Civil Service Examination Mathematics Preliminary Syllabus
1, Algebra: Elements of set Theory; Algebra of Real and Complex numbers including DeMoivre’s theorem; Polynomials and Polynomial equations relations between Coefficients and Roots, symmetric functions of roots; Elements of Group Theory; Sub-Group ,Cyclic groups ,Permutation, Group and their elementary properties.Rings,Integral Domains and Fields and their elementary properties
2. Vector Spaces and Matrices: Vector Space, Linear Dependence and Indepence .Sub-spaces. Basis and Dimensions. Finite Dimensional Vector Spaces. Linear Transformation of a Finite Dimensional vector Space, Matrix Representation. Singular and Non –singular Transformations. Rank and Nullity
Matrices:Addition,Multiplication,Determinants of a Matrix, Properties of Determinants of order n,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 to area, Length of a plane curve, Volume and Surface of revolution.
5. Ordinary Differential Equations: Order and Degree of a Differential Equation, First order different Equations, Singular solution, Geomerical interpretation, second order equations with constant coefficients.
Mechanics: Concept of particle, 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, Law’s of motion; motion of particle in a straight line; Simple Harmonic Motion; motion under conservative forces; Motion under gravity ;Projectile; Escape velocity; Motion of artificial satellites
7. Element 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 DeMoivre’s theorem; Polynomials and Polynomial equations relations between Coefficients and Roots, symmetric functions of roots; Elements of Group Theory; Sub-Group ,Cyclic groups ,Permutation, Group and their elementary properties.Rings,Integral Domains and Fields and their elementary properties
2. Vector Spaces and Matrices: Vector Space, Linear Dependence and Indepence .Sub-spaces. Basis and Dimensions. Finite Dimensional Vector Spaces. Linear Transformation of a Finite Dimensional vector Space, Matrix Representation. Singular and Non –singular Transformations. Rank and Nullity
Matrices:Addition,Multiplication,Determinants of a Matrix, Properties of Determinants of order n,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 to area, Length of a plane curve, Volume and Surface of revolution.
5. Ordinary Differential Equations: Order and Degree of a Differential Equation, First order different Equations, Singular solution, Geomerical interpretation, second order equations with constant coefficients.
Mechanics: Concept of particle, 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, Law’s of motion; motion of particle in a straight line; Simple Harmonic Motion; motion under conservative forces; Motion under gravity ;Projectile; Escape velocity; Motion of artificial satellites
7. Element 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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