Calculus: The Mathematical Core of Science and Technology is not a conventional calculus textbook. It is a civilizational reconstruction of why calculus became the deepest operating language of modern society-powering physics and engineering, simulation and control, optimization and AI. The book offers a "Copernican" reinterpretation: differentiation is faithful to reality, while integration is creative and imaginative. The derivative reads real differences-local rates, sensitivity, and direction-inside changing systems. The integral does more than sum what already exists: it constructs coherent wholes from fragmented relations, generating stable models that were never given as single objects in experience. Calculus is therefore not only representation, but disciplined ideal creation. To ground this claim, the monograph develops SIO Ontology (Subject-Interaction-Object), where reality is not made of isolated subjects and objects but of integral interactive wholes. A feature is defined as the emergence of consciousness identity-stable sameness becoming available to awareness under repeatable conditions.

When features drive and bind other features, feature entanglement forms; stabilized entanglement aggregates become entities. Calculus becomes the universal grammar of entities: differentiation reads their local difference-rates, while integration reconstructs their wholes. The book then elevates the argument to a new division of civilizational labor. Science constructs ideal entities: laws, equations, mechanisms, and models-structures that can be computed, reasoned with, reproduced, and upgraded. Technology constructs real entities: instruments, systems, materials, platforms, and infrastructures-structures that can be manufactured, deployed, maintained, and iterated in the physical world. Calculus is the shared mathematical core that binds these two kinds of construction: it turns local differences into global structure, and converts changing reality into operable models that can be embodied as working systems. Across ordinary and partial differential equations, numerical simulation, stochastic calculus, fractional dynamics (memory and long-range dependence), and AI training, the book shows a single engine at work: reading difference faithfully, reconstructing wholes creatively, and upgrading entities continuously. Written for educators, philosophers, scientists, and builders, it unifies mathematics, logic, philosophy, and scientific practice into a new explanation of how science and technology build-and rebuild-the modern world.