2023 13th International Conference on Applied Physics and Mathematics (ICAPM 2023) was held in Singapore during March 10-12, 2023. In the past years, ICAPM was held in many large capital cities, such as Tokyo, Phuket, Singapore, Busan, Lisbon, Hong Kong, and Bangkok, etc. This conference provides a remarkable opportunity for the academic and industrial communities to address new challenges and share solutions, and discuss future research directions.The conference invited three internationally recognized experts in the field of applied physics and mathematics. They are Prof. Bakhodirzhon Siddikov, Ferris State University, USA, Prof. Naoyuki Ishimura, Chuo University, Japan, and Prof. Cheng-kuo Lee, National University of Singapore, Singapore. Scholars and researchers from China, Canada, India, Norway, Malaysia, Thailand, Indonesia, Philippines, Russia, and so on took this opportunity to share their research results and discuss the future development of related fields.All papers in the conference proceeding have passed vigorous preliminary review and peer review by the technical committee. Professional comments are given according to the aspects of originality, innovation, applicability, technical merit, organizing and writing, relevance to conference, and so on. Authors benefit from the valuable comments and improve their submissions to meet the satisfaction of the reviewers. The proceeding contains a collection of research papers, and is divided into 3 chapters: Chapter 1 is entitled Basic Mathematics and Mathematical Computation; Chapter 2 is entitled Application of Mathematical Calculations and Models in Engineering; Chapter 3 is entitled Physical Theory and Engineering Physics.List of Organizing Committees, Statement of Peer Review are available in this Pdf.