Course Specification (Official)

This is official information for the course (only minor grammatical and typographical errors have been corrected here). The official document can be downloaded from the university’s Teaching Management System.
P.S. Please note that certain information and requirements within the official document do not necessarily reflect my perspectives or align with my views.

Course Information

• Course Code: UESTC1001 (UoG11108.06).
• Language: English.
• Level: Undergraduate Year-1.
• Class Hours: 56
• Short Description: This course introduces the fundamental concepts, methods and theories of linear algebra, vector spaces and quadratic forms.
• Course Aims: This course aims to provide a foundation in linear algebra, vector spaces and quadratic forms to prepare students for their applications in engineering.

Intended Learning Outcomes of the Course:

• perform linear operations, multiplication, transpose and invert a matrix;
• solve linear equations by Gaussian elimination;
• compute the determinant of a matrix, and use Cramer’s rule to solve linear equations;
• evaluate the rank of a matrix and state its significance;
• apply the equations of lines and planes in vector form, to establish the relationship of several lines and that between a line and a plane;
• explain the linear combination and the linear dependence of a vector set, including the rank and the concept of a maximum independent set of a vector set;
• establish a basis, dimension and coordinates for an n-dimensional vector space;
• interpret the solutions of system of linear homogeneous equations in the context of a vector space;
• explain the concepts and properties of eigenvalues and eigenvectors, and compute them;
• diagonalize a matrix; Inner product, and use Schmidt’s orthogonalization to construct an orthonormal basis;
• derive the canonical (standard) form of quadratic forms by invertible transformations and orthogonal transformations;
• explain the concept of linear space, including bases, dimension and coordinates;

Assessment:

• Coursework: 25% (homework assignments and group project)
• Examinations: 75%
  • Closed-book mid-term exam: 25%
  • Closed-book final exam: 50%

Textbook:

• David C. Lay, Steven R. Lay, Judi J. McDonald, Linear Algebra and its Applications, 5th edition, Pearson, 2015.

Reference:

• David C. Lay, Steven R. Lay, Judi J. McDonald, 线性代数及其应用（原书第5版）, 机械工业出版设, 2018.
• Gilbert Strang, Linear Algebra and its Applications, 4th edition, Cengage, 2006.
• Erwin Krewsig, Advanced Engineering Mathematics, 10th edition, Wiley, 2011.
• Peter V O’Neil, Advanced Engineering Mathematics, 7th edition, Cengage, 2012.

• Textbook:

• G. Thomas, M. D. Weir, and J. Hass, Thomas’ Calculus, 13th edition, Pearson, 2016.

Course Team Slides

The course has a set of standardized slides developed by the Calculus Course Team at Glasgow College, UESTC.Out of respect for copyright and the team’s intellectual property, these official slides are not hosted here. Students who wish to consult them may typically obtain copies through internal academic channels (e.g., from senior students or peers within Glasgow College).

All rights to the course team slides are reserved by the course team.