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Calculus is the mathematical study of continuous change, in the same way that geometry is the study of shape, and algebra is the study of generalizations of arithmetic operations. Originally called infinitesimal calculus or "the calculus of infinitesimals", it has two major branches, differential calculus and integral calculus.
AP Physics 1 is an algebra-based, introductory college-level physics course that includes mechanics topics such as motion, fluids, force, momentum, energy, harmonic motion, and rotation. The College Board published a curriculum framework that includes eight big ideas on which AP Physics 1 is based.
Despite the close relationship between math and physics, they are not synonyms. In mathematics objects can be defined exactly and logically related, but the object need have no relationship to experimental measurements. In physics, definitions are abstractions or idealizations, approximations adequate when compared to the natural world.
AP Physics C: Mechanics and AP Physics 1 are both introductory college-level courses in mechanics, with the former recognized by more universities. [1] The AP Physics C: Mechanics exam includes a combination of conceptual questions, algebra-based questions, and calculus-based questions, while the AP Physics 1 exam includes only conceptual and algebra-based questions.
Advanced Placement (AP) Physics 2 is a year-long introductory physics course administered by the College Board as part of its Advanced Placement program. It is intended to proxy a second-semester algebra-based university course in thermodynamics, electromagnetism, optics, and modern physics. [1]
This division into four main areas—arithmetic, geometry, algebra, and calculus [9] —endured until the end of the 19th century. Areas such as celestial mechanics and solid mechanics were then studied by mathematicians, but now are considered as belonging to physics. [10]
Physics makes particular use of calculus; all discrete concepts in classical mechanics and electromagnetism are related through discrete calculus. The mass of an object of known density that varies incrementally, the moment of inertia of such objects, as well as the total energy of an object within a discrete conservative field can be found by ...
Marston Morse applied calculus of variations in what is now called Morse theory. [6] Lev Pontryagin, Ralph Rockafellar and F. H. Clarke developed new mathematical tools for the calculus of variations in optimal control theory. [6] The dynamic programming of Richard Bellman is an alternative to the calculus of variations. [7] [8] [9] [c]