Matrices - definition, concept and types of matrices,operations of transpose, scalar multiplication, multiplying a row or column by a number, adding two rows/columns,reducing a matrix into triangular and echelon form

addition and multiplication of matrices, solving simultaneous linear equations by Gaussian Elimination Method; Determinants - definition of a determinant and its evaluations

properties of determinants, using properties of determinants to evaluate the value, product of determinants, determinant of a square matrix, singular and non-singular matrices

Vectors –I

Scalars and Vector, Concept of scalars and vectors, Magnitude and direction of a general vector, fre vectors, localized vectors, zero vector, unit vector, negative of a vector, algebra of vectors, resolution of a vector, vector Arithmetic in space (3D) using i,j,k direction ratios and direction cosines

Vector Algebra-equality of vectors, collinear vectors, co-planar vectors, co-initial vectors , like vectors, unlike vectors, triangle law, parallelogram law, Polygon law, Applications of Vector Algebra-position vector of a point, distinction between position vectors and free vectors, section formulae, problems

Product of two vectors-angle between two vectors, definition of dot product , geometrical meaning, properties, definition of cross product, geometrical meaning, properties, applications to geometry, trigonometry and physica.

Unit 9 : Limits,Continuity and Differentiability

Limits - approximations and errors, intuitive understanding of limit as an extension of approximation,Left hand limits and Right hand limits, definition of Limit,properties of limit, Limit theorems, Standard limits

Evaluation of limits; Continuity - graphical meaning of continuity of a function, visual identification of continuity and discontinuity, formal definition of continuity , examples, points of discontinuity, kinds of discontinuity, algebra of continuous functions, composite function theorem, standard problems

Slope as Limits - finding the slope of straight lines and curves, definition of a derivative as limit, evaluation of simple derivatives; Differentiability - graphical understanding of differentiability and nondifferentiability, formal definition of differentiability and examples, relation between continuity and differentiability,formal definition of differentiability and examples, relation between continuity and diffentiability , evlauaion of derivatives using first principle, properties of derivatives, derivatives as a rate of change, slope of a straight line.

Unit 10 : Differential Calculus

Methods of differentiation - differentiation formulae:addition, product, quotient rules, derivative of composite functions, power functions, trigonometric functions,

derivative of implicit functions, parametric differentiation, meaning of second, third and higher order derivatives (with problems restricted to second order),

Unit 11 : Integral Calculus

Indefinite integral as Anti-derivative - integration as antiderivative, properties of integrals and integrals of standard functions and also functions of the form

Methods of Integration - properties of integration, indefinite integrals: decomposition, substitution, partial fractions and integration by parts methods

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