Calculus Homework
Calculus means a computational method or a growth. Calculus is a branch of mathematics focused on limits, functions, derivatives, integral and infinite series. Calculus is basically just very advanced algebra and geometry. In one sense, it’s not even a new subject — it takes the ordinary rules of algebra and geometry and tweaks them so that they can be used on more complicated problems. Calculus originates from describing the basic physical properties of our universe, such as the motion of planets, and molecules. The branch of mathematics called Calculus approaches the paths of objects in motion as curves, or functions, and then determines the value of these functions to calculate their rate of change, area, or volume. In the 18th century, Sir Isaac Newton and Gottfried Leibniz simultaneously, yet separately, described calculus to help solve problems in physics. The two divisions of calculus, differential and integral, can solve problems like the velocity of a moving object at a certain moment in time, or the surface area of a complex object like a lampshade. This subject constitutes a major part of modern mathematics education. Calculus is the study of change, in the same way that geometry is the study of shape and algebra is the study of operations and their application to solving equations.
All of calculus relies on the fundamental principle that you can always use approximations of increasing accuracy to find the exact answer. For instance, you can approximate a curve by a series of straight lines: the shorter the lines, the closer they are to resembling a curve. You can also approximate a spherical solid by a series of cubes that get smaller and smaller with each iteration, which fits inside the sphere. Using calculus, you can determine that the approximations tend toward the precise end result, called the limit, until you have accurately described and reproduced the curve, surface, or solid.
Some of its main topics are:
1.Limit and continuity
2.Differentiation
3.Successive differentiation
4.Tangents and normals
5.Maxima and minima
6.Mean value theorems
7.Intermediate forms
8.Asymptotes
9.Curvature
10.Partial differentiation
11.Singular points and curve tracing
12.Envelopes
13.Methods of integration
14.Integration of rational and irrational functions
15.Integration of trigonometric functions
16.Definite integrals
17.Geometrical applications of the definite integral
18.Centre of gravity and moment of inertia
19.Differential equations of first order
20.Linear differential equations