# Mathematics – 3

AIMS
• To make understand the basic concept and techniques of composition and resolution of vectors and computing the resultant of vectors.
• To enable to use the knowledge of gradient of a straight line in finding speed, acceleration etc.
• To enable to use the knowledge of conic in finding the girder of a railway bridge, cable of a suspension bridge and maximum height of an arch.
• To provide ability to apply the knowledge of differential calculus in solving problem like slope, gradient of a curve, velocity, acceleration, rate of flow of liquid etc.
• To enable to apply the process of integration in solving practical problems like calculation of area of a regular figure in two dimensions and volume of regular solids of different shapes.

SHORT DESCRIPTION
Vector : Addition and subtraction, dot and cross product.
Co-ordinate Geometry : Co-ordinates of a point, locus and its equation, straight lines, circles and conic.
Differential Calculus : Function and limit of a function, differentiation with the help of limit, differentiation of functions, geometrical interpretation of dydx , successive differentiation and Leibnitz theorem, partial differentiation.
Integral Calculus : Fundamental integrals, integration by substitutions, integration by parts, integration by partial fraction, definite integrals.
DETAIL DESCRIPTION
Vector
1 Apply the theorems of vector algebra.
1.1 Define scalar and vector.
1.2 Explain null vector, free vector, like vector, equal vector, collinear vector, unit vector, position vector, addition and subtraction of vectors, linear combination, direction cosines and direction ratios, dependent and independent vectors, scalar fields and vector field.
1.3 Prove the laws of vector algebra.
1.4 Resolve a vector in space along three mutually perpendicular directions
1.5 solve problems involving addition and subtraction of vectors.