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The essence of mathematics is a thought process in constructing, applying abstract ideas, and their logical interrelationships. This process is essential in solving quantitative and qualitative physics problems, where abstract ideas are required to represent physical phenomena. This study aims to give detail description of the process of mathematical methods for physics lectures. Improvement in pre-service physics teachers' critical thinking is designed to strengthen their critical thinking and problem-solving skills. The methodology of research is qualitative descriptive. The research subjects were 97 preservice physics teachers who had followed the mathematical methods for physics courses and teaching lecturers. Data collection consisted of questionnaires, and interviews. Observations are needed for describing the implementation of mathematical methods for physics courses, document analysis, and data collection, including lesson plan and assessment. The results showed that mathematical methods for physics courses need improvement in the learning process. It is concluded that lecture activities integrating computers into physics and mathematics are necessary to be implemented. It is expected that the program will improve students' ability in problem-solving, critical thinking skills, communication, digital era literacy, creative and innovative creations, and group work. Specifically, implementation of the program in the ordinary differential equations course can provide learning experiences to students regarding the process of reasoning in physics using mathematical principles.

Description in course of mathematical methods for physics and possible development of course program