Pdf mathematics formulas

The author of the book is Somen Saha. It is the best and most accurate book on the market out of more than 60 books written by the author. There is no age to teach mathematics. In order to be proficient in mathematics, it is important to remember the general formulas. It is common to see high school students making more mistakes in mathematics. They turn a blind eye to the formulas and forget them again. They then try to memorize the formulas on a piece of paper. Bessel Functions Kei x Legendre Polynomials Pn x Incomplete Elliptic Integral of the First Kind Areas Under the Standard Normal Curve Ordinates of the Standard Normal curve Percentile Values tp for Student's t Distribution This is called the binomial formula.

It can be extended to other values of n, and also to an infinite series [see Binomial Coefficients Formula 3. The triangle has the following two properties: 1 The first and last number in each row is 1. Equality of Complex Numbers 4. For example, the point P in Fig.

The complex number can also be interpreted as a vector from the origin O to the point P. The point P can also be represented by polar coordinates r, q. Then 4. See Table 29 for numerical values. If the area is zero, the points all lie on a line. Polar Coordinates r, p A point P can be located by rectangular coordinates x, y or polar coordinates r, u. The transformation between these coordinates is as follows: 8. Hypocycloid with Four Cusps 9.

The curve is also a special case of the limacon of Pascal see 9. The cardioid Fig. Folium of Descartes 9. The curve is as in Fig. It is used in the problem of Fig. Spiral of Archimedes 9. Relationship Between Direction Cosines The relationship between them is given by L M N Normal Form for Equation of Plane Cylindrical Coordinates r, p, z A point P can be located by cylindrical coordinates r, u, z see Fig. The transformation between those coordinates is If the center is at the origin the equation is In all cases it is assumed the body has uniform i.

Thin rod of length a a about axis perpendicular to the rod through the center 1 12 Ma 2 of mass b about axis perpendicular to the rod through one end 1 3 Ma 2 Thin circular ring of radius a a about axis perpendicular to plane of ring through center Ma2 b about axis coinciding with diameter 1 2 Ma 2 Sphere of radius a a about axis coinciding with a diameter 2 5 Ma 2 7 b about axis tangent to the surface 5 Ma 2 Hollow spherical shell of radius a a about axis coinciding with a diameter 2 3 Ma 2 5 b about axis tangent to the surface 3 Ma 2 The trigonometric functions of angle A are defined as follows: a opposite The angle A described counter- clockwise from OX is considered positive.

If it is described clockwise from OX it is considered negative. In Fig. Powers of Trignometric Functions Similarly, the other inverse trigonometric functions are multiple-valued.

For many purposes a particular branch is required. This is called the principal branch and the values for this branch are called principal values. Solid portions of curves correspond to principal values. Similar relations involving angles B and C can be obtained. See also formula 7. Sides a, b, c which are arcs of great circles are measured by their angles subtended at center O of the sphere. A, B, C are the angles opposite sides a, b, c, respectively.

Then the following results hold. Similar results hold for other sides and angles. Any one of the parts of this circle is called a middle part, the two neighboring parts are called adjacent parts, and the two remaining parts are called opposite parts.

The sine of any middle part equals the product of the tangents of the adjacent parts. The sine of any middle part equals the product of the cosines of the opposite parts. Laws of Logarithms The common logarithm of N is denoted by log10 N or briefly log N. For numerical values of common logarithms, see Table 1.

The natural logarithm of N is denoted by loge N or In N. For numerical values of natural logarithms see Table 7. For values of natural antilogarithms i. Here i is the imaginary unit [see page 10]. Similarly we define the other inverse hyperbolic functions. The inverse hyperbolic functions are multiple-valued and as in the case of inverse trigo- nometric functions [see page 49] we restrict ourselves to principal values for which they can be considered as single-valued.

The following list shows the principal values unless otherwise indicated of the inverse hyperbolic func- tions expressed in terms of logarithmic functions which are taken as real valued. The process of taking a derivative is called differentiation. Thus, As examples we observe that Extensions to functions of more than two variables are exactly analogous. Note that dz is a function of four variables, namely x, y, dx, dy, and is linear in the variables dx and dy. Since the derivative of a du constant is zero, all indefinite integrals differ by an arbitrary constant.

For the definition of a definite integral, see The process of finding an integral is called integration. The following list gives some transformations and their effects. It is assumed in all cases that division by zero is excluded.

General Formulas Involving Definite Integrals b b b b Rectangular formula: b Then there equation are 3 cases. Case 1. Linear, nonhomogeneous second There are 3 cases corresponding to those of entry Such quantities are called scalars. Other quantities such as force, velocity, and momentum require for their specification a direction as well as magnitude. Such quantities are called vectors.

A vector is represented by an arrow or directed line segment indicating direction. The magnitude of the vector is determined by the length of the arrow, using an appropriate unit. Notation for Vectors A vector is denoted by a bold faced letter such as A Fig. The magnitude is denoted by A or A. The tail end of the arrow is called the initial point, while the head is called the terminal point.

Fundamental Definitions 1. Equality of vectors. Two vectors are equal if they have the same magnitude and direction.

Multiplication of a vector by a scalar. Sums of vectors. This definition is equivalent to the parallelogram law for vector addition as indicated in Fig. Thus, Fig. Unit vectors. A unit vector is a vector with unit magnitude. If i, j, k are unit vectors in the directions of the positive x, y, z axes, then k A A3k y Cross or Vector Product Fundamental results follow: i j k We assume that all derivatives exist unless otherwise specified. Formulas Involving Derivatives d dB dA Divide the curve into n parts by P2 points of subdivision x1, y1, z1 ,.

The result The line integral Properties of Line Integrals p2 P1 In such a case, C P2 Subdivide the region into n parts by lines parallel to the x and y axes as indicated. In such a case, the integral can also be written as b f2 x Fig. The result can also be written as These are called double integrals or area integrals. The ideas can be similarly extended to triple or volume integrals or to higher multiple integrals. Grewal is one of the famous authors in the market for Engg.

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