Chapters | Topics |
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Matrices and their Applications | - Adjoint, inverse – properties, computation of inverses, solution of a system of linear equations by matrix inversion method
- The 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
- The solution of linear programming problems (LPP) in two variables
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Trigonometry and Complex Numbers | - Definition, range, domain, principal value branch, graphs of inverse trigonometric functions and their elementary properties
- 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
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Analytical Geometry of two dimensions | - Definition of a conic – general equation of a conic, classification concerning the general equation of a conic, classification of conics concerning eccentricity
- Equations of conic sections (parabola, ellipse and hyperbola) in standard forms and general forms- Directrix, Focus and Latus-rectum - a parametric form of conics and chords
- Tangents and normals – Cartesian form and parametric 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
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Vector Algebra | - Scalar Product – the angle between two vectors, properties of scalar product, and applications of the dot product
- Vector product, right-handed and left-handed systems, properties of vector
product, applications of the cross product - Product of three vectors – Scalar triple product, properties of the scalar triple product, vector triple product, vector product of four vectors, scalar product of four vectors
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Analytical Geometry of Three Dimensions | - Direction cosines – direction ratios - equation of a straight line passing through a given point and parallel to a given line, passing through two given points, the 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 given point and parallel to two given lines, passing through two given points and parallel to a given line, 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 (co-planar lines), angle between a line and a plane
- Skew lines - the shortest distance between two lines, condition for two lines to intersect, point of intersection, collinearity 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
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Differential Calculus | - Limits, continuity and differentiability of functions - Derivative as a rate of change, velocity, acceleration, related rates, derivative as a measure of slope, tangent, normal and the angle between curves
- 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, convexity and points of inflexion - Errors and approximations – absolute, relative, percentage errors - curve tracing, partial derivatives, Euler’s theorem
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Integral Calculus and its Applications | - Simple definite integrals – fundamental theorems of calculus, properties of definite integrals.
- Reduction formulae – reduction formulae for ∫sin n x dx and ∫cos nx dx, Bernoulli’s formula
- Area of bounded regions, length of the curve
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Differential Equations | - Differential equations - formation of differential equations, order and degree, solving differential equations (1st order), variables separable, homogeneous, linear equations and applications
- Second-order linear differential equations - second order linear differential equations with constant coefficients, finding the particular integral of f(x)=e MX, sin MX, cos MX,x,x 2
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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)- Continuous distributions (Normal distribution)
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Discrete Mathematics | - Functions–Relations –Sequence and series (AP, GP, HP)- Binomial theorem-Basics of counting
- Mathematical logic – logical statements, connectives, truth tables, logical equivalence,
tautology, contradiction - Groups-binary operations, semigroups, monoids, groups, an order of a group, order of an element, properties of groups
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