History & Evolution of Department: 1952 establishment year
Vission:
 To Conduct One Certificate course in our subject concerned.
 To Practice some more formative evaluation methods.
 To extend Guest/ Extension Lectures/Programmes in good number.
 To improve number of student study projects.
 To apply MRPs by our faculty to UGC SERO.
Mission;
 To be strengthen the Research abilities
 To Organize more no. of Seminars, Workshops and Training Programmes
 Special Attention to the School level students to develop Mathematical basic knowledge through our “Math Club”
 Special Attention to the students to practice “MATH GYM” for stress management & some competitions like poster presentations, Quizzes, preparation of Cross word puzzles etc…to create interest on Mathematics.
 Special Attention to the students to development of Leadership Qualities and Team work skills through the formation of “Team Achievers ”
 Special attention to the training and development of Analytical skills
 Updated ICT enabled teachinglearning ambience
Every year conducting additional classes for final year students to attend P.G entrance test.
Succession List Of Heads of Department
Sno  Name  Qualification 
1  Sri.S.A.Rahiman  B.SC(Hons) 
2  Sri.K.Sabasiva Rao  M.Sc 
3  Sri.P.V.Subrahmanyam  M.Sc 
4  Sri.B.A.Vijayakumar  M.Sc 
5  Sri.O.Arjuna rao  M.Sc 
6  Sri.G.Atchi Reddy  M.A 
7  Sri.P.L.V.Nageswara Rao  M.A,M.Phil 
8  Sri.K.P.Sastry  M.Sc 
9  Smt.Saraswathi  M.Sc 
10  Sri.K.Siva Prasad  M.Sc 
11  Sri.P.Latchanna  M.Sc,B.Ed 
12  Sri.R.Gopalarao  M.Sc 
13  Sri.P.Surekha  M.Sc 
14  Sri.Ch.Vijaya Kumar  M.Sc,B.Ed 
Conventional Courses:1(MPC)
Restructured Courses:4(MPCs,MPE,MCIc,MECs)
Students Strength(Last 3 Years)
2018 2019
S.No  CLASS  BOYS + GIRLS  TOTAL 
1  Ist  216 + 27  243 
2  2nd  217+27  244 
3  3rd  163+20  183 
Total Strength  596+74  670 
2017 2018
S.No  CLASS  BOYS + GIRLS  TOTAL 
1  1^{st}  256+29  285 
2  2nd  178+19  197 
3  3rd  184+18  202 
Total Strength  618+66  684 
2016 2017
S.No  CLASS  BOYS + GIRLS  TOTAL 
1  1st  200+20  220 
2  2nd  204+21  225 
3  3rd  152+10  162 
Total Strength  556+51  607 
List of Enrollments Category wise in first year
Year  SC  ST  BC  Others  Total 
201819  30  09  200  04  243 
201718  27  08  243  07  285 
201617  24  05  181  10  220 
Facilities available in the department
Books in the Departmental Library
 Data Analytics Books: 255
 Complimentary copies and personal books: 90
SNO  PHOTO  NAME  QUALIFICATION  DESIGNATION  EMAILID  PROFILE 

1  CH.VIJAY KUMAR  M.Sc, B.ED  HOD  Vijay.chalumuri123 @gmail.com  click here  
2  L.VENKATARAMANA  M.Sc, B.ED  LECTURER  tarunnaidu39 @gmail.com  click here  
3  Y.PRASANTHI  M.Sc, B.ED  LECTURER  Prasanthi.yetchena @gmail.com  click here 
B.Sc., MATHEMATICS SEMESTERWISE SYLLABUS
THEORY AND MODEL QUESTION PAPERS
(AS PER CBCS AND SEMESTER SYSTEM)
I, II & III YEARS
w.e.f. 201516
(REVISED IN APRIL, 2016)Andhra Pradesh State Council of Higher Education
CBCS B.A./B.Sc. Mathematics Course Structure
w.e.f. 201516 (Revised in April, 2016)
Year  Seme ster  Paper  Subject  Hrs.  Credits  IA  EA  Total 
1 
I  I  Differential Equations
& Differential Equations Problem Solving Sessions 
6  5  25  75  100 
II  II  Solid Geometry
& Solid Geometry Problem Solving Sessions 
6  5  25  75  100  
2 
III  III  Abstract Algebra
& Abstract Algebra Problem Solving Sessions 
6  5  25  75  100 
IV  IV  Real Analysis
& Real Analysis Problem Solving Sessions 
6  5  25  75  100  
3 
V  V  Ring Theory & Vector Calculus
& Ring Theory & Vector Calculus Problem Solving Sessions 
5  5  25  75  100 
VI  Linear Algebra
& Linear Algebra Problem Solving Sessions 
5  5  25  75  100  
VI

VII  Electives: (any one)
VII(A) Laplace Transforms VII(B) Numerical Analysis VII(C) Number Theory & Elective Problem Solving Sessions 
5  5  25  75  100  
VIII  Cluster Electives:
VIIIA1: Integral Transforms VIIIA2: Advanced Numerical Analysis VIIIA3: Project work or VIIIB1: Principles of Mechanics VIIIB2: Fluid Mechanics VIIIB3: Project work or VIIIC1: Graph Theory VIIIC2: Applied Graph Theory VIIIC3: Project work 
5  5  25  75  100  
5  5  25  75  100  
5  5  25  75  100  
Andhra Pradesh State Council of Higher Education
w.e.f. 201516 (Revised in April, 2016)
B.A./B.Sc. FIRST YEAR MATHEMATICS SYLLABUS
SEMESTER –I, PAPER – 1
DIFFERENTIAL EQUATIONS
60 Hrs
UNIT – I (12 Hours), Differential Equations of first order and first degree :
Linear Differential Equations; Differential Equations Reducible to Linear Form; Exact Differential Equations; Integrating Factors; Change of Variables.
UNIT – II (12 Hours), Orthogonal Trajectories.
Differential Equations of first order but not of the first degree :
Equations solvable for p; Equations solvable for y; Equations solvable for x; Equations that do not contain. x (or y); Equations of the first degree in x and y – Clairaut’s Equation.
UNIT – III (12 Hours), Higher order linear differential equationsI :
Solution of homogeneous linear differential equations of order n with constant coefficients; Solution of the nonhomogeneous linear differential equations with constant coefficients by means of polynomial operators.
General Solution of f(D)y=0
General Solution of f(D)y=Q when Q is a function of x.
is Expressed as partial fractions.
P.I. of f(D)y = Q when Q=
P.I. of f(D)y = Q when Q is b sin ax or b cos ax.
UNIT – IV (12 Hours), Higher order linear differential equationsII :
Solution of the nonhomogeneous linear differential equations with constant coefficients.
P.I. of f(D)y = Q when Q=
P.I. of f(D)y = Q when Q=
P.I. of f(D)y = Q when Q=
P.I. of f(D)y = Q when Q=
UNIT –V (12 Hours), Higher order linear differential equationsIII :
Method of variation of parameters; Linear differential Equations with nonconstant coefficients; The CauchyEuler Equation.
Reference Books :
 Differential Equations and Their Applications by Zafar Ahsan, published by PrenticeHall of India Learning Pvt. Ltd. New DelhiSecond edition.
 A text book of mathematics for BA/BSc Vol 1 by N. Krishna Murthy & others, published by Chand & Company, New Delhi.
 Ordinary and Partial Differential Equations Raisinghania, published by S. Chand & Company, New Delhi.
 Differential Equations with applications and programs – S. Balachandra Rao & HR Anuradhauniversities press.
Suggested Activities:
Seminar/ Quiz/ Assignments/ Project on Application of Differential Equations in Real life
B.A./B.Sc. FIRST YEAR MATHEMATICS SYLLABUS
SEMESTER – II, PAPER – 2
SOLID GEOMETRY
60 Hrs
UNIT – I (12 hrs) : The Plane :
Equation of plane in terms of its intercepts on the axis, Equations of the plane through the given points, Length of the perpendicular from a given point to a given plane, Bisectors of angles between two planes, Combined equation of two planes, Orthogonal projection on a plane.
UNIT – II (12 hrs) : The Line :
Equation of a line; Angle between a line and a plane; The condition that a given line may lie in a given plane; The condition that two given lines are coplanar; Number of arbitrary constants in the equations of straight line; Sets of conditions which determine a line; The shortest distance between two lines; The length and equations of the line of shortest distance between two straight lines; Length of the perpendicular from a given point to a given line;
UNIT – III (12 hrs) : Sphere :
Definition and equation of the sphere; Equation of the sphere through four given points; Plane sections of a sphere; Intersection of two spheres; Equation of a circle; Sphere through a given circle; Intersection of a sphere and a line; Power of a point; Tangent plane; Plane of contact; Polar plane; Pole of a Plane; Conjugate points; Conjugate planes;
UNIT – IV (12 hrs) : Sphere &Cones :
Angle of intersection of two spheres; Conditions for two spheres to be orthogonal; Radical plane; Coaxial system of spheres; Simplified from of the equation of two spheres.
Definitions of a cone; vertex; guiding curve; generators; Equation of the cone with a given vertex and guiding curve; Enveloping cone of a sphere; Equations of cones with vertex at origin are homogenous; Condition that the general equation of the second degree should represent a cone; Condition that a cone may have three mutually perpendicular generators;
UNIT – V (12 hrs) Cones & Cylinders :
The intersection of a line and a quadric cone; Tangent lines and tangent plane at a point; Condition that a plane may touch a cone; Reciprocal cones; Intersection of two cones with a common vertex; Right circular cone; Equation of the right circular cone with a given vertex; axis and semivertical angle.
Definition of a cylinder; Equation to the cylinder whose generators intersect a given conic and are parallel to a given line; Enveloping cylinder of a sphere; The right circular cylinder; Equation of the right circular cylinder with a given axis and radius.
Reference Books :
 Analytical Solid Geometry by Shanti Narayan and P.K. Mittal, Published by S. Chand & Company Ltd. 7th Edition.
 A textbook of Mathematics for BA/B.Sc Vol 1, by V Krishna Murthy & Others, Published by S. Chand & Company, New Delhi.
 A text Book of Analytical Geometry of Three Dimensions, by P.K. Jain and Khaleel Ahmed, Published by Wiley Eastern Ltd., 1999.
 Coordinate Geometry of two and three dimensions by P. Balasubrahmanyam, K.Y. Subrahmanyam, G.R. Venkataraman published by TataMC GranHill Publishers Company Ltd., New Delhi.
Suggested Activities:
Seminar/ Quiz/ Assignments/ Project on Application of Solid Geometry in Engineering
B.A./B.Sc. SECOND YEAR MATHEMATICS SYLLABUS
SEMESTER – III, PAPER – 3
ABSTRACT ALGEBRA
60 Hrs
UNIT – 1 : (10 Hrs) GROUPS : –
Binary Operation – Algebraic structure – semi groupmonoid – Group definition and elementary properties Finite and Infinite groups – examples – order of a group. Composition tables with examples.
UNIT – 2 : (14 Hrs) SUBGROUPS : –
Complex Definition – Multiplication of two complexes Inverse of a complexSubgroup definition – examplescriterion for a complex to be a subgroups.
Criterion for the product of two subgroups to be a subgroupunion and Intersection of subgroups.
Cosets and Lagrange’s Theorem :
Cosets Definition – properties of Cosets–Index of a subgroups of a finite groups–Lagrange’s Theorem.
UNIT –3 : (12 Hrs) NORMAL SUBGROUPS : –
Definition of normal subgroup – proper and improper normal subgroup–Hamilton group – criterion for a subgroup to be a normal subgroup – intersection of two normal subgroups – Sub group of index 2 is a normal sub group – simple group – quotient group – criteria for the existence of a quotient group.
UNIT – 4 : (10 Hrs) HOMOMORPHISM : –
Definition of homomorphism – Image of homomorphism elementary properties of homomorphism – Isomorphism – aultomorphism definitions and elementary properties–kernel of a homomorphism – fundamental theorem on Homomorphism and applications.
UNIT – 5 : (14 Hrs) PERMUTATIONS AND CYCLIC GROUPS : –
Definition of permutation – permutation multiplication – Inverse of a permutation – cyclic permutations – transposition – even and odd permutations – Cayley’s theorem.
Cyclic Groups :
Definition of cyclic group – elementary properties – classification of cyclic groups.
Reference Books :
 Abstract Algebra, by J.B. Fraleigh, Published by Narosa Publishing house.
 A text book of Mathematics for B.A. / B.Sc. by B.V.S.S. SARMA and others, Published by S.Chand & Company, New Delhi.
 Modern Algebra by M.L. Khanna.
Suggested Activities:
Seminar/ Quiz/ Assignments/ Project on Group theory and its applications in Graphics and Medical image Analysis
B.A./B.Sc. SECOND YEAR MATHEMATICS SYLLABUS
SEMESTER – IV, PAPER 4
REAL ANALYSIS
60 Hrs
UNIT – I (12 hrs) : REAL NUMBERS :
The algebraic and order properties of R, Absolute value and Real line, Completeness property of R, Applications of supreme property; intervals. No. Question is to be set from this portion.
Real Sequences: Sequences and their limits, Range and Boundedness of Sequences, Limit of a sequence and Convergent sequence.
The Cauchy’s criterion, properly divergent sequences, Monotone sequences, Necessary and Sufficient condition for Convergence of Monotone Sequence, Limit Point of Sequence, Subsequences and the Bolzanoweierstrass theorem – Cauchy Sequences – Cauchey’s general principle of convergence theorem.
UNIT –II (12 hrs) : INFINITIE SERIES :
Series : Introduction to series, convergence of series. Cauchey’s general principle of convergence for series tests for convergence of series, Series of NonNegative Terms.
 Ptest
 Cauchey’s n^{th} root test or Root Test.
 D’Alemberts’ Test or Ratio Test.
 Alternating Series – Leibnitz Test.
Absolute convergence and conditional convergence, semi convergence.
UNIT – III (12 hrs) : CONTINUITY :
Limits : Real valued Functions, Boundedness of a function, Limits of functions. Some extensions of the limit concept, Infinite Limits. Limits at infinity. No. Question is to be set from this portion.
Continuous functions : Continuous functions, Combinations of continuous functions, Continuous Functions on intervals, uniform continuity.
UNIT – IV (12 hrs) : DIFFERENTIATION AND MEAN VALUE THEORMS :
The derivability of a function, on an interval, at a point, Derivability and continuity of a function, Graphical meaning of the Derivative, Mean value Theorems; Role’s Theorem, Lagrange’s Theorem, Cauchhy’s Mean value Theorem
UNIT – V (12 hrs) : RIEMANN INTEGRATION :
Riemann Integral, Riemann integral functions, Darboux theorem. Necessary and sufficient condition for R – integrability, Properties of integrable functions, Fundamental theorem of integral calculus, integral as the limit of a sum, Mean value Theorems.
Reference Books :
 Real Analysis by Rabert & Bartely and .D.R. Sherbart, Published by John Wiley.
 A Text Book of B.Sc Mathematics by B.V.S.S. Sarma and others, Published by S. Chand & Company Pvt. Ltd., New Delhi.
 Elements of Real Analysis as per UGC Syllabus by Shanthi Narayan and Dr. M.D. Raisingkania Published by S. Chand & Company Pvt. Ltd., New Delhi.
Suggested Activities:
Seminar/ Quiz/ Assignments/ Project on Real Analysis and its applications
B.A./B.Sc. THIRD YEAR MATHEMATICS SYLLABUS
SEMESTER – V, PAPER 5
RING THEORY & VECTOR CALCULUS
60 Hrs
UNIT – 1 (12 hrs) RINGSI : –
Definition of Ring and basic properties, Boolean Rings, divisors of zero and cancellation laws Rings, Integral Domains, Division Ring and Fields, The characteristic of a ring – The characteristic of an Integral Domain, The characteristic of a Field. Sub Rings, Ideals
UNIT – 2 (12 hrs) RINGSII : –
Definition of Homomorphism – Homorphic Image – Elementary Properties of Homomorphism –Kernel of a Homomorphism – Fundamental theorem of Homomorphism –Maximal Ideals – Prime Ideals.
UNIT –3 (12 hrs) VECTOR DIFFERENTIATION : –
Vector Differentiation, Ordinary derivatives of vectors, Differentiability, Gradient, Divergence, Curl operators, Formulae Involving these operators.
UNIT – 4 (12 hrs) VECTOR INTEGRATION : –
Line Integral, Surface Integral, Volume integral with examples.
UNIT – 5 (12 hrs) VECTOR INTEGRATION APPLICATIONS : –
Theorems of Gauss and Stokes, Green’s theorem in plane and applications of these theorems.
Reference Books :
 Abstract Algebra by J. Fralieh, Published by Narosa Publishing house.
 Vector Calculus by Santhi Narayana, Published by S. Chand & Company Pvt. Ltd., New Delhi.
 A text Book of B.Sc., Mathematics by B.V.S.S.Sarma and others, published by S. Chand & Company Pvt. Ltd., New Delhi.
 Vector Calculus by R. Gupta, Published by Laxmi Publications.
 Vector Calculus by P.C. Matthews, Published by Springer Verlag publicattions.
 Rings and Linear Algebra by Pundir & Pundir, Published by Pragathi Prakashan.
Suggested Activities:
Seminar/ Quiz/ Assignments/ Project on Ring theory and its applications
B.A./B.Sc. THIRD YEAR MATHEMATICS SYLLABUS
SEMESTER – V, PAPER 6
LINEAR ALGEBRA
60 Hrs
UNIT – I (12 hrs) : Vector SpacesI :
Vector Spaces, General properties of vector spaces, ndimensional Vectors, addition and scalar multiplication of Vectors, internal and external composition, Null space, Vector subspaces, Algebra of subspaces, Linear Sum of two subspaces, linear combination of Vectors, Linear span Linear independence and Linear dependence of Vectors.
UNIT –II (12 hrs) : Vector SpacesII :
Basis of Vector space, Finite dimensional Vector spaces, basis extension, coordinates, Dimension of a Vector space, Dimension of a subspace, Quotient space and Dimension of Quotientspace.
UNIT –III (12 hrs) : Linear Transformations :
Linear transformations, linear operators, Properties of L.T, sum and product of LTs, Algebra of Linear Operators, Range and null space of linear transformation, Rank and Nullity of linear transformations – Rank – Nullity Theorem.
UNIT –IV (12 hrs) : Matrix :
Matrices, Elementary Properties of Matrices, Inverse Matrices, Rank of Matrix, Linear Equations, Characteristic Roots, Characteristic Values & Vectors of square Matrix, Cayley – Hamilton Theorem.
UNIT –V (12 hrs) : Inner product space :
Inner product spaces, Euclidean and unitary spaces, Norm or length of a Vector, Schwartz inequality, Triangle in Inequality, Parallelogram law, Orthogonality, Orthonormal set, complete orthonormal set, Gram – Schmidt orthogonalisation process. Bessel’s inequality and Parseval’s Identity.
Reference Books :
 Linear Algebra by J.N. Sharma and A.R. Vasista, published by Krishna Prakashan Mandir, Meerut 250002.
 Matrices by Shanti Narayana, published by S.Chand Publications.
 Linear Algebra by Kenneth Hoffman and Ray Kunze, published by Pearson Education (low priced edition), New Delhi.
 Linear Algebra by Stephen H. Friedberg et al published by Prentice Hall of India Pvt. Ltd. 4^{th} Edition 2007.
Suggested Activities:
Seminar/ Quiz/ Assignments/ Project on “Applications of Linear algebra Through Computer Sciences”
B.A./B.Sc. THIRD YEAR MATHEMATICS SYLLABUS
SEMESTER – VI, PAPER – VII(A)
ELECTIVEVII(A); LAPLACE TRANSFORMS
60 Hrs
UNIT – 1 (12 hrs) Laplace Transform I : –
Definition of – Integral Transform – Laplace Transform Linearity, Property, Piecewise continuous Functions, Existence of Laplace Transform, Functions of Exponential order, and of Class A.
UNIT – 2 (12 hrs) Laplace Transform II : –
First Shifting Theorem, Second Shifting Theorem, Change of Scale Property, Laplace Transform of the derivative of f(t), Initial Value theorem and Final Value theorem.
UNIT – 3 (12 hrs) Laplace Transform III : –
Laplace Transform of Integrals – Multiplication by t, Multiplication by t^{n} – Division by t. Laplace transform of Bessel Function, Laplace Transform of Error Function, Laplace Transform of Sine and cosine integrals.
UNIT –4 (12 hrs) Inverse Laplace Transform I : –
Definition of Inverse Laplace Transform. Linearity, Property, First Shifting Theorem, Second Shifting Theorem, Change of Scale property, use of partial fractions, Examples.
UNIT –5 (12 hrs) Inverse Laplace Transform II : –
Inverse Laplace transforms of Derivatives–Inverse Laplace Transforms of Integrals – Multiplication by Powers of ‘P’– Division by powers of ‘P’– Convolution Definition – Convolution Theorem – proof and Applications – Heaviside’s Expansion theorem and its Applications.
Reference Books :
 Laplace Transforms by A.R. Vasistha and Dr. R.K. Gupta Published by Krishna Prakashan Media Pvt. Meerut.
 Fourier Series and Integral Transforms by Dr. S. Sreenadh Published by S.Chand and Co., Pvt. Ltd., New Delhi.
 Laplace and Fourier Transforms by Dr. J.K. Goyal and K.P. Gupta, Published by Pragathi Prakashan, Meerut.
 Integral Transforms by M.D. Raising hania, – H.C. Saxsena and H.K. Dass Published by S. Chand and Co., Pvt.Ltd., New Delhi.
Suggested Activities:
Seminar/ Quiz/ Assignments
B.A./B.Sc. THIRD YEAR MATHEMATICS SYLLABUS
SEMESTER – VI, PAPER – VII(B)
ELECTIVE–VII(B); NUMERICAL ANALYSIS
60 Hrs
UNIT I: (10 hours)
Errors in Numerical computations : Errors and their Accuracy, Mathematical Preliminaries, Errors and their Analysis, Absolute, Relative and Percentage Errors, A general error formula, Error in a series approximation.
UNIT – II: (12 hours)
Solution of Algebraic and Transcendental Equations: The bisection method, The iteration method, The method of false position, Newton Raphson method, Generalized Newton Raphson method. Muller’s Method
UNIT – III: (12 hours) Interpolation – I
Interpolation : Errors in polynomial interpolation, Finite Differences, Forward differences, Backward differences, Central Differences, Symbolic relations, Detection of errors by use of Differences Tables, Differences of a polynomial
UNIT – IV: (12 hours) Interpolation – II
Newton’s formulae for interpolation. Central Difference Interpolation Formulae, Gauss’s central difference formulae, Stirling’s central difference formula, Bessel’s Formula, Everett’s Formula.
UNIT – V : (14 hours) Interpolation – III
Interpolation with unevenly spaced points, Lagrange’s formula, Error in Lagrange’s formula, Divided differences and their properties, Relation between divided differences and forward differences, Relation between divided differences and backward differences Relation between divided differences and central differences, Newton’s general interpolation Formula, Inverse interpolation.
Reference Books :
 Numerical Analysis by S.S.Sastry, published by Prentice Hall of India Pvt. Ltd., New Delhi. (Latest Edition)
 Numerical Analysis by G. Sankar Rao published by New Age International Publishers, New –
 Finite Differences and Numerical Analysis by H.C Saxena published by S. Chand and Company, Pvt.Ltd., New Delhi.
 Numerical methods for scientific and engineering computation by M.K.Jain, S.R.K.Iyengar, R.K. Jain.
Suggested Activities:
Seminar/ Quiz/ Assignments
B.A./B.Sc. THIRD YEAR MATHEMATICS SYLLABUS
SEMESTER – VI, PAPER – VII(C)
ELECTIVE– VII(C) : NUMBER THEORY
UNITI (12 hours)
Divisibility – Greatest Common Divisor – Euclidean Algorithm – The Fundamental Theorem of Arithmetic
UNITII (12 hours)
Congruences – Special Divisibility Tests – Chinese Remainder Theorem Fermat’s Little Theorem – Wilson’s Theorem – Residue Classes and Reduced Residue Classes – Solutions of Congruences
UNITIII (12 hours)
Number Theory from an Algebraic Viewpoint – Multiplicative Groups, Rings and Fields
UNITIV (12 hours)
Quadratic Residues – Quadratic Reciprocity – The Jacobi Symbol
UNITV (12 hours)
Greatest Integer Function – Arithmetic Functions – The Moebius Inversion Formula
Reference Books:
 “Introduction to the Theory of Numbers” by Niven, Zuckerman & Montgomery (John Wiley & Sons)
 “Elementary Number Theory” by David M. Burton.
 Elementary Number Theory, by David, M. Burton published by 2^{nd} Edition (UBS Publishers).
 Introduction to Theory of Numbers, by Davenport , Higher Arithmetic published by 5^{th }Edition (John Wiley & Sons) Niven,Zuckerman & Montgomery.(Camb, Univ, Press)
 Number Theory by Hardy & Wright published by Oxford Univ, Press.
 Elements of the Theory of Numbers by Dence, J. B & Dence T.P published by Academic
B.A./B.Sc. THIRD YEAR MATHEMATICS SYLLABUS,
SEMESTER – VI, CLUSTER – A, PAPER – VIIIA1
Cluster Elective VIIIA1: INTEGRAL TRANSFORMS
60 Hrs
UNIT – 1 (12 hrs) Application of Laplace Transform to solutions of Differential Equations : –
Solutions of ordinary Differential Equations.
Solutions of Differential Equations with constants coefficient
Solutions of Differential Equations with Variable coefficient
UNIT – 2 (12 hrs) Application of Laplace Transform : –
Solution of simultaneous ordinary Differential Equations.
Solutions of partial Differential Equations.
UNIT – 3 (12 hrs) Application of Laplace Transforms to Integral Equations : –
Definitions : Integral EquationsAbel’s, Integral EquationIntegral Equation of Convolution Type, Integro Differential Equations.Application of L.T. to Integral Equations.
UNIT –4 (12 hrs) Fourier TransformsI : –
Definition of Fourier Transform – Fourier’s in Transform – Fourier cosine Transform – Linear Property of Fourier Transform – Change of Scale Property for Fourier Transform – sine Transform and cosine transform shifting property – modulation theorem.
UNIT – 5 (12 hrs) Fourier TransformII : –
Convolution Definition – Convolution Theorem for Fourier transform – parseval’s Indentify – Relationship between Fourier and Laplace transforms – problems related to Integral Equations.
Finte Fourier Transforms : –
Finte Fourier Sine Transform – Finte Fourier Cosine Transform – Inversion formula for sine and cosine Transforms only statement and related problems.
Reference Books :
 Integral Transforms by A.R. Vasistha and Dr. R.K. Gupta Published by Krishna Prakashan Media Pvt. Ltd. Meerut.
 A Course of Mathematical Analysis by Shanthi Narayana and P.K. Mittal, Published by S. Chand and Company Ltd., New Delhi.
 Fourier Series and Integral Transforms by Dr. S. Sreenadh Published by S.Chand and Company Pvt. Ltd., New
 Lapalce and Fourier Transforms by Dr. J.K. Goyal and K.P. Gupta, Published by Pragathi Prakashan, Meerut.
 Integral Transforms by M.D. Raising hania, – H.C. Saxsena and H.K. Dass Published by S.Chand and Company pvt. Ltd., New Delhi.
Suggested Activities:
Seminar/ Quiz/ Assignments
B.A./B.Sc. THIRD YEAR MATHEMATICS SYLLABUS
SEMESTER – VI: PAPER – VIIIA2
ELECTIVE – VIIIA2: ADVANCED NUMERICAL ANALYSIS
60 Hrs
Unit – I (10 Hours)
Curve Fitting: Least – Squares curve fitting procedures, fitting a straight line, nonlinear curve fitting, Curve fitting by a sum of exponentials.
UNIT II : (12 hours)
Numerical Differentiation: Derivatives using Newton’s forward difference formula, Newton’s backward difference formula, Derivatives using central difference formula, stirling’s interpolation formula, Newton’s divided difference formula, Maximum and minimum values of a tabulated function.
UNIT III : (12 hours)
Numerical Integration: General quadrature formula on errors, Trapozoidal rule, Simpson’s 1/3 – rule, Simpson’s 3/8 – rule, and Weddle’s rules, Euler – Maclaurin Formula of summation and quadrature, The Euler transformation.
UNIT – IV: (14 hours)
Solutions of simultaneous Linear Systems of Equations: Solution of linear systems – Direct methods, Matrix inversion method, Gaussian elimination methods, GaussJordan Method ,Method of factorization, Solution of Tridiagonal Systems,. Iterative methods. Jacobi’s method, Gausssiedal method.
UNIT – V (12 Hours)
Numerical solution of ordinary differential equations: Introduction, Solution by Taylor’s Series, Picard’s method of successive approximations, Euler’s method, Modified Euler’s method, Runge – Kutta methods.
Reference Books :
 Numerical Analysis by S.S.Sastry, published by Prentice Hall India (Latest Edition).
 Numerical Analysis by G. Sankar Rao, published by New Age International Publishers, New –Hyderabad.
 Finite Differences and Numerical Analysis by H.C Saxena published by S. Chand and Company, Pvt.Ltd., New Delhi.
 Numerical methods for scientific and engineering computation by M.K.Jain, S.R.K.Iyengar, R.K. Jain.
Suggested Activities:
Seminar/ Quiz/ Assignments
B.A./B.Sc. THIRD YEAR MATHEMATICS SYLLABUS
SEMESTER – VI, CLUSTERB, PAPER – VIIIB1
Cluster Elective – VIIIB1 : PRINCIPLES OF MECHANICS
60 Hrs
Unit – I : (10 hours)
D’Alembert’s Principle and Lagrange’s Equations : some definitions – Lagrange’s equations for a Holonomic system – Lagrange’s Equations of motion for conservative, nonholonomic system.
Unit – II: (10 hours)
Variational Principle and Lagrange’s Equations: Variatonal Principle – Hamilton’s Principle – Derivation of Hamilton’s Principle from Lagrange’s Equations – Derivation of Lagrange’s Equations from Hamilton’s Principle – Extension of Hamilton’s Principle – Hamilton’s Principle for Nonconservative, Nonholonomic system – Generalised Force in Dynamic System – Hamilton’s Principle for Conservative, Nonholonomic system – Lagrange’s Equations for Nonconservative, Holonomic system – Cyclic or Ignorable Coordinates.
Unit –III: (15 hours)
Conservation Theorem, Conservation of Linear Momentum in Lagrangian Formulation – Conservation of angular Momentum – conservation of Energy in Lagrangian formulation.
Unit – IV: (15 hours)
Hamilton’s Equations of Motion: Derivation of Hamilton’s Equations of motion – Routh’s procedure – equations of motion – Derivation of Hamilton’s equations from Hamilton’s Principle – Principle of Least Action – Distinction between Hamilton’s Principle and Principle of Least Action.
Unit – V: (10 hours)
Canonical Transformation: Canonical coordinates and canonical transformations – The necessary and sufficient condition for a transformation to be canonical – examples of canonical transformations – properties of canonical transformation – Lagrange’s bracket is canonical invariant – poisson’s bracket is canonical invariant – poisson’s bracket is invariant under canonical transformation – Hamilton’s Equations of motion in poisson’s bracket – Jacobi’s identity for poisson’s brackets.
Reference Text Books :
 Classical Mechanics by C.R.Mondal Published by Prentice Hall of India, New Delhi.
 A Text Book of Fluid Dynamics by F. Charlton Published by CBS Publications, New Delhi.
 Classical Mechanics by Herbert Goldstein, published by Narosa Publications, New Delhi.
 Fluid Mechanics by T. Allen and I.L. Ditsworth Published by (McGraw Hill, 1972)
 Fundamentals of Mechanics of fluids by I.G. Currie Published by (CRC, 2002)
 Fluid Mechanics : An Introduction to the theory, by Chiashun Yeh Published by (McGraw Hill, 1974)
 Introduction to Fluid Mechanics by R.W Fox, A.T Mc Donald and P.J. Pritchard Published by (John Wiley and Sons Pvt. Ltd., 2003)
B.A./B.Sc. THIRD YEAR MATHEMATICS SYLLABUS
SEMESTER – VI, CLUSTERB, PAPER – VIIIB2
Cluster Elective–VIIIB2 : FLUID MECHANICS
60 Hrs
Unit – I : (10 hours)
Kinematics of Fluids in Motion
Real fluids and Ideal fluids – Velocity of a Fluid at a point – Streamlines and pthlines – steady and Unsteady flows – the velocity potential – The Vorticity vector – Local and Particle Rates of Change – The equation of Continuity – Acceleration of a fluid – Conditions at a rigid boundary – General Analysis of fluid motion.
Unit – II : (10 hours)
Equations of motion of a fluid Pressure at a point in fluid at rest – Pressure at a point in a moving fluid – Conditions at a boundary of two inviscid immiscible fluids – Euler’s equations of motion – Bernoulli’s equation – Worked examples.
Unit – III : (10 hours)
Discussion of the case of steady motion under conservative body forces – Some flows involving axial symmetry – Some special twodimensional flows – Impulsive motion – Some further aspects of vortex motion.
Unit – IV : (15 hours)
Some Two – dimensional Flows, Meaning of twodimensional flow – Use of Cylindrical polar coordinates – The stream function – The complex potential for twodimensional, Irrotational, Incompressible flow – Uniform Stream – The MilneThomson Circle theorem – the theorem of Blasius.
Unit – V : (15 hours)
Viscous flow,Stress components in a real fluid – Relations between Cartesian components of stress – Translational motion of fluid element – The rate of strain quadric and principal stresses – Some further properties of the rate of strain quadric – Stress analysis in fluid motion – Relations between stress and rate of strain – the coefficient of viscosity and laminar flow – The NavierStokes equations of motion of a viscous fluid.
Reference Text Books :
 A Text Book of Fluid Dynamics by F. Charlton Published by CBS Publications, New Delhi.
 Classical Mechanics by Herbert Goldstein, published by Narosa Publications, New Delhi.
 Fluid Mechanics by T. Allen and I.L. Ditsworth published by (McGraw Hill, 1972)
 Fundamentals of Mechanics of fluids by I.G. Currie published by (CRC, 2002)
 Fluid Mechanics, An Introduction to the theory by Chiashun Yeh published by (McGraw Hill, 1974)
 Fluids Mechanics by F.M White published by (McGraw Hill, 2003)
 Introduction to Fluid Mechanics by R.W Fox, A.T Mc Donald and P.J. Pritchard published by (John Wiley and Sons Pvt. Ltd., 2003
B.A./B.Sc. THIRD YEAR MATHEMATICS SYLLABUS
SEMESTER – VI, CLUSTERC, PAPER – VIIIC1
Cluster Elective–VIIIC1: GRAPH THEORY
60 Hrs
UNIT – I (12 hrs) Graphs and Sub Graphs :
Graphs , Simple graph, graph isomorphism, the incidence and adjacency matrices, sub graphs, vertex degree, Hand shaking theorem, paths and connection, cycles.
UNIT – II (12 hrs)
Applications, the shortest path problem, Sperner’s lemma.
Trees :
Trees, cut edges and Bonds, cut vertices, Cayley’s formula.
UNIT – III (12 hrs) :
Applications of Trees – the connector problem.
Connectivity
Connectivity, Blocks and Applications, construction of reliable communication Networks,
UNIT – IV (12 hrs):
Euler tours and Hamilton cycles
Euler tours, Euler Trail, Hamilton path, Hamilton cycles , dodecahedron graph, Petersen graph, hamiltonian graph, closure of a graph.
UNIT – V (12 hrs)
Applications of Eulerian graphs, the Chinese postman problem, Fleury’s algorithm – the travelling salesman problem.
Reference Books :
 Graph theory with Applications by J.A. Bondy and U.S.R. Murthy published by Mac. Millan Press
 Introduction to Graph theory by S. Arumugham and S. Ramachandran, published by scitech Publications, Chennai17.
 A TextBook of Discrete Mathematics by Dr. Swapan Kumar Sankar, published by S.Chand & Co. Publishers, New Delhi.
 Graph theory and combinations by H.S. Govinda Rao published by Galgotia Publications.
B.A./B.Sc. THIRD YEAR MATHEMATICS SYLLABUS
SEMESTER – VI, CLUSTERC, PAPER – VIIIC2
Cluster Elective –VIIIC2: APPLIED GRAPH THEORY
60 Hrs
UNIT – I (12 hrs) :
Matchings
Matchings – Alternating Path, Augmenting Path – Matchings and coverings in Bipartite graphs, Marriage Theorem, Minimum Coverings.
UNIT –II (12 hrs) :
Perfect matchings, Tutte’s Theorem, Applications, The personal Assignment problem The optimal Assignment problem, KuhnMunkres Theorem.
UNIT –III (12 hrs) :
Edge Colorings
Edge Chromatic Number, Edge Coloring in Bipartite Graphs – Vizing’s theorem.
UNITIV (12 hrs) :
Applications of Matchings, The timetabling problem.
Independent sets and Cliques
Independent sets, Covering number, Edge Independence Number, Edge Covering Number – Ramsey’s theorem.
UNIT –V (12 hrs) :
Determination of Ramsey’s Numbers – Erdos Theorem, Turan’s theorem and Applications, Schur’s theorem. A Geometry problem.
Reference Books:
 Graph theory with Applications by J.A. Bondy and U.S.R. Murthy, published by Mac. Millan Press.
 Introduction to graph theory by S. Arumugham and S. Ramachandran published by SciTech publications, Chennai17.
 A text book of Discrete Mathematics by Dr. Swapan Kumar Sarkar, published by S. Chand Publishers.
 4. Graph theory and combinations by H.S. Govinda Rao, published by Galgotia Publications.
ACTION PLAN
 Our Department Will Conduct Student Seminars, Quiz, Group Discussions.
 Our Department Formed Math Club. The Club Students Will Conducting Student Projects.
 Our Department Will Conduct Mathematics Day Celebrations On 22122018. In This Occasion We Will Planning Week Day Programme.
 We Will Planning Guest Lecture In Prof .G .Ravindrababu (A.U) In February
 Our Department Will Conduct 30 Days Coaching Programme In The Month Of February To Prepare Our Students For Pg Entrance Exams.
 Our Department Will Conduct 30 Days Programme To Arithmetic And Reasoning Classes To Our Students For The Purpose Of Competitive Exams.
 Our Department Was Conducting The Arithmetic Classes For Sc students by the support of AMBEDKAR UNIVERSITY,SRIKAKULAM.
20172018
Competitive Exams
Sno  Student Name  Selected Department 
1  P.Naresh (M.P.E)  Constable,Police Dept 
20162017
Ranks in PG Entrance
Sno  Student Name  Subject  Name of the Entrance Test details  Hall Ticket No  Rank Secured 
1  T.Anil Kumar  Mathematics  A.U CET  211030013  149 
2  B.Murali  Mathematics  A.U CET  799 
Competitive Exams
Sno  Student Name  Selected Department 
1  K.Paparao (M.P.Cs)  Indian Air Force Airmen 
2  R.Vishnu Vardhan (M.P.E)  Indian Navy 
3  K.Janardhana (M.E.Cs)  CISF 
4  S.kumar (M.P.E)  CISF 
20152016
Competitive Exams
Sno  Student Name  Selected Department 
1  S.Suresh (M.P.E)  Indian Air Force 
Guest Lecture By Ch.Naidu Lecturer In Maths
Guest Lecture By K.Ravi Babu Lecturer In Maths, Subbavaram On Real Analysis
Guest Lecture Dr.G.Vasanthi Hod Basic And Humanities
Lecture By Prof.G.Ravi Babu, Dept Of Mathematics