**Price:** INR 7000

## Course Description

IIT JAM MATHS is jointly conducted by IITs and IISc for admission into their two year M.Sc maths,Integrated M.Sc PhD,M.Sc-PhD dual degree and joint M.Sc PhD degree courses.Off late IIT JAM MATHS score has benchmark for admission into other colleges and universities like IISERs,NITs etc.TRAJECTORY EDUCATION has developed a comprehensive integrated classroom course for training students for IIT JAM and other M.Sc entrance exams like ISI,TIFR,CMI,BHU,DU etc. The topics covered in this course are:

- Integral Calculus
- Differential Calculus
- Differential Equations
- Vector Calculus
- Linear Algebra
- Group Theory
- Real Analysis

## Course Content

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DOUBLE INTEGRAL

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BETA AND GAMMA FUNCTION

Dirichlet Theorem
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VOLUME

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Centre of Mass
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Moment of Inertia
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SURFACE AREA

Surface Area
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GRADIENT, DIVERGENCE AND CURL

Gradient
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Problems on Gradient
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Divergence and Curl
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LINE INTEGRAL

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GREENS THEOREM

Greens Theorem
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SURFACE INTEGRAL

Surface Integral
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GAUSS DIVERGENCE THEOREM

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STOKES THEOREM

Stokes Theorem
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CONSERVATIVE VECTOR FIELD

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LIMITS

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CONTINUITY

Continuity
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DIFFERENTIABILITY

Differentiability
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APPLICATION OF DERIVATIVES

Monotonicity
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Critical Points
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Maxima and Minima
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MEAN VALUE THEOREM

Rolle Theorem
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Taylors Theorem
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Part B: FUNCTION OF TWO VARIABLES

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INTRODUCTION

DIFFERENTIAL EQUATIONS OF FIRST ORDER AND FIRST DEGREE

ORTHOGONAL TRAJECTORY

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DIFFERENTIAL EQUATION WITH CONSTANT COEFFICIENTS

CAUCHY EULER EQUATIONS

DIFFERENTIAL EQUATION OF SECOND ORDER

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Section 5: LINEAR ALGEBRA

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Rank of Matrix
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Linear Equations
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VECTOR SPACE AND LINEAR EQUATIONS

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Vector Spaces
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Change of Basis
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ORTHOGONALITY

Orthogonality
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EIGENVALUES AND EIGENVECTORS

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Symmetric Matrices
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Similar Matrices
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LINEAR TRANSFORMATION

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Section 6: GROUP THEORY

Defining Groups
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Modulo Arithmetic
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Cayley Table
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Unit Group
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Group of Matrices
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Subgroup
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Problems on Groups
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CYCLIC GROUP

Cyclic Groups
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PERMUTATION GROUP

Permutation Group
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ISOMORPHISM OF GROUPS

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EXTRNAL DIRECT PRODUCT

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HOMOMORPHISM OF GROUP

SET THEORY

Set Theory
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Countability of Sets
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REAL NUMBERS

Real Numbers
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TOPOLOGY ON REAL LINE

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Open Sets
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Closed Sets
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Limit Points
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REAL SEQUENCES

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Monotonic Sequence
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Limit Points
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Subsequence
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Cauchy Sequence
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INFINITE SERIES

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Alternating Series
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POWER SERIES

Power Series
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