MATHEMATICS SYLLABUS
1. Algebra: Elements of Set Theory; Algebra of Real and Complex numbers including
Demovire’s between Coefficients and Roots, symmetric functions of roots; Elements of
Group Theory; Sub Group, Cyclic groups, Permutation, Groups and their elementary
properties. Rings, Integral Domains and Fields and their elementary properties.
2. Vector Spaces and Matrices: Vector Space, Linear Dependence and Independence. Sub
spaces. Basis and Dimensions, Finite Dimensional Vector Spaces. Linear Transformation of
a Finite dimensional vector Space, Matrix Representation. Singular and Nonsingular
Transformations. Rank and nullity. Matrices: Addition, Multiplication, Determinants of a
Matrix, Properties of Determinants of order in, Inverse of a Matrix, Cramer’s rule.
3. Geometry and Vectors: Analytic Geometry of straight lines and conics in Cartesian and
Polar coordinates; Three Dimensional geometry for planes, straight lines, sphere, cone and
cylinder. Addition, Subtraction and Products of Vectors and Simple applications to
Geometry.
4. Calculus: Functions, Sequences, Series, Limits, Continuity, Derivatives. Application of
Derivatives: Rates of change, Tangents, Normals, Maxima, Minima, Rolle’s Theorem, Mean
value Theorems of Lagrange and Cauchy, Asymptotes, Curvature. Methods of finding
indefinite integrals, Definite Integrals, Fundamental Theorem of integrals Calculus.
Application of definite integrals to area, Length of a plane curve, Volume and Surfaces of
revolution.
5. Ordinary Differential Equations: Order and Degree of a Differential Equation, First order
differential Equations, Singular solution, Geometrical interpretation, Second order equations
with constant cooefficients.
6. Mechanics: Concepts of particles Lamina; Rigid body; Displacement; force, Mass; Weight;
Motion, Velocity; Speed; Acceleration; Parallelogram of forces; Parallelogram of velocity,
acceleration; resultant; equilibrium of coplanar forces; Moments; Couples; Friction; Centre
of mass, Gravity; Laws of motion; Motion of a particle in a straight line; simple Harmonic
motion; Motion under conservative forces; Motion under gravity; Projectile; Escape velocity;
Motion of artificial satellites.
7. Elements of Computer Programming: Binary system, Octal and Hexadecimal systems.
Conversion to and from Decimal systems. Codes, Bits, Bytes and Words. Memory of a
computer, Arithmetic and Logical operations on numbers. Precision. AND, OR, XOR, NOT
and Shit/Rotate operators, Algorithms and Flow charts.
1. Algebra: Elements of Set Theory; Algebra of Real and Complex numbers including
Demovire’s between Coefficients and Roots, symmetric functions of roots; Elements of
Group Theory; Sub Group, Cyclic groups, Permutation, Groups and their elementary
properties. Rings, Integral Domains and Fields and their elementary properties.
2. Vector Spaces and Matrices: Vector Space, Linear Dependence and Independence. Sub
spaces. Basis and Dimensions, Finite Dimensional Vector Spaces. Linear Transformation of
a Finite dimensional vector Space, Matrix Representation. Singular and Nonsingular
Transformations. Rank and nullity. Matrices: Addition, Multiplication, Determinants of a
Matrix, Properties of Determinants of order in, Inverse of a Matrix, Cramer’s rule.
3. Geometry and Vectors: Analytic Geometry of straight lines and conics in Cartesian and
Polar coordinates; Three Dimensional geometry for planes, straight lines, sphere, cone and
cylinder. Addition, Subtraction and Products of Vectors and Simple applications to
Geometry.
4. Calculus: Functions, Sequences, Series, Limits, Continuity, Derivatives. Application of
Derivatives: Rates of change, Tangents, Normals, Maxima, Minima, Rolle’s Theorem, Mean
value Theorems of Lagrange and Cauchy, Asymptotes, Curvature. Methods of finding
indefinite integrals, Definite Integrals, Fundamental Theorem of integrals Calculus.
Application of definite integrals to area, Length of a plane curve, Volume and Surfaces of
revolution.
5. Ordinary Differential Equations: Order and Degree of a Differential Equation, First order
differential Equations, Singular solution, Geometrical interpretation, Second order equations
with constant cooefficients.
6. Mechanics: Concepts of particles Lamina; Rigid body; Displacement; force, Mass; Weight;
Motion, Velocity; Speed; Acceleration; Parallelogram of forces; Parallelogram of velocity,
acceleration; resultant; equilibrium of coplanar forces; Moments; Couples; Friction; Centre
of mass, Gravity; Laws of motion; Motion of a particle in a straight line; simple Harmonic
motion; Motion under conservative forces; Motion under gravity; Projectile; Escape velocity;
Motion of artificial satellites.
7. Elements of Computer Programming: Binary system, Octal and Hexadecimal systems.
Conversion to and from Decimal systems. Codes, Bits, Bytes and Words. Memory of a
computer, Arithmetic and Logical operations on numbers. Precision. AND, OR, XOR, NOT
and Shit/Rotate operators, Algorithms and Flow charts.
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