Saturday, April 20, 2013

JEE (Advanced) 2013 Mathematics Syllabus



Mathematics
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 submultiple 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 (2 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.

Analytical geometry (3 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.

Monday, April 15, 2013

Eulerian form of a complex number





Eulerian form of a complex number

    eθ  = cosθ + i sinθ  and e = cos θ  - i sin θ

These two are called Eulerian forms of a complex number.

Monday, April 30, 2012

Using Logarithmic Tables

Using Logarithmic Tables

Using Logarithmic Tables

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

Vectors - Videos

Vectors - Videos

Vectors - Videos

Basic Trigonometry - Videos

Basic Trigonometry - Videos

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
Study guide and notes
2. Cartesian product of sets and relations
Study guide and notes
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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7. Quadratic equations and expressions
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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
Study guide and notes