Calculus I
Undergraduate Course, University of Electronic Science and Technology of China, Building, 2023
Calculus I
Course Information
- Calculus I (UoG11107.06)
- This is an English taught course for first-year undergraduate students.
- This course introduces the basic theory of functions of a single variable. Topics include function, limit and continuity; differential calculus of one variable functions; integral calculus of one variable functions and differential equations with constant coefficients.
- Teaching QQ group (slides, lecture notes): 949748117
Purpose of the Course:
This course aims to provide a mathematical foundation for functions of a single variable encountered throughout engineering, including both theory and extensive practice.
Requirements by the end of this course:
- find the limits of functions; analyse the continuity of a function, classify discontinuous points and describe the general properties of a continuous function in 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 form, and evaluate limits using l’Hôpital’s rule;
- describe the concepts of primitive function and indefinite integral, and apply basic integration formulas;
- describe the concept of definite integral, prove the fundamental theorem of Calculus, use the substitution rule and integration by parts; describe the geometrical and physical applications of definite integrals;
- describe the basic concepts of differential equations and 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 problems in engineering.
Textbook:
- G. Thomas, M. D. Weir and J. Hass, Thomas’ Calsulus, 13th edition, Pearson, 2016.
Reference:
- 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。