Advanced Mathematics (Second Edition) consists of eleven chapters, the main contents of which are function and limit, derivative and differential, mean value theorem and application of derivative, indefinite integral, definite integral, application of definite integral, differential equation, space analytic geometry and vector algebra, differential calculus of multivariate function, integral calculus and series of multivariate function. There are self-test questions, exercise reference answers, self-test reference answers and tips, and integral table at the back of the book.
Chapter 1 Functions and limitations
The concept of 1. 1 function
1.2 inverse function, composite function, elementary function
The concept of 1.3 limit
Algorithm of 1.4 limit
Two Important Limits of 1.5
Comparison of 1.6 infinitesimals
1.7 function
Chapter II Derivative and Differential
2. The concept of1derivative
2.2 Derivative of basic elementary functions
2.3 Derivation rules of sum, difference, product and quotient of functions
2.4 Derivation rules of composite functions
2.5 Implicit functions and function derivatives determined by parametric equations
2.6 Functional distinction
2.7 Higher derivative and higher differential
Chapter III Application of Mean Value Theorem and Derivative
3. 1 mean value theorem
3.2 Laws of L'H?pital
3.3 Taylor formula
3.4 Determination of Monotonicity of Functions
3.5 Extreme value of function and its solution
3.6 Maximum and Minimum Problems
3.7 Protrusions and inflection points of curves
3.8 Functional graphic description
3.9 the application of derivative in economic analysis.