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Chapters
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JTET Maths Syllabus
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Coordinate Geometry
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Change of RECTANGULAR AXES, Condition for the general equation of second degree to represent parabola, ellipse, hyperbola and reduction into standard forms, Equations of tangent and normal (using Calculus). Chord of contact, pole and polar, pair of tangents in reference to general equation of conic. Rectangular, spherical- polar and cylindrical co-ordinates, Direction cosines, Angle between straight lines, equation of planes and straight lines, Shortest distance between the lines, Sphere.
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Trigonometry
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Statement and proof of binomial theorem for any index, Exponential and Logarithmic series. De Moiver’s theorem and its applications, Trigonometric and Exponential function of complex argument and hyperbolic functions. Summation of Trigonometrically series.
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Differential Calculus
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Successive differentiation, Leibnitz’s theorem, Maclaurin’s and Taylor’s series expansions, Partial differentiation, Euler’s theorem for homogeneous functions of two variables, Total differential, jacobian, Tangent and normal, curvature, Asymptotes, Maxima and Minima of functions of two variables, Lagrange’s multipliers.
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Integral Calculus
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Integration of rational and irrational function, Evaluation of definite integrals, Special integrals, differentiation and integration under the sign of integration (Beta and Gamma functions are excluded). Reduction formula. Curve tracing. Length of plane curve and area bounded by plane curves. Volume and surface area of solid of revolution.
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Real Analysis Limit of functions
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Limit, algebra of limit of functions. Continuity and discontinuities, algebra of continuous functions, Intermediate value theorem, location of roots theorem, preservation of intervals theorem, Uniform continuity. Differentiation: Derivability, relationship with continuity, Rolle’s theorem, Lagrange’s and Cauchy Mean val
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Group Theory Binary operations
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Groups- Definition and examples. Uniqueness of identity and inverse of an element in a group, Finite group and group tables, Abelian groups, non-abelian groups, Order of a group, order of an element in a group. Subgroups, Subgroup test, intersection of subgroups. Cyclic group, Permutation group, cycle notation for permutations, product of disjoint cycles,
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Matrices
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Rank of a matrix Echelon form of a matrix, Elementary transformations of a matrix, Elementary matrices, Invariance of rank under elementary transformations, Reduction to normal form, Equivalence of matrices, Rank of sum an product of matrices. Solution of a system of linear equations via matrix methods, Conditions for consistency and inconsistency, Matrix polynomials, Characteristic polynomial, Characteristic equation, Characteristic roots and Characteristic vectors of a matrix. Cayley Hamilton theorem.
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Differential Equations
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Differential equation of firs order but not of first degree, differential equation with constant co-efficient, Equations of the first order but not of the first degree including Clairaut’s form, Singular Solutions. Partial differential equation: Solution of linear partial differential equation by Lagrange’s method. Non linear partial differential equations of order one, Complete integral, Particular integral, Singular integral, general solution, Charpit’s method
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Complex Analysis
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Complex numbers, Continuity and differentiability of functions of complex variable, Analytic functions, Cauchy-Riemann differential equations in Cartesian and polar forms. Conform representation: Transformation, jacobian, Conformal transformation, some general transformations, bilinear transformation, Critical points, fixed points, Cross ratio, fixed points of bilinear transformation
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Linear Algebra
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Vector spaces, subspace, algebra of subspaces, linear combination of vectors, linear span, linear dependence and linear independence, basis and dimension, co-ordinate vector of vector relative to a basis, Complement of a subspace, direct sum and quotient space. Linear 5 transformations, null space, range, rank and nullity of a linear transformation, Sylvester low of nullity, Matrix representation of a linear transformation, algebra of linear transformations, Isomorphism and related theorems, inevitability and isomorphism
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