Lecture Notes on the Principles and Methods of Applied Mathematics (1版)

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【簡介】 This textbook aims to equip readers with a deep understanding of mathematical techniques essential for modeling, analyzing, and solving real-world problems across diverse disciplines. Written for graduate students and professionals, the book emphasizes practical applications of applied mathematics in the context of modern challenges, especially in the age of artificial intelligence and data-driven sciences.The text is structured around core areas including complex analysis, differential equations, variational calculus, optimal control, stochastic processes, statistical inference and learning. These foundational topics are developed through a balance of theoretical principles and practical methods, with examples drawn from physics, engineering, and data science to illustrate each technique’s relevance and application. Throughout the book, exercises are proposed to help readers practice and refine these techniques, and the appendices include a collection of past midterm and final exam papers from the University of Arizona’s Math 581 course, offering students a valuable resource for further study and self-assessment.

Applied Theories in Occupational Therapy (2版)

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Dedication v About the Authors ix Preface xi Section I: Applied Theories of Health and Wellness Chapter 1. Current Trends: Occupational Therapy's Visions for the Future The American Occupational Therapy Association's Centennial Visions Trends From the Slagle Lectures and AOTA's Official Documents The Evolution of Occupational Therapy Paradigm Shifts in 20th Century Occupational Therapy Theoretical History of Occupational Therapy Learning Activities Chapter 2. Models of Health and Wellness The Medical Approach to Continuums of Care The Biopsychosocial Model A Global Perspective: The World Health Organization's Model The Recovery Model in Mental Health A Client-Centered Model of Health Care Public Health Models of Health Care Wilcock's Occupational Perspective of Health Learning Activities Chapter 3. The New Paradigm of Occupation Occupation as a Core Concept Systems Theory Social Cognitive Theory Future Directions for Occupational Therapy Learning Activities Chapter 4. Organization of Theory in Occupational Therapy What Is Theory? Levels of Theory Contributions of Occupational Science Occupation-Based Models Frames of Reference How to Evaluate Models and Frames of Reference Learning Activities Section II: Occupation-Based Models Chapter 5. Occupational Behavior Chapter 6. Model of Human Occupation Chapter 7. The Person–Environment–Occupation–Performance Model Chapter 8. Occupational Adaptation Chapter 9. Ecology of Human Performance Chapter 10. International Models: Person–Environment–Occupation, Canadian Model of Occupational Performance, and Japanese Kawa Chapter 11. Model Integration Section III: Frames of Reference Chapter 12. Applied Behavioral Frames Chapter 13. Cognitive Behavioral Frames Chapter 14. Social Cognition and Third Wave Cognitive Frames of Reference Chapter 15. Biomechanical and Rehabilitative Frames Chapter 16. Allen's Cognitive Levels Frame of Reference Chapter 17. Toglia's Dynamic Interactional Approach Chapter 18. Ayres' Sensory Integration Frame Chapter 19. Sensory Motor and Processing Frames Chapter 20. Motor Control Frames Chapter 21. Motor Learning and Task-Oriented Frames Chapter 22. Psychoanalytic Frames Chapter 23. Psychodynamic–Ego-Adaptive Frames Chapter 24. Frames of Reference Integration Appendix 1. Theories of Lifespan Development Appendix 2. An Existential/Humanistic Approach Index