Applications of Matrices and Determinants:
Adjoint, inverse – properties, computation of inverses, solution of system of linear equations by matrix inversion method.
Rank of a matrix – elementary transformation on a matrix consistency of a system of linear equations, Cramer's rule, non-homogeneous equations, homogeneous linear system and rank method.
Complex Numbers:
Complex number system – conjugate, properties, ordered pair representation.
Modulus – properties, geometrical representation, polar form, principal value, conjugate, sum, difference, product, quotient, vector interpretation, solutions of polynomial equations, De Moivre's theorem and its applications.
Roots of a Complex Number – nth roots, cube roots, fourth roots.
Analytical Geometry of two dimensions:
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.
Equations of conic sections (parabola, ellipse and hyperbola) in standard forms and general forms – Directrix, Focus and Latus rectum – parametric form of conics and chords – Tangents and Normal's, Cartesian form and paramagnetic form – Equation of Chord of contact of tangents from a point (X1,Y1) to all the above said curves.
Asymptotes, Rectangular hyperbola – Standard equation of a rectangular hyperbola.
Vector Algebra:
Scalar Product – Angle between two vectors, properties of scalar product, applications of dot products. Vector product – right handed and left handed systems, properties of vector product, and 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.
Analytical Geometry of Three Dimensions:
Directions cosines- Direction ratios – Equations of a straight line passing through a given point and Parallel to a given line, Passing through two given points, Angle between two lines.
Planes – Equation of a plane, passing through a given point and perpendicular to a line, given the distance from the origin and unit normal, passing through a/(two) given point and parallel to two given lines, 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 line (co-planar lines), angle between a line and a plane.
Skew Lines – Shortest distance between two lines, Condition for two lines to intersect, Point of intersection, Co linearity of three points.
Sphere – Equation of the sphere whose centre and radius are given, equation of a sphere when the extremities of the diameter are given.
Differential Calculus:
Derivative as a rate measure – Rate of change of 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 Maclaurin's series, L' Hospital's Rule, Stationary points, Increasing, Decreasing, Maxima, Minima, Concavity and points of Inflexion.
Errors and Approximations – absolute, relative, percentage errors – Curve Tracing, Partial Derivatives, Euler's theorem.
Integral Calculus and its Applications:
Simple definite Integrals – Fundamental theorems of Calculus, Properties of Definite Integrals.
Reduction formulae – Reduction formulae for ?sinnx.dx and ?cosnx.dx, Bernoulli's formula.
Area of Bounded Regions, Length of the curve.
Differential Equations:
Differential Equations – Formation of differential equations, order and degree, solving differential equations (1st order), variable separable homogeneous, linear equations.
Second order linear Differential Equations – Second order Linear Differential Equations with constant co-efficient, Finding the particular Integral if f(x) =e(power mx), sin mx, cos mx, x, x².
Probability Distributions:
Probability – Axioms – Addition Law – Conditional Probability – Multiplicative Law – Baye's theorem – Random variable – probability density function, distribution function, mathematical expectation, variance.
Theoretical distributions – discrete distributions, Binomial, Poisson distributions, Binomial, Poisson distributions – Continuous distributions, Normal distribution.
Discrete Mathematics:
Mathematical Logic – Logical statements, Connectives, Truth Tables, Logical Equivalence, Tautology, Contradiction.
Groups – Binary Operations, Semi groups, Monoids, Groups, Order of a group, Order of an element, Properties of Groups.
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