Elementary mathematics studies constants and advanced mathematics studies variables.

Advanced mathematics (also known as calculus) is an important basic subject in science and engineering colleges. As a science, advanced mathematics has its inherent characteristics, namely, high abstraction, strict logic and wide application. Abstract is the most basic and remarkable feature of mathematics-high abstraction and unity, which can profoundly reveal its essential laws and make it more widely used. Strict logic refers to the induction and arrangement of mathematical theories. Whether it is concept and expression, judgment and reasoning, we should use logical rules and follow the laws of thinking. Therefore, mathematics is also a way of thinking, and the process of learning mathematics is the process of thinking training. The progress of human society is inseparable from the wide application of mathematics. Especially in modern times, the appearance and popularization of electronic computers have broadened the application field of mathematics, and modern mathematics is becoming a powerful driving force for the development of science and technology. At the same time, it penetrates into the field of social science extensively and deeply. Therefore, it is very important for us to learn advanced mathematics well. However, many students are confused about how to learn this course well. To learn advanced mathematics well, we must at least do the following four things:

First, understand the concept. There are many concepts in mathematics. Concepts reflect the essence of things. Only by figuring out how it is defined and what its nature is can we really understand a concept.

Secondly, master the theorem. Theorem is a correct proposition, which is divided into two parts: condition and conclusion. In addition to mastering its conditions and conclusions, we should also understand its scope of application and be targeted.

Third, do appropriate exercises on the basis of understanding the examples. In particular, learners need to be reminded that the examples in the textbook are very typical, which is helpful to understand concepts and master theorems. Pay attention to the characteristics and solutions of different examples. Do appropriate exercises on the basis of understanding the examples. Good at summing up problems-not only methods, but also mistakes. After doing this, you will gain something and be able to draw inferences from others.

Fourth, clear the context. We should have an overall grasp of the knowledge we have learned and sum up the knowledge system in time, which will not only deepen our understanding of knowledge, but also contribute to further study.

Advanced mathematics includes calculus and three-dimensional analytic geometry, series and ordinary differential equations, among which calculus is the most systematic and widely used in other courses. The theory of calculus was completed by Newton and Leibniz. (Of course, calculus was applied before them, but it was not systematic enough. ) The basic concepts of calculus and extreme calculus are difficult to understand.

Advanced mathematics is divided into several parts:

First, the function limit continuity.

Second, the differential calculus of unary function

3. Integral calculus of unary function

4. Vector Algebra and Spatial Analytic Geometry

Verb (abbreviation of verb) Differential calculus of multivariate functions

Six, multivariate function integral calculus

Seven, infinite series

Eight, ordinary differential equations

The high figures mainly include

First, function and limit are divided into

Constants and variables

function

Simple behavior of function

inverse function

Elementary function

Sequence limit

functional limit

Infinite quantity and infinite quantity

Comparison of infinitesimal quantities

Functional continuity

Properties of continuous functions and functional continuity of elementary functions

Second, derivative and differential

The concept of derivative

Derivation rule of sum and difference of functions

Derivation rule of product sum quotient of functions

Derivation rule of compound function

Inverse function derivation rule

higher derivative

Implicit function and its derivative rule

Differential of function

Third, the application of derivatives.

Differential mean value theorem

Uncertain problem

Determination of monotonicity of function

Extreme value of function and its solution

Maximum and minimum values of functions and their applications

Concave direction and inflection point of curve

Fourth, indefinite integral

Concept and properties of indefinite integral

The method of finding indefinite integral

Examples of several special function integrals

Five, definite integral and its application

The concept of definite integral

Integral formula of calculus

Partial substitution integral method for definite integral

Generalized integral

Six, spatial analytic geometry

Space rectangular coordinate system

Direction cosine and direction number

Plane and spatial straight line

Surfaces and space curves

Eight, multivariate function differential calculus

The concept of multivariate function

Limit and continuity of binary function

partial derivative

complete differential

Derivation method of multivariate composite function

Extreme value of multivariate function

Nine, multivariate function integral calculus

The Concept and Properties of Double Integral

Calculation method of double integral

The concept of triple integral and its calculation method

Ordinary differential equation

Basic concepts of differential equations

Differential equation and homogeneous equation of separable variables

linear differential equation

Degradable higher order equation

Structure of solutions of linear differential equations

Solution of second-order homogeneous linear equation with constant coefficients

Solution of second-order non-homogeneous linear equation with constant coefficients