Introduction Calculus is a branch of mathematics involving or leading to calculations dealing with continuously varying functions. To a in the days of the empire a was a “calculus” pebble used in counting and gambling. Centuries later came to mean “calculare” “to To the mathematician, physical scientist, and social compute”, reckon”, figure out”. “to “to scientist of today, calculus is elementary mathematics (algebra, geometry, trigonometry) enhanced by the limit process. Calculus ideas from elementary mathematics and extends them to a more general situation. The table below contains some examples. On the left-hand side, you will find an idea from elementary mathematics; on the right, this same idea as extended by calculus. Elementary Mathematics Calculus Slope of a line = + of a curve = f(x) y mx c y Tangent line to a circle Tangent line to a more general curve Average velocity, Average acceleration Instantaneous velocity, Instantaneous acceleration Distance moved under a constant velocity. Distance moved under varying velocity. Area of a region bounded by curves Area of a region bounded by line segments. Length of a curve Length of a line segment Differentiation is used in calculations involving velocity and acceleration, of change and maximum and minimum values of curves. Before, we proceed; let us first revise some concepts which we encountered in earlier grades.
Introduction Calculus is a branch of mathematics involving or leading to calculations dealing with continuously varying functions. To a in the days of the empire a “calculus” was a pebble used in counting and gambling. Centuries later “calculare” came to mean “to compute”, “to reckon”, “to figure out”. To the mathematician, physical scientist, and social scientist of today, calculus is elementary mathematics (algebra, geometry, trigonometry) enhanced by the limit process. Calculus ideas from elementary mathematics and extends them to a more general situation. The table below contains some examples. On the left-hand side, you will find an idea from elementary mathematics; on the right, this same idea as extended by calculus. Elementary Mathematics Calculus Slope of a line y = mx + c of a curve y = f(x) Tangent line to a circle Tangent line to a more general curve Average velocity, Average acceleration Instantaneous velocity, Instantaneous acceleration Distance moved under a constant velocity. Distance moved under varying velocity. Area of a region bounded by line segments. Area of a region bounded by curves Length of a line segment Length of a curve Differentiation is used in calculations involving velocity and acceleration, of change and maximum and minimum values of curves. Before, we proceed; let us first revise some concepts which we encountered in earlier grades.
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