Calculus Early Transcendentals 10th Edition by Howard Anton, Irl Bivens and Stephen Davis
Contents of Calculus Early Transcendentals :
1 LIMITS AND CONTINUITY
2 THE DERIVATIVE
3 TOPICS IN DIFFERENTIATION
4 THE DERIVATIVE IN GRAPHING AND APPLICATIONS
5 INTEGRATION
6 APPLICATIONS OF THE DEFINITE INTEGRAL IN GEOMETRY, SCIENCE, AND ENGINEERING
7 PRINCIPLES OF INTEGRAL EVALUATION
8 MATHEMATICAL MODELING WITH DIFFERENTIAL EQUATIONS
9 INFINITE SERIES
10 PARAMETRIC AND POLAR CURVES; CONIC SECTIONS
11 THREE-DIMENSIONAL SPACE; VECTORS
12 VECTOR-VALUED FUNCTIONS
13 PARTIAL DERIVATIVES
14 MULTIPLE INTEGRALS
15 TOPICS IN VECTOR CALCULUS
THE ROOTS OF CALCULUS
Today’s exciting applications of calculus have roots that can be traced to the work of the Greek mathematician Archimedes, but the actual discovery of the fundamental principles of calculus was made independently by Isaac Newton (English) and Gottfried Leibniz (German) in the late seventeenth century. The work of Newton and Leibniz was motivated by four major classes of scientific and mathematical problems of the time: • Find the tangent line to a general curve at a given point. • Find the area of a general region, the length of a general curve, and the volume of a general solid. • Find the maximum or minimum value of a quantity—for example, the maximum and minimum distances of a planet from the Sun, or the maximum range attainable for a projectile by varying its angle of fire. • Given a formula for the distance traveled by a body in any specified amount of time, find the velocity and acceleration of the body at any instant. Conversely, given a formula that specifies the acceleration of velocity at any instant, find the distance traveled by the body in a specified period of time. Newton and Leibniz found a fundamental relationship between the problem of finding a tangent line to a curve and the problem of determining the area of a region. Their realization of this connection is considered to be the “discovery of calculus.” Though Newton saw how these two problems are related ten years before Leibniz did, Leibniz published his work twenty years before Newton. This situation led to a stormy debate over who was the rightful discoverer of calculus. The debate engulfed Europe for half a century, with the scientists of the European continent supporting Leibniz and those from England supporting Newton. The conflict was extremely unfortunate because Newton’s inferior notation badly hampered scientific development in England, and the Continent in turn lost the benefit of Newton’s discoveries in astronomy and physics for nearly fifty years. In spite of it all, Newton and Leibniz were sincere admirers of each other’s work.
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