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: UESTC1003 (UoG11014.06).
• Language: English.
• Level: Undergraduate Year-1.
• Class Hours: 80
• Short Description: This course builds upon foundational calculus, covering infinite series, multivariable differential and integral calculus, and the integration of vector-valued functions.
• 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:

• Apply calculus to parametric and vector-valued functions; demonstrate an understanding of inner and cross products of vectors and apply them to lines and planes in space; and utilize polar coordinates and their associated equations.
• Calculate partial derivatives, total differentials, and higher-order partial derivatives of multivariable functions, and determine the derivatives of implicit functions.
• Explain the concepts of directional derivatives and gradients, and compute them in two and three dimensions; apply partial derivatives to determine tangent planes and normal lines of surfaces; and locate unconstrained and constrained extreme values of multivariable functions using the Lagrange multiplier method.
• Describe the conceptual basis of double integrals (in Cartesian and polar coordinates) and triple integrals (in Cartesian, cylindrical, and spherical coordinates) and perform their evaluation.
• Define line integrals for scalar-valued functions and vector fields; recognize the general path dependence of line integrals; and identify the conditions for path independence within conservative fields.
• Apply Green’s theorem to planar integrals; parameterize given surfaces to evaluate surface integrals; and apply the theorems of Green, Gauss, and Stokes to line, surface, and volume integrals, while explaining their significance in engineering contexts.
• Define sequences and series and determine their limits; apply convergence criteria for series with positive or alternating terms; distinguish between absolute and conditional convergence; establish convergence conditions for power series, functional series, and Taylor series; derive Maclaurin expansions for elementary transcendental functions, such as \(sin(x)\) and \(\cos(x)\); and utilize direct and indirect expansion methods for power series in approximate calculations.

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.