Modern Approach to Chemical Calculations<\/td> R. C. Mukherjee<\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n<\/span>VITEEE Syllabus for Maths 202<\/strong>3<\/span><\/h2>\n\n\n\nYou can check the VITEEE Maths syllabus 2023\u00a0 below.<\/p>\n\n\n\nUnits<\/strong><\/th>Topics<\/strong><\/th><\/tr>Matrices and their Applications<\/td> Adjoint, inverse \u2013 properties, computation of inverses, solution of system of linear equations by matrix inversion method. Rank of a matrix \u2013 elementary transformation on a matrix, consistency of a system of linear equations, Cramer\u2019s rule, non-homogeneous equations, homogeneous linear system and rank method. Solution of linear programming problems (LPP) in two variables.<\/td><\/tr> Trigonometry and Complex Numbers<\/td> Definition, range, domain, principal value branch, graphs of inverse trigonometric functions and their elementary properties. Complex number system – conjugate, properties, ordered pair representation. Modulus \u2013 properties, geometrical representation, polar form, principal value, conjugate, sum, difference, product, quotient, vector interpretation, solutions of polynomial equations, De Moivre\u2019s theorem and its applications. Roots of a complex number – nth roots, cube roots, fourth roots.<\/td><\/tr> Analytical Geometry of two dimensions<\/td> Definition of a conic \u2013 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 normals \u2013 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 \u2013 Standard equation of a rectangular hyperbola.<\/td><\/tr> Vector Algebra<\/td> Scalar Product \u2013 angle between two vectors, properties of scalar product, and applications of dot product. Vector product, right handed and left handed systems, properties of vector product, applications of cross product. Product of three vectors \u2013 Scalar triple product, properties of scalar triple product, vector triple product, vector product of four vectors, scalar product of four vectors.<\/td><\/tr> Analytical Geometry of Three Dimensions<\/td> Direction cosines \u2013 direction ratios – equation 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 \u2013 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 – shortest distance between two lines, condition for two lines to intersect, point of intersection, collinearity of three points. 2 Sphere \u2013 equation of the sphere whose centre and radius are given, equation of a sphere when the extremities of the diameter are given.<\/td><\/tr> Differential Calculus<\/td> 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 angle between curves. Mean value theorem – Rolle\u2019s Theorem, Lagrange Mean Value Theorem, Taylor\u2019s and Maclaurin\u2019s series, L\u2019 Hospital\u2019s Rule, stationary points, increasing, decreasing, maxima, minima, concavity, convexity and points of inflexion. Errors and approximations \u2013 absolute, relative, percentage errors – curve tracing, partial derivatives, Euler\u2019s theorem.<\/td><\/tr> Integral Calculus and its Applications<\/td> Simple definite integrals \u2013 fundamental theorems of calculus, properties of definite integrals. Reduction formulae \u2013 reduction formulae for x dx n sin and x dx n cos , Bernoulli\u2019s formula. Area of bounded regions, length of the curve.<\/td><\/tr> Differential Equations<\/td> Differential equations – formation of differential equations, order and degree, solving differential equations (1st order), variables separable, homogeneous and linear equations. Second order linear differential equations – second order linear differential equations with constant co-efficients, finding the particular integral if f(x) = emx, sin mx, cos mx, x, x2.<\/td><\/tr> Probability Distributions<\/td> Probability \u2013 Axioms \u2013 Addition law – Conditional probability \u2013 Multiplicative law – Baye\u2019s Theorem – Random variable – probability density function, distribution function, mathematical expectation, variance Theoretical distributions – discrete distributions, Binomial, Poisson distributions- Continuous distributions, Normal distribution.<\/td><\/tr> Discrete Mathematics<\/td> Functions \u2013 Relations \u2013 Basics of counting. Mathematical logic \u2013 logical statements, connectives, truth tables, logical equivalence, tautology, a contradiction. Groups-binary operations, semi groups, monoids, groups, order of a group, order of an element, properties of groups<\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n
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