to tension/compression and torsion treated in Mechanics of Materials I. Beams subjected to bending moments are extensively analyzed. This course covers topics such as (1) Theory of beams, which allows us to calculate bending/shear stresses in beams and their deflections; (2) Energy methods such as Castigliano’s theorem, and (3) Compression-induced failure such as buckling. 

By the end of the course, students should be able to calculate the stresses and deformation and determine the condition of buckling in simple structures/components such as beams and frames.