Students will learn the fundamentals of probability statistics and linear algebra in this course.
During the first half of the lecture, students will focus on the basics of probability statistics. In the field of civil engineering, various aspects of planning, design, construction, and maintenance rely on experimental and statistical data. To analyze this data objectively and rationally, a solid understanding of probability statistics is essential.
In the second half of the course, students will delve into basic linear algebra. Many fields, such as surveying and structural design, involve computerized mass calculations, which rely on the principles of vectors and matrices in linear algebra.
During the first half of the lecture, students will focus on the basics of probability statistics. In the field of civil engineering, various aspects of planning, design, construction, and maintenance rely on experimental and statistical data. To analyze this data objectively and rationally, a solid understanding of probability statistics is essential.
In the second half of the course, students will delve into basic linear algebra. Many fields, such as surveying and structural design, involve computerized mass calculations, which rely on the principles of vectors and matrices in linear algebra.
Understand how to analyze statistical data and how statistics is utilized and used in the field of civil engineering. Learn
and understand computational examples utilizing linear algebra vectors and matrices in the field of civil engineering.
- Students will be able to understand various probability distributions (normal, lognormal, Weibull, and Poisson) and can draw distribution shapes using Excel.
- Using statistical test methods (t-test and chi-square test), students can calculate tests of difference of means and tests of distribution shapes by Excel.
- Students can understand the fundamentals of matrices and eigenvalue problems, and be able to compute solutions to simultaneous equations in Excel.
- Students will be able to understand and explain the mathematical fundamentals of matrices used in civil engineering.
| Assignment | 1st examination | 2nd examination | Total. | |
|---|---|---|---|---|
| 1. | 5% | 20% | 0% | 25% |
| 2. | 5% | 20% | 0% | 25% |
| 3. | 5% | 0% | 20% | 25% |
| 4. | 5% | 0% | 20% | 25% |
| Total. | 20% | 40% | 40% | - |
The evaluation method is based on homework (20%), mid-term exam (40%), and final exam (40%), with a total score of 100 points.
A score of 60 or higher is considered to be a passing grade (achievement of learning and educational objectives).
| Class schedule | HW assignments (Including preparation and review of the class.) | Amount of Time Required | |
|---|---|---|---|
| 1. | The Role of probability statistics in engineering - Design and decision making under uncertainty |
Read the syllabus to get an overview of the lecture objectives and lecture content. Purchase a reference book | 120minutes |
| 2. | Analytical Model for Uncertain Phenomena 1 - Normal distribution - Log-normal distribution |
Study normal distribution and lognormal distribution. | 120minutes |
| 3. | Analytical Model for Uncertain Phenomena 2 - Poisson distribution |
Study Poisson distribution. | 120minutes |
| 4. | Statistical inference based on observed data 1 - Role of statistical inference in engineering - Sample mean - Sample variance |
Study statistical inference using observed data. | 120minutes |
| 5. | Statistical inference based on observed data 2 - Reliability test - Reliability Interval |
Study statistical tests and confidence intervals. | 120minutes |
| 6. | Statistical inference based on observed data 3 - chi-square test |
Study the chi-square test. | 120minutes |
| 7. | Mid-term examination | Understand the first half of the lecture contents and prepare for the exam | 240minutes |
| 8. | Basics of matrices - Matrix and vector arithmetic - Four arithmetic operations on matrices, transposed matrices, and inverse matrices - Matrix representation and solution of simultaneous equations (both in Excel (using inverse matrix) and by hand (sweep method)) |
Students who have difficulty with matrices should review the basics. | 120minutes |
| 9. | Regression and correlation analysis - Estimation of regression equations by the least squares method - Correlation coefficient |
Understand regression equations using the least-squares method. | 120minutes |
| 10. | Eigenvalue problems 1 - Matrix formulas - Eigenvalue problem |
Review determinants. | 120minutes |
| 11. | Eigenvalue problems 2 - Application of eigenvalue problems |
Review and deepen understanding of eigenvalue problems. | 120minutes |
| 12. | Applications of matrices 1 - Image processing for photogrammetry and remote sensing - Rotation and translation matrices, affine transforms |
Review matrices used in image processing. | 120minutes |
| 13. | Applications of matrices 2 - Projective transformation, Adamar product |
Review the concept of projective transformations and Adamar products | 120minutes |
| 14. | Final examination | Understand the second half of the lecture contents and prepare for the exam | 240minutes |
| Total. | - | - | 1920minutes |
- Course that cultivates a basic problem-solving skills
| Work experience | Work experience and relevance to the course content if applicable |
|---|---|
| N/A | N/A |
Last modified : Thu Mar 06 10:02:16 JST 2025