BCS-012: Basic Mathematics

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Syllabus

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)