Functions are the core of algebra, and the teaching of function concepts is also the main task of high school mathematics Students' learning of functions and their concepts shifts from understanding specific quantitative relationships to understanding abstract quantitative relationships The monotonicity of functions, as the property of the first function that students learn in high school, lays a certain foundation for learning function related knowledge in the future.

The current with the rapid development of Internet and new media technology, the information openness and diversity makes ideological education is facing big challenge, in accordance with the "five a three-ring four law" teaching mode,the fundamental task of implementing ideological and political education, fostering values and cultivating talents is comprehensively carried out. We are advancing the resonance of the “three classrooms” and promoting the synchronous implementation of the “four transformations”, aiming to enhance the “five capacities” of students, according to the current construction of" big education courses "concept, change education thought and idea.

While the rapid development of artificial intelligence has affected people's daily lives, it has also brought huge challenges to high school mathematics teaching, such as restructuring the classroom teaching structure, transforming the role of teachers, and selecting classroom teaching methods. Based on this, the article explores the application strategies of AI technology in improving knowledge introduction, improving mathematics classroom efficiency and stimulating students' learning interest, with a view to optimizing classroom teaching links, improving students' core discipline quality, and promoting the development of high school mathematics teaching informatization.

Global energy agencies and commissions report a sharp increase in energy demand based on commercial, industrial, and residential activities. At this point, we need energy-efficient and high-performance systems to maintain a sustainable environment. More than 30% of the generated electricity has been consumed by HVAC-R units, and heat exchangers are the main components affecting the overall performance. This study combines experimental measurements, numerical investigations, and ANN-aided optimization studies to determine the optimal operating conditions of an industrial shell and tube heat exchanger system. The cold/hot stream temperature level is varied between 10 ℃ and 50 ℃ during the experiments and numerical investigations. Furthermore, the flow rates are altered in a range of 50–500 L/h to investigate the thermal and hydraulic performance under laminar and turbulent regime conditions. The experimental and numerical results indicate that U-tube bundles dominantly affect the total pumping power; therefore, the energy consumption experienced at the cold side is about ten times greater the one at the hot side. Once the required data sets are gathered via the experiments and numerical investigations, ANN-aided stochastic optimization algorithms detected the C10H50 scenario as the optimal operating case when the cold and hot stream flow rates are at 100 L/h and 500 L/h, respectively.