BA/B.Sc 1st Year Maths Syllabus RML Avadh University Course Details | RMLAUExams – Results Portal of www.rmlauexams.in

## Wednesday, February 12, 2020

Bachelor of Arts (BA)/Bachelor of Science (B.Sc) Part 1 Mathematics syllabus and course input details have been confirmed by Dr. Ram Manohar Lohia Avadh University, Ayodhya.

 BA/B.Sc Maths 1st Year Syllabus of Faizabad University:

 Paper – I Algebra and Trigonometry of Avadh University BA/B.Sc Maths Part 1 Syllabus:

 Algebra:

Unit I: Sequence, Subsequence, Bounded sequence, Limit of sequence, Convergent sequence, Monotone Sequence, Cauchy sequence, Cauchy’s Convergence, Bolzano Weierstrass Theorem for Sequences.

Infinite series, Convergence and Divergence of infinite series, Tests for convergence: Comparison test, Ratio Test, Cauchy’s nth root test, Rabbe’s test, Logarithmic Ratio test, De-Morgan and Bertrand test and Higher Logarithmic Ratio test, Alternating series, Leibnitz test, Absolute and Conditional convergence.

Unit II: Definition of examples of groups, elementary properties of groups, order of an element, Subgroups, properties of subgroups, product of two subgroups. Normalizer, Center of a group, Cyclic groups, properties of cyclic groups, classification of subgroups of cyclic groups.

Unit III: Permutation groups, even and odd permutations, alternating group, Coasets, index of subgroup, Lagrange’s theorem and consequences including fermat’s theorem.

Normal subgroups, Quotient groups. Group homomorphism and isomorphism, Cayley’s theorem, Fundamental theorem of homomorphism.

Unit IV: Definition and examples of rings, properties of rings. Characteristic of a ring, Subrings, Integral domains and Fields, Examples of fields: Zp, Q, R and C, Ideals, operations of ideals.

 Trigonometry:

Unit V: Complex functions and separation into real and imaginary parts, Exponential, direct and inverse trigonometric and hyperbolic functions, logarithmic function, Gregory’s series, Summation of series.

 Paper – II Calculus of RMLAU BA/B.Sc Maths Part 1 Syllabus:

 Differential Calculus:

Unit 1: ε-ᵹ definition of the limit of a function, Continuous functions and classification of discontinuities, Differentiability, Chain rule of differentiability, Rolle’s theorem, First and Second mean value theorems, Taylor’s theorems with Language’s and Cauchy’s forms of remainder, Indeterminate forms.

Unit 2: Successive differentiation and Leibnit’z theorem, Expansion of functions (In Taylor’s and Maclaurin’s series), Partial differentiation and Euler’s theorem, Jacobians, Maxima and Minima (for functions and two variables).

Unit 3: Tangents and normals (polar and only), Curvature, Envelopes and evolures, Asymptotes, Tests for concavity and convexity, Points of inflexion, Multiple points, tracing of curves in Cartesian and polar coordinates

 Integral Calculus:

Unit 4: Reduction formulae, Beta and Gmma functions, Double and triple integrals, Change of order of integration, Dirichlet’s integral formula

Unit 5: Rectification, Quadraturemoo, Volumes and Surfaces of solids of revolution, Pappus theorem.

 Paper – III Geometry and Vector Calculus of RMLAU Faizabad BA/B.Sc Maths Part 1 Syllabus:

 Geometry:

Unit 1: Confocal conics, Polor equation of a conic and its properties. Three dimensional system of co-ordinates, Projection and direction cosines, Plane, Straight line

Unit 2: Sphere, Cone and Cylinder, Central conicoids

Unit 3: Tangent plane and normal to be conicold, Pole and Polar, Conjugate Diameters, Generating lines, Plane sections of conicoid

 Vector Calculus:

Unit 4: Vector differentiation and integration, Gradient, Divergence and Curl and their properties

Unit 5: Line integral, Surface integral, Volume integral, Theorems of Gauss Divergence, Green and Stokes, and problems based on these