2020 Mathematical Methods in Architectural Planning and Engineering

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Academic unit or major
Undergraduate major in Architecture and Building Engineering
Osaragi Toshihiro  Asawa Takashi  Oki Takuya  Okaze Tsubasa 
Course component(s)
Mode of instruction
Day/Period(Room No.)
Tue7-8(M114)  Fri1-2(M114)  
Course number
Academic year
Offered quarter
Syllabus updated
Lecture notes updated
Language used
Access Index

Course description and aims

To learn mathematical techniques in architectural design and research.

Student learning outcomes

To acquire mathematical skills contributing architectural design and research.



Competencies that will be developed

Specialist skills Intercultural skills Communication skills Critical thinking skills Practical and/or problem-solving skills

Class flow


Course schedule/Required learning

  Course schedule Required learning
Class 1 Fundamental of statistical analysis Learn probability distribution, probability density function, central limit theorem, and confidence interval for analyzing built environmental data.
Class 2 Estimation of regional population Introduction of the flow for planning size and location of facilities. Estimation of regional population.
Class 3 Error analysis and hypothesis test Learn error analysis and hypothesis test for environmental and social data.
Class 4 Estimation of the number of facility users Estimation of the number of facility users using user's choice behavior of facilities.
Class 5 Regression analysis Learn least square method, regression analysis, correlation coefficient, and multiple regression analysis for environmental and social data.
Class 6 Planning of facility size Learn how to plan facility size based on the estimated number of users.
Class 7 Mathematics and physics of heat conduction Learn differential and difference method, Taylor expansion, and Fourier's law for heat conduction analysis.
Class 8 Mathematics and physics of convection Learn mathematics and physics of convective heat transfer in architectural spaces.
Class 9 Planning of facility location Learn how to determine the optimum location of facilities.
Class 10 Basics of land use building coverage ratio, lot area, road area ratio, floor area ratio, access cost, location requirement, bid rent curve
Class 11 Mathematics and physics of convection-diffusion equation Learn mathematics and physics of convection-diffusion equation by discretizing and solving one-dimensional equation as an example.
Class 12 Land use change revenue and expenses, supply and demand, land price factors, land market
Class 13 Application of heat transfer and fluid dynamics Understand applications of heat transfer analysis and fluid dynamics to thermal environment simulation and CFD simulation.
Class 14 Land use data and models land use data, aggregated model, disaggregated model

Out-of-Class Study Time (Preparation and Review)

To enhance effective learning, students are encouraged to spend approximately 100 minutes preparing for class and another 100 minutes reviewing class content afterwards (including assignments) for each class.
They should do so by referring to textbooks and other course material.



Reference books, course materials, etc.


Assessment criteria and methods

Report, Quiz, etc.

Related courses

  • ARC.P301 : Architectural Planning II
  • ARC.S303 : Structural Design III
  • ARC.E201 : Environmental Engineering

Prerequisites (i.e., required knowledge, skills, courses, etc.)


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