DISCRETE MATHEMATICS UNIT- I Recall of statements and logical connectives, tautologies and contradictions, logical equivalence. UNIT– II Boolean algebra and its properties, algebra of propositions as an example, De Morgan's Laws, partial order relations g.l.b, l.u.b., Algebra of electric circuits and its applications. UNIT - III Boolean functions -disjunctive and conjunctive normal forms. Boolean's expansion theorem, fundamental forms. Many terminal Networks. UNIT– IV Arbitrary Cartesian product of sets. Equivalence relations, partition of sets, injective, surjective, bijective maps, binary operations, countable, uncountable sets. UNIT –V Basic Concept of Graph Theory, Sub graphs, Trees and their properties, Binary Trees, Spanning Trees, Directed Trees, Planar graphs, Euler Circuit, Hamiltonian Graph. Chromatic number. TEXTBOOK: 1. Discrete Mathemeatics: H.K.Pathak 2. Discrete Mathematics : B.R.Thakur REFERNCE BOOKS: 1 Graph theory and its applications: Narsingh Dev. 2 Discrete Maths : C.L.Liu DIFFERENTIAL EQUATIONS UNIT –I Introduction to differential equation: Definition, order and degree of differential equation, derivation of a differential equation, general and particular solution of differential equation, solution of differential equation by separation of variables. UNIT-II Differential equation of first order and first degree: Homogenous differential equation, linear differential equation, Bernoulli’s equation, exact differential equation, integrating functions UNIT-III Differential Equation of first order but of higher degree: Singular solution, Equation solvable for p, x, y, one variable missing, homogeneous equation in x and y, Clairaut’s Equation. UNIT- IV Geometrical meaning of differential equation: Definition, Trajectories, orthogonal trajectories, self orthogonal family. UNIT-V Linear Differential equation with constant coefficient: Definition, Auxiliary equations, Particular Integrals, Short method of finding particular integrals in special cases, homogenous linear differential equation. TEXTBOOK: 1. Differential Equations and Fourier Series: H.K. Pathak REFERENCE: 1. Introductory course in differential equations : D. A. Murray 2. Differential equations(Awkl Sameekaran) : B.P. Parashar & L.P. Rajpal NUMERICAL ANALYSIS UNIT – I Solution of Polynomial and Transcendental Algebraic Equations: Bisection method, Regula falsi method & Newton’s method, Solution of Cubic & Biquadratic Equation. UNIT – II Simultaneous Equations And Matrix: Gauss-Jordan method, Cholesky’s method, Reduction to lower or upper Triangular forms, Inversion of matrix, method of partitioning. UNIT – III Interpolation - Single Variable Functions: Newton’s Interpolation formula, Newton's Forward and Backward Difference Interpolation Formula, Langranges Interpolation formula, Newton's Divided Difference Interpolation Formula. UNIT – IV Numerical Differentiation And Integration: Newton - cotes integration formula, Trapezoidal Rule, Simpson’s One-Third and Three-Eight Rule, Waddle's Rule. UNIT – V Numericals Solution of Ordinary Differential and Integral Equation: Euler’s, Picard's and Taylor's series Methods, Picard's Methods for successive approximations, Runga-Kutta Method. TEXTBOOK: 1. Numerical Analysis: H.K. Pathak 2. Numerical Methods: Gupta & Mallik REFERNCE BOOKS: 1. Introductory Method of Numerical Analysis: B.S. Grewal 2. Numerical methods for Science and Engineering: Jain M.K 3. calculations (John Willey & Sons): Iyengar S.R.K CALCULUS Differentiation UNIT – I Limit, continuity and differentiability of functions of one variable. UNIT – II Differentiation of functions, differentiation of function of function, function in product and quotient form, parametric and logarithmic differentiation. UNIT – III Tangent & Normal, subtangent, subnormal. Monotonic increasing and decreasing function, simple examples of maxima and minima. Integration UNIT – IV Integration of rational, irrational functions, integration of transcendental and hyperbolic function. UNIT - V Definite Integral and its properties. TEXTBOOK: 1. Calculus and Statistical Methods: H.K. Pathak. 2. Differentiation and Integeration: H.K. Pathak REFERENCE BOOKS 1. Differential Calculus: Gorakh Prasad 2. Integral Calculus : Gorakh Prasad STATISTICAL ANALYSIS UNIT- I Permutations and Combinations: Fundamental principle of counting. Factorial n. ( n!) . Permutations and combinations, derivation of formulae and their connections, simple applications. UNIT – II Probability: Sample space, Types of events (mutually exclusive, equally, likely event, favorable events, dependent and independent events), composition of events, additive and multiplicative law of probability, conditional probability, inverse probability, Baye’s Theorem. UNIT – III Frequency distribution: Frequency distribution and measures of dispersions( mean deviation, standard deviation, quartile deviation) UNIT – IV Binomial(renovsky formula), Poisson(application of poission distribution) and Normal distribution. UNIT –V Curve fitting and Principle of least square, Correlation and Regressions lines. TEXTBOOK: 1. Calculus & Statistical Analysis: H.K. Pathak 2. Descrete Mathematics : H.K. Pathak REFERENCE BOOK 1. Statistics: Rey & Sharma 2. Statistical Analysis: S.M. Shukla TRIGNOMETRY AND CO-ORDINATE GEOMETRY UNIT –I Trignometrical ratios, simple formula, compound angles, trigonometric ratios of multiple and multiple angles, properties of triangle, height and distance. UNIT-II Inverse Trigonometric Function, Solution of Trigonometric Equations, Expansion of trigonometrical function. UNIT-III Direct & inverse hyperbolic function, logarithm of complex quantities. Geometry UNIT- IV Rectangular Cartesian coordinate, equations of line, midpoint, intersection etc., equation of circle, distance formula. UNIT-V Pair of straight line, Centre, foci, length of major axis, length of minor axis, equation of major axis, equation of minor axis, equation of directrix, length and equation of letus rectum, eccentricity of parabola, ellipse and hyperbola. TEXTBOOK: 1. Vector Calculus & Geometry: H.K.Pathak 2. Trigonometry & Algebra: H.K.Pathak REFERENCE: 1. Trigonometry : S.L. Loney 2. Vector Calculus & Geometry: B. R. Thakur.