1, function and limit: function and limit are mathematical tools to study the trend properties of numerical sequences and the trend and extreme value of function changes. A function is a mapping relationship that maps the value of an independent variable to the value of a dependent variable. Limit describes the changing trend of function value when the independent variable approaches a certain value, including left limit, right limit and infinite limit. Limit theory is the foundation of calculus, which provides basic mathematical ideas and tools for solving derivatives and integrals.
2. Derivative and differential: Derivative and differential are mathematical tools to study the rate of change of functions and the tangent of curves. The derivative represents the rate of change of the function at a certain point and is the slope of the tangent of the function curve. Differential is a small change that describes the function when it changes with the independent variable. Derivative and differential theories play an important role in analyzing the properties of functions and solving optimization problems, and are widely used mathematical tools in engineering and science.
3. Integral and indefinite integral: Integral and indefinite integral are mathematical tools to study the area under the curve, the length of the curve and the accumulation of some quantities. The integral represents the area of the next section of the curve, and can also be regarded as the inverse derivative of the function. Indefinite integral represents the inverse operation of solving the original function of a function. Integration is an important mathematical tool for solving differential equations, calculating curve length and solving probability density function.
Significance of undergraduate education
College students have opportunities for further study. College students have the opportunity to further improve their academic qualifications and academic level through college entrance examination. Obtaining an undergraduate degree means higher academic status and broader employment opportunities. At the same time, continuing to receive higher education can also improve their professional quality and comprehensive ability, and lay a solid foundation for their future career development and academic research. College entrance examination plays a positive role in personal growth and the cultivation of independent thinking ability.
Undergraduate education focuses on cultivating students' logical thinking ability, innovative thinking ability and critical thinking ability. The study and research from university to undergraduate will provide students with more academic challenges and opportunities, help them think and solve problems in academic fields independently, and cultivate critical thinking and creative thinking. Higher education also has a positive impact on personal employment and career development. Bachelor degree is one of the basic requirements for many enterprises and institutions to recruit talents.