Advanced Mathematics

Author: National Medical Administration Science and Education Department, General Higher Education Pharmaceutical Specialty College Teaching Committee
Publisher:
Publish Date: 2000-01-01
Features: This book is a unified textbook organized by the National Medical Administration Science and Education Department and the General Higher Education Pharmaceutical Specialty College Teaching Committee. The main content of this book includes: Functions and Limits, Derivatives and Differentiation, Applications of Derivatives, Indefinite Integrals, Definite Integrals, Applications of Definite Integrals, Differential Equations, Partial Derivatives of Multivariable Functions, and Double Integrals. At the end of the book, there are commonly used elementary mathematical formulas, a Greek alphabet table, an indefinite integral table, a brief table of Laplace transforms, plane and spatial graphics, calculations of second and third-order determinants, exercise answers, and main reference books. To facilitate students' review and self-assessment, in addition to providing exercises after each section, self-assessment questions are arranged at the end of some chapters. This book is suitable for teachers and students of general higher education pharmaceutical specialty colleges.
Excerpt: Surrounding. If a function is given by a mathematical expression without specifying its range, then the domain of the function refers to the set of all possible values of the independent variable that make the expression meaningful, i.e., the so-called "natural domain." To make the expression meaningful, it is generally necessary to consider the following three aspects: (1) When the function contains even-order radicals, the expression inside the radical must be greater than or equal to zero; (2) When the function is a fraction, the denominator cannot be zero; (3) When the function contains a logarithmic expression, the argument must be greater than zero. If the function contains trigonometric or inverse trigonometric functions, the range of the independent variable must be determined according to the definition of the function. For example, in the function y = arcsin(x), it is required that |x| ≤ 1. In practical problems, the domain of the function is determined by the actual meaning of the problem. In many cases, the domain of the function can be expressed using intervals. Table 1-1 is a comparison list of inequalities and intervals, where a and b are definite real numbers.
II. Methods of Representing Functions
According to the definition of a function mentioned above, a functional relationship is the correspondence between two variables. This correspondence can be represented in different ways.