Engineering mathematics is the general name of several kinds of mathematics. After engineering students finish advanced mathematics in their freshman year. We should study integral transformation, complex variable function, linear algebra, probability theory, field theory and other mathematics according to our major, which belong to engineering mathematics. Engineering mathematics is to let engineering students use more convenient theoretical tools to deal with common engineering problems.
Higher mathematics refers to a more complicated part of mathematical objects and methods compared with elementary mathematics.
Advanced mathematics
In Chinese mainland, it is very difficult for students majoring in science and engineering (except mathematics and mathematical analysis) to learn mathematics, and the textbook is often called "advanced mathematics"; Students majoring in literature and history learn mathematics a little shallower, and their textbooks are often called "calculus". Different majors in science and engineering, literature and history have different degrees of depth. It is advanced mathematics that studies variables, but advanced mathematics does not only study variables. As for the courses related to "advanced mathematics", there are usually: linear algebra (advanced algebra for mathematics majors), probability theory and mathematical statistics (some mathematics majors study independently).
The development of mathematical analysis
In the early days of ancient Greek mathematics, the results of mathematical analysis were given implicitly. For example, Zhi Nuo's dichotomy paradox implies the sum of geometric series. Later, ancient Greek mathematicians such as eudoxus and Archimedes made the mathematical analysis more explicit, but it was not very formal. When they calculate the area and volume of regions and solids by exhaustive method, they use the concepts of limit and convergence. In the early days of ancient Indian mathematics, Pashgaro, a mathematician in the12nd century, gave a second example of derivative.
Basic knowledge of engineering mathematics
How to establish a mathematical model
Vector algebra, vector analysis, tensor analysis
Matrix algebra, matrix analysis
Analytic geometry
Functional analysis, variational method
ordinary differential equation
optimization method
Graphics and network model
Stochastic mathematics (probability, statistics, stochastic process)
Computational intelligence (artificial neural network, genetic algorithm, SVM, etc.). ) model
Pattern recognition, machine learning, data mining
How to solve the mathematical model
Computational linear algebra, linear programming, numerical analysis
Numerical solutions of nonlinear problems (nonlinear equations, nonlinear function minimization, nonlinear least square method)
function of a complex variable
Boundary value problem of differential equation
Combinatorial optimization, graph theory algorithm
computing geometry