## Monday, April 30, 2012

### Using Logarithmic Tables

Using Logarithmic Tables

# Using Logarithmic Tables

### Authors

Express the given number "n" in the form of m * 10p       where 1≤m<10 and p is an integer(positive or negative whole number).

For example number 2 is expressed as 2*100

log n become equal to p + log m

log 2 becomes equal to 0 + log 2

p is called the characeristic and log m is called the mantissa. Mantissa is read from the logarithmic tables.

Logarithmic tables are show three sets of columns
i) the first set of column on the extreme left contains numbers from 10 to 99.
ii) in the seocnd set there 10 columns headed by 0,1,2,...,9
iii) after this, in the third set there 9 more columns headed by 1,2,3...9. These are known as mean differences.

As 1≤m<10, the mantissa is for a number between 1 and 10. Hence the interpretation of the first set of column in the table is 1.0 to 9.9, If you add the digit in the second set one more digit is added to the number. Which mean 1.0 becomes 1.01. If we add a digit in the third column on more digit is added to the number. Which means 1.01 becomes 1.011.

Hence log 2 = 0 + 0.3010 = 0.3010

How to see its antilogarithm.

Antilogaritm tables are written from .00. If mantissa of a logarithm is .00, then antilogarithm is 1.000
Antilogarithm of .3010 is equal to 2.000
As the characteristic of the number is 0 the number is 2.0*100. Which is equal to 2.

Suppose the problem is to find 2^(1/6). It is 2 to the power (1/6).

When we take logarithms, it becomes (1/6)* log 2 which is equal to (1/6)*(0.3010) = 0.0617 (rounded)

What is antilogarithm of 0.0617 = 1.153*100. = 1.153

So the answer of 2^(1/6) is equal to 1.153.

### Mathematics - Blogs and Web Sites

Mathematics - Blogs and Web Sites

# Mathematics - Blogs and Web Sites

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Mathematics knol directory

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### Basic Trigonometry - Videos

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# Basic Trigonometry - Videos

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### Home Page - IIT JEE Mathematics - Study Plans and Revision Notes

Study Plans and Revision Notes are created on the basis of the chapters in R.D. Sharma's Book

1. Sets
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2. Cartesian product of sets and relations
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3. Functions
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4. Binary operations
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5. Complex numbers
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6. Sequences and series
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8. Permutations and Combinations
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9. Binomial theorem
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10. Exponential and logarithmic series
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11.Matrices
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12. Determinants
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13 Cartesian System of Rectangular Coordinates and straight lines
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14. Family of lines
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Ch.15 Circle
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Ch. 16. Parabola
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Ch. 17. Ellipse
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Ch. 18. Hyperbola
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19. Real Functions
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20. Limits
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21. Continuity and Differentiability
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22. Differentiation
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23. Tangents , Normals and other applications of derivatives
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24. Increasing and decreasing functions
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25 Maximum and minimum values
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26. Indefinite integrals
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27. Definite Integration
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28. Areas of Bounded regions
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29. Differential equations
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30. VECTORS
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31. THREE DIMENSIONAL GEOMETRY
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32. Probability
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33. Trigonometric ratios, Identities and Maximum & Minimum Values of Trigonometrical Expressions
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Ch.34 properties of Triangles and circles connected with them
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Ch. 35. Trigonometrical equations
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36. Inverse Trigonometrical functions
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Ch. 37 Solution of Triangles
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Ch. 38 Heights and distances
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## Sunday, April 22, 2012

### IIT JEE Mathematics Syllabus

2008
IIT JEE Mathematics Syllabus

A Blog of Help in Learning Mathematics

# BOARD

Algebra: Algebra of complex numbers, addition, multiplication, conjugation, polar representation, properties of modulus and principal argument, triangle inequality, cube roots of unity, geometric interpretations.

Quadratic equations with real coefficients, relations between roots and coefficients, formation of quadratic equations with given roots, symmetric functions of roots.

Arithmetic, geometric and harmonic progressions, arithmetic, geometric  and harmonic means, sums of finite arithmetic and geometric progressions, infinite geometric series, sums of squares and cubes of the first n natural numbers.

Logarithms and their properties.

Permutations and combinations.

Binomial theorem for a positive integral index, properties of binomial coefficients.

Matrices as a rectangular array of real numbers, equality of matrices, addition, multiplication by a scalar and product of matrices, transpose of a matrix, determinant of a square matrix of order up to three, inverse of a square matrix of order up to three, properties of these matrix operations, diagonal, symmetric and skew-symmetric matrices and  their properties, solutions of simultaneous linear equations in two or three variables.

Addition and multiplication rules of probability, conditional probability, Bayes Theorem, independence of events, computation of probability of events using permutations and combinations.

Trigonometry: Trigonometric functions, their periodicity and graphs, addition and subtraction formulae, formulae involving multiple and sub-multiple angles, general solution of trigonometric equations.

Relations between sides and angles of a triangle, sine rule, cosine rule, half-angle formula and the area of a triangle, inverse trigonometric functions (principal value only).

Analytical geometry:
Two dimensions: Cartesian coordinates, distance between two points, section formulae, shift of origin.

Equation of a straight line in various forms, angle between two lines, distance of a point from a line; Lines through the point of intersection of two given lines, equation of the bisector of the angle between two lines, concurrency of lines;  Centroid, orthocentre, incentre and circumcentre of a triangle.

Equation of a circle in various forms, equations of tangent, normal and chord.

Parametric equations of a circle, intersection of a circle with a straight line or a circle, equation of a circle through the points  of  intersection of two circles and those of a circle and a straight line.

Equations of a parabola, ellipse and hyperbola in standard form, their foci, directrices and eccentricity, parametric equations, equations of tangent and normal.
Locus Problems.

Three dimensions: Direction cosines and direction ratios, equation of a straight line in space, equation of a plane, distance of a point from a plane.

Differential calculus: Real valued functions of a real variable, into, onto and one-to-one functions, sum, difference, product and quotient of two functions, composite functions, absolute value, polynomial, rational, trigonometric, exponential and logarithmic functions.

Limit and continuity of a function, limit and continuity of the sum, difference, product and quotient of two functions, L’Hospital rule of evaluation of limits of functions.

Even and odd functions, inverse of a function, continuity of composite functions, intermediate value property of continuous functions.
Derivative of a function, derivative of the sum, difference, product and quotient of two functions, chain rule, derivatives of polynomial, rational, trigonometric, inverse trigonometric, exponential and logarithmic functions.

Derivatives of implicit functions, derivatives up to order two, geometrical interpretation of the derivative, tangents and normals, increasing and decreasing functions, maximum and minimum values of a function, Rolle’s Theorem and Lagrange’s Mean Value Theorem.

Integral calculus: Integration as the inverse process of differentiation, indefinite integrals of standard functions, definite integrals and their properties, Fundamental Theorem of Integral Calculus.

Integration by parts, integration by the methods of substitution and partial fractions, application of definite integrals to the determination of areas involving simple curves.

Formation of ordinary differential equations, solution of homogeneous differential equations, separation of variables method, linear first order differential equations.

Vectors: Addition of vectors, scalar multiplication, dot and cross products, scalar triple products and their geometrical interpretations.

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