BCS-012: Basic Mathematics
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IGNOU Study Material in pdf
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BLOCK 1: Algebra I
Unit 1 : Determinants
Determinants of order 2 and 3, properties of determinants; evaluation of determinants. Area of triangles using determinants, cramer’s rule.
Unit 2 : Matrices-1
Definition, equality, addition and multiplication of matrices. Adjoint and inverse of a matrix. Solution of a system of linear equations – homogeneous and non-homogeneous.
Unit 3 : Matrices-2
Elementary row operations; rank of a matrix, reduction to normal form,Inverse of a matrix using elementary row operations.
Unit 4 : Mathematical Induction
Principle of mathematical induction -1 and 2
BLOCK 2 : Algebra II
Unit 1 : Sequence and Series
Definition of sequence and series; A.P, G.P, H.P and A.G.P. ?n, ?n2 and ?n3,Idea of limit of a sequence.
Unit 2 : Complex Number
Complex number in the form of a+ib. Addition, multiplication, division of complex numbers. Conjugate and modulus of complex numbers. De Moivre’s Theorem.
Unit 3 : Equations
Quadratic, cubic and biquadratic equations. Relationship between roots and co-efficient. Symmetric functions of roots.
Unit 4 : Inequalities
Solution of linear and quadratic inequalities.
BLOCK 3: Calculus (Without Trigonometry)
Unit 1 : Differential Calculus
Concept of limit and continuity; differentiation of the sum, difference, product and quotient of two functions, chain rule. Differentiation of parametric functions. 2nd order derivatives.
Unit 2 : Simple Application of Differential Calculus
Rate of change; monotoncity-increasing and decreasing; maxima and minima.
Unit 3 : Integration
Integration as an anti-derivative. Integration by substitution and by parts.
Unit 4 : Application of Integration
Finding area under a curve. Rectification.
BLOCK 4: Vectors and Three-Dimensional Geometry
Unit 1 : Vector-1
Vectors and scalars, magnitude and direction of a vector. Direction cosines/ratio of vectors. Addition of two vectors. Multiplication of a vector by a scalar. Position vector of a point and section formula.
Unit 2 : Vector-2
Scalar (Dot) product of vectors, Vector (Cross) product of vectors. Scalar triple product and vector triple product.
Unit 3 : Three-Dimensional Geometry-1
Introduction, Distance formula. Direction cosines/ratio of a line passing through two points. Equations of a line in different forms; angle between two lines; Coplanar and skew lines. Distance between skew lines.
Unit 4 : Linear Programming
Introduction, definition and related terminology such as constrains, objective function, optimization. Mathematical Formulation of LPP. Graphical method of solving LPP in two variables. Feasible and inferring solution (up to three non-trivial constraints)