BSAU EEE 2015 Mathematics Syllabus:
Applications of Matrices and Determinants:
Adjoint, Inverse-Properties; Computation of inverses; solution of system of linear equations by matrix inversion method. Rank of Matrix- Elementary transformation on a matrix; consistency of a system of linear equations; Cramer’s rule; Non-homogeneous equations; homogeneous linear system; rank method.
Scalar Product-Angle between two vectors; properties of scalar product; applications of dot product. Vector product-Right handed and left handed system; properties of vectors product; applications of cross product.
Product of three vectors – Scalar triple product; properties of scalar triple product; vector triple product; vector product of four vectors; scalar product of four vectors. Lines – Equation of a straight line passing through a given point and parallel to a given vector; passing through two given points (derivations are not required). Angle between two lines. Skew lines – Shortest distance between two lines; condition for two lines to intersect; point of intersection; collinearity of 3 points.
Planes- Equation of a plane (derivations are not required); passing through a given point and perpendicular to a vector; given the distance from the origin and unit normal; passing through a given point and parallel to two given vectors; passing through two given points and parallel to a given vector; passing through three given non-collinear points; passing through the line of intersection of two given planes; the distance between a point and a plane; the plane which contains two given lines; angle between two given planes; angle between a line and a plane. Sphere- Equation of the sphere (derivations are not required) whose centre and radius are given; equation of a sphere when the extremities of the diameter are given.
Complex number system; Conjugate – properties; ordered pair representation. Modulus – properties; geometrical representation; meaning; polar form; principal value; conjugate; sum; difference; product; quotient; vector interpretation; solutions of polynomial equation; De Moivre’s theorem and its applications. Roots of a complex number – nth roots; cube roots; fourth roots.
Definition of a Conic – general equation of a conic, classification with respect to the general equation of a conic, classification of conics with respect to eccentricity. Parabola- Standard equation of a parabola (derivation and tracing the parabola are not required), other standard parabolas; the process of shifting the origin; general form of the standard equation; some practical problems. Ellipse – Standard equation of the ellipse (derivation and tracing the ellipse are not required); other standard from the ellipse; general forms; some practical problems; Hyperbola-standard equation (derivation and tracing the hyperbola are not required); other form of the hyperbola; parametric form of conics; chords. Tangents and Normals- Cartesian form and Paramedic form; equation of chord of contact of tangents from a point; Asymptotes; Rectangular hyperbola- standard equation of a rectangular hyperbola.
Differential Calculus- Applications I:
Derivatives as rate measure – rate of change – velocity – acceleration – related rates – Derivative as a measure of slope- tangent; normal and angle between curves. Maxima and Minima. Mean value theorem – Rolle’s theorem- Lagrange Mean Value Theorem – Taylor’s and Maclauein’s series; I’ Hopital rule; stationary points- increasing; decreasing; maxima; minima; concavity convexity; points of infexion.
Differential Calculus – Application II:
Errors and approximations- absolute, relative, percentage errors, curve tracing, partial derivatives – Euler’s theorem.
Integral Calculus & its Applications:
Properties of definite integrals; reduction formulae for sinnx and cosnx (only results); Area; length; volume and surface area.
Formation of differential equations; order and degree; solving differential (1st order) variable separable homogeneous; linear equations. Second order linear equations with constant coefficients.
Mathematical Logic – Logic statements; connectives; truth tables; Tautologies.
Binary Operations – Semi groups – monoids, groups (problems and simple properties only); order of a group; order of an element.
Random Variable; Probability density function; distribution function; mathematical expectation; variance; Discrete Distributions- Binomial; Poisson; Continuous Distribution- Normal distribution.