Rings, Integral Domains and Fields and their elementary properties.
Basis and Dimensions, Finite Dimensional Vector Spaces. Linear Transformations 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, Inverse of a Matrix, Cramers rule.
Addition, Subtraction and Products of Vectors and Simple applications of Geometry.
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.
Motion; Velocity; Speed; Accelaration; 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.
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