Calc1 - MATH 104 study guide PDF

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MATH 104 study guide...

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Calculus the mathematical study of change, in the same way that geometry is the study of shape and algebra is the study of operations and their applications to solving equations. both forms of this look at the fundamental notions of convergence of infinite sequences and infinite series to a well-defined limit. associated with the study of functions and limits, for example. this term comes from Latin and refers to a small stone used for counting. more generally, this refers to any method or system of calculation guided by the symbolic manipulation of expressions. "The ______ was the first achievement of modern mathematics and it is difficult to overestimate its importance. I think it defines more unequivocally than anything else the inception of modern mathematics, and the system of mathematical analysis, which is its logical development, still constitutes the greatest technical advance in exact thinking." —John von Neumann The development of this was built on earlier concepts of instantaneous motion and area underneath curves Mathematics the study of topics such as quantity (numbers), structure, space, and change Geometry a branch of mathematics concerned with questions of shape, size, relative position of figures, and the properties of space Algebra one of the broad parts of mathematics, together with number theory, geometry and analysis. In its most general form, it is the study of mathematical symbols and the rules for manipulating these symbols; it is a unifying thread of almost all of mathematics. it is the study of operations and their applications to solving equations Differential Calculus concerns rates of change and slopes of curves. the primary objects of study in this subfield are the derivative of a function, related notions such as the differential, and their applications.

Integral Calculus concerns the accumulation of quantities and the areas under and between curves. it assigns numbers to functions in a way that can describe displacement, area, volume, and other concepts that arise by combining infinitesimal data Fundamental Theorem of Calculus a theorem that links the concept of the derivative of a function with the concept of the function's integral. The first part of this theorem is that the definite integration of a function is related to its antiderivative, and can be reversed by differentiation. This part of the theorem is also important because it guarantees the existence of antiderivatives for continuous functions. The second part of the theorem is that the definite integral of a function can be computed by using any one of its infinitely-many antiderivatives. This part of the theorem has key practical applications because it markedly simplifies the computation of definite integrals...