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: UESTC1002 (UoG11107).
• Language: English.
• Level: Undergraduate Year-1.
• Class Hours: 80
• Short Description: The course introduces the basic theories of functions of a single variable, covering topics such as functions, limits, and continuity; differential calculus of one-variable functions; integral calculus of one-variable functions; and differential equations with constant coefficients.
• Course Aims: This course aims to provide a solid mathematical foundation for understanding functions of a single variable, as encountered across various engineering disciplines. It encompasses both theoretical knowledge and extensive practical applications.

Intended Learning Outcomes of the Course:

• Find the limits of functions; analyze the continuity of a function, classify discontinuous points, and describe the general properties of a continuous function on a closed interval.
• Calculate first and higher-order derivatives, find the derivative of an implicit function, and apply derivatives to solve extreme value problems.
• Explain the concept of a differential and derive a linear approximation of a function.
• Explain the concept of indeterminate forms and evaluate limits using l’Hôpital’s rule.
• Describe the concepts of primitive functions and indefinite integrals, and apply basic integration formulas.
• Describe the concept of definite integrals, prove the Fundamental Theorem of Calculus, use the substitution rule and integration by parts; describe the geometric and physical applications of definite integrals.
• Describe the basic concepts of differential equations, solve separable differential equations, first-order and second-order linear differential equations, and selected nonhomogeneous linear differential equations; apply linear differential equations with constant coefficients to solve related engineering problems.

Assessment:

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

Textbook:

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

Textbook and Recommended References:

• 同济大学数学系编,《高等数学》(第五版)，上、下册，高等教育出版社，2001。

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.