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First Year 1st Semister
Session: 2015-16, 2016-17, 2017-18
MTH-111: Fundamentals Of Mathematics
3 Credits 100 Marks
1.Basic concepts of sets, Subsets, Enpty sets, Universal sets, Ven diagram, Classes of sets.
2.Basic set Operations, Algebra of sets and Classes.
3.Relations and Functions, different types of relations and functions, equvalence relation and partitions.
4.Cardinal number of a set, countable and uncountable sets, Cardinal arithmetic, Cantors theorem, Continum hypothesis.
5.Logic: Statements, basic connectives for combining statements and their truth tables, Propositions and trfuth tables, tatuologies and falacies, logical implication, quantification theory, arguments and Propositions.
6.Number Theory: Elementary number theory: Numbers, Integers, Prime Numbers, Divisibiity, The unique factorization theorem, The Arithmetic Functions , Fundamental theorem of arithmetic, Congruences (Basic properties).
MTH-112: Differential Calculus
3 Credits 100 Marks
1.Functions and their graphs: Polynomials and rationall functions, logarithmic and exponential functions, trigometric functions and their inverses, hyperbolic functions and their inverses, combinations of such functions ,Compositions of functions, Inverse functions.
2.Limit and Continuty: Definations and basic theorems on limit and continuty, Limit at infinity and infinite limits with computation.
3.Derivatives: Tangents lines and rates of change, Defination of derivative, One sided derivatives. Rules of differention of various functions (proof and applications) . The product and quotient rules. The chain rule, Imolicit differentation. Related rates. Linear approximations and differentials.
4.Successive differentation: Higher order Derivatives, Liebnitz’s theorem and its applications.
5. Tangents and Normals: (for both Cartesian and Polar curves).
6.Appllications of Derivatives: Rolle’s theorem, Mean value theorem. Incresing and Decresing Functions, Concavity and points of inflection, saddle points, Maximum and minimum values of functions. Optimizations problems.
7.Approximations and Serries: Taylor polynomials and serries, convergence of serries, Taylor’s theorem with remainders, Differentitation of serries, vaidity of regions of Taylor’s serries and computations with serries.
8.Indeterminate Forms: L’Hospital’s rule.
9.Asymptotes, curvature and envelopes.
MTH-113: Geometry Of Two Dimensions
3 Credits 100 Marks
1.Cartesian and Polar co-ordinates. Translation and Rotation of axes, invarients.
2.Pair of straight lines (homogeneous second degree equations, general second degree equations representing pair of straight lines).
3.General equations of second degree, Conic Sections (Reduction to standard forms, identifications, properties and tracing of conics).
4.Circles and system of circles.
5.Parabola, Ellipse, Hyperbola.
6.Equations of conic in polar and parametric forms.
MTH-114: Basic Algebra
3 Credits 100 Marks
1.Historical background of the formation of Algebra.
2.Inequalities: Arithmetic Mean, Geometric Mean, Weierstras’s Inequality, Cauchy-Schwarz Inequality, Tchebychef’s inequality.
3.Theory Of Equations: Equations and identities, algebric solution of equations with graphical representaions, Relations between roots and co-efficients of the nth degree equations, Synthetic division. Descarte’s Rule of Signs, Newton’s methods, Reciprocal Equations and Strurm’s Theorem.
4.Serries: Basic defination of serries, Techniques of summing up serries, Tests for convergence and divergence of serries (with less emphasis on proofs of theorems), Methods of difference, Successive difference method.
5.Plane Trigonometry: Complex numbers, addition, multiplication, subtraction, division, Forms of complex numbers, De Moivre’s theorem and its applications, Complex variable, Function of a complex variabe, Circular functions and inverse circular functions of a complex quantities, Exponential series for complex quantity, Euer’s exponential values, Hyperbolic functions, Summation of trigonometric series, method of difference, C+iS method. Powerseries, Expansion of series.
6.Spherical Trigonometry: Importance of spherical trigonometry, Geometry of sphere, Axis and poles. Spherical triangle, polar triangel, Properties of polar triangle, Cosine and Sine formula, Sine of angles in terms of sides, Relation between two sides.
CSE-115: Computer Fundamentals
3 Credits 100 Marks
Introduction: History, Basic organization of Computer, Types of computer, Main frame, mini and micro computer, Different types of micro computer, Input Output devices, Bit, Byte and words, Number systems: Binary, Decimal, Hexadecimal and Octal number, Different types of memory, BIOS, Software, Types of software, System software: Opereting System, Assembler, Compiler, Interpreter, Mutimedia.
2.Peripheral Devices: Printer, Keyboard, Mouse, Scanner, Monitor, Disk, Storage: CD and DVD.
3.Computer Networks: Data Communication, Components of Data Communication, Direction of data flow,Computer Network, Types of network, LAN, MAN, and WAN, Network topologies, Network card and accessories, Internet, Email and URL.
4.Application Package: Different application package like Word processing, Speed sheet and Database Management System.
5.Progamming Concepts: Algorithm, Flowchart and Pseudo code, Problem analysis, Structured Programming Language: Overview of C, Data types, Variablles, Constants, Operators, EXpressions, Control structures, Arrays, Strings.
6.Computer Arithmetic: Why binary, Binary arithmetic, Addition, Subtraction, Additive method of subtraction, 1’s compliment, 2’s compliment, Subtraction using 1’s and 2’s compliment.
STA-116: Basic Statistics
3 Credits 100 Marks
1.Introduction: Defination of statistics. Its nature and scope. Nature of statistical data. Attributes & Variables. Population and sample.
2.Data Colection & Representation: Classification of data. Frequency distribution. Graphical representation of data.
3.Measure of Location: Defination of measure of location. Arithmetic Mean, Geometric Mean, Harmonic Mean, Median & Mode. Important properties of measure of location. Merits, Demerites & applications.
4.Measure of Dispersion: Defination & Difference of absolute and relative measures. Properties of Mean deviation, Variance & S.D Merits, Demerits & Applications.
5.Moments, Skewness & Kurtosis: Defination of moments, skewness & kurtosis. Properties of the measures, Relationship between skewness & Kurtosis. Shape and Nature of the measures.
6.Correlation & Regression: Defination & Difference of correlation and regression. Check Origin and scale on the measures. Properties and uses of the measures. Least square methods. Rank Correlation.
7.Index Number: Defination & classification of index number. Construction of index Number. T.R.T & F.R.T. Ideal index number.
8.Time Series Analysis: Detailed study of time series analysis. Component of time sries. Evaluation of trend. Applications of time series analysis.
Second Year 1st Semister
Session:2015-16, 2016-17, 2017-16.
MTH-211: Real Analysis I
3 Credits 100 Marks
1.Real numbers as complete ordered fieds: Bounded sets, Supremum Principle, Infimum Principle, Completeness axiom and Dedekind’s Theorem with their equivalence. Archimedean property, Countable and uncountable sets, Denseness of rational and irrational numbers.
2.Topology of real line: Neighborhoods, Open and closed sets, Limit/cluster points and Bolzano-Weierstrass theorem, Interior, Boundary and closer, Derived sets, Compact sets, Hiene-Borel theorem, Connected sets.
3.Real sequences: Defination of sequence, Bounded sequence, Convergence of a sequence, Null sequence, Theorems on limits of a sequence, Sub-sequental limits, Bolzano-Weierstrass theorem for sequences, Cauchy’s general principle of convergence, Cauchy’s theorems on limits of sequences, Limit superior and limit inferior, Monotone sequence and its convergence, Cauchy sequence, Absolute convergence.
4.Infinite series of real numbers: Convergence and sum of infinite series, Cauchy’s general principle of convergence, Series of positive terms, Alternating series, Absolute convergence, Test for convergence (Comparison test, root test, ratio test, integral test, Raabe’s test, Gauss’s test, Liebnitz’s test, Abel’s test, Dirichlet’s test etc.), Rearrangements.
5.Uniform Convergence: Interchangeability of limiting processes, Power Series.
MTH-212: Calculus of Several Variables
3 Credits 100 Marks
1.Functions of several variables: Limit and Continuty, Partial derivatives, Differentiability, Maxima, Minima, Saddle point, Differentials, Chain rule, Second Derivatives, Euler’s theorem on homogeneous functions, derivatives with constrained variables, Extreme values of several variables, Lagrange multipliers, Mean value theorem for function of several variables, Taylor’s theorem for functions of two and more than two variables.
2.Multiple Integration: Double integrals and iterated integrals. Double integrals over nonrectangular regions, Double integrals in Polar co-ordinates, Area by double integrals, Jacobians. Triple integrals and iterated integrals, Volume as a triple integral, Triple integral in cylindrical and spherical co-ordinates, General multiple integrals, Changes of variables in multiple integrall.
MTH-213: Linear Algebra I
3 Credits 100 Marks
1.Vectors in Rn and Cn: Review of geometric vectors in R2 and C2 space. Vectors in Rn and Cn. Inner product, norm and distance in Rn and Cn.
2.Matrices and Determinants: Defination of matrix, Different types of matrices, aws of Matrix Algebra, Determinant function and its properties, minors, cofactors. Expansion and evaluation of determinants, Cramer’s rule. Adjoint matrix, Invertible matrices and their inverses with applications, Matrix operations, Elemetary row or column operations, Echelon forms of matrices, Block matrices, Row rank and column rank of a matrix and their equivalence, Rank of Matrix.
3.System of Linear Equations: Introduction to system of linear equations, Solutions of the system of inear equations (homogeneous and non-homogeneous), Application of matrices and determinants for solving the system of inear equations (using echelon forms and rank of matrices).
4.Vector Space: Notion of Groups and fields. Vectors space, Subspaces, Linear combinations of vectors, Linear independence and dependence of vectors, Linear span, Basis and dimension of vector space, Solution spaces of systems of linear equations, Row space, Column space, null space.
5.Linear Transformations: Linear transformation, Karnel and image of lenear transformation and their properties, Rank and nullity of Linear Transformation, Matrix representation of linear transformation, Change of basis.
6.Eigenvalues and Eigenvectors: Defination of Eigenvalues and Eigenvectors, Matrix polynomial, Characteristics equation, Cayley-Hamilton theorem, Diagonalization of matrices, Appication.
MTH-214: Ordinary Differential Equations I
3 Credits 100 Marks
1.Ordinary Differential Equations and their Solutions: Classification of differential equations, Solutions, Implicit solutions, Singular solutions, Initial value problems, Boundary value problems, Basic Existence and uniqueness (statement and illustration only), Direction fields, Phase Line.
2.Solution of first order equation: Variables separable equations, Linear equations, Exact equations, Special integrating factors, Substitutions and transformations, Homogeneous equations, Bernoulli equation, Riccati equation, First order higher degree equation-solvable for x, y and p. Clairaut’s equation, Singular solutions.
3.Modeling with first order differential equations: Constrution of differential equations as mathematical models (exponential growth and decay, heating and cooling, mixture of solutions, series circuit, logistic growth, chemical reaction, failing bodies). Model solutions and interpretation of results. Orthogonal trajectories.
4.Solution of higher-order linear equations: Linear differential operations. Basic theory of linear differential equations, Solution space of homogeneous linear equations, Fundamentals solutions of homogeneous equations, Reduction of orders, Homogeneous linear equations with constant co-efficients, Method of undetermined co-efficients, Variation of parameters, Euler-Cauchy differential equation.
5.Modeling with second-order equations: Spring-mass systems, Electrical networks, Rocket motion.
CSE-215: Programming with C and C++
3 Credits 100 Marks
1.C: Overview of C, Data types, Variables, Constants, Operators, Expressions, Control Structures, Arrays, Strings, Functions and program Structure: Parameter passing conventions, Recursion; Pointers, User defined data types: Structures, Unions, Enumerations, Input and Output: standard input and output, formatted input and output, Files.
2.C++: Introduction to object oriented programming (OOP); Advantages of OOP over structured programming; C++ as an object oriented language; Declaration and constants, Expression and statements, Data types, Operator, Functions.
3.Classes: Base, Derived virtual class, Encapsulation, Objects, Access Specifiers, Static and Non-static numbers; Constructions, Destructions and Copy Constructions, Array of objects, Object Pointers and objects References; Inheritance: single and multiple inheritance; Polymorphism: Overloading, Abstract Classes, Virtual Functions and Overriding; Exceptions; Object Oriented I/O; Streams, Exception Handling, Multi-threaded Programming.
PHY-216: Physics II
3 Credits 100 Marks
SECTION: A
1.Guss’s law, Application of Guss’s Law, Dielectrics and Guss’s law, Ohm’s Law, Energy transfer in an electric circuit, Kirchhoff’s laws and their applivations. Magnetic Induction, Motion of a charged particle in uniform electric and Magnetic field.
2.Concept of r.m.s. and average value of current and voltage, CR, LR and LCR circuits in series and parallel, Resonance, Q-factor.
SECTION: B
3.Planck’s radiation formula, Photoelectric effect, Einstein’s Photon theory, The Compton effect, The Hydrogen atom and correspondence principle.
4.Matter waves, Atomic structure, wave mechanics, Uncertainy principle, Atomic excitation.
5.The nucleus; nuclear force, nuclear radius, mass defect and packing fraction. Radio activity, unstable nuclei, exponential decay law, half life, mean life and units of radioactivity, Basic ideas of nuclear reactor, nuclear fission and nuclear fusion.
2nd Year 2nd Semister
Session: 2015-16, 2016-17, 2017-18.
MTH-221: Real Analysis II
3 Credits 100 Marks
1.Real continuous functions: Limit and continuity of functions, Local properties, Global properties (global continuity theorem, preservation of compactness, maximum and minimum value theorem, intermediate value theorem, preservation of connectedness), uniform continuity of functions.
2.Differentiability of real functions: Basic properties, Rolle’s theorem, Mean value theorem, Taylor’s theorem.
3.Integration of real functions: Riemann sum and Riemann integral, Conditions for integrability, Properties of integrals, Darboux sums, Darboux theorem, Fundamental theorem of integral calculus, Mean value theorem for integrals, Leibnitz’s theorem on differentiation under integral sign, Riemann-Stieltjes integration.
4.Sequences and series of real functions: Pointwise convergence and uniform convergence, Test for uniform convergence, Cauchy criterion, Weirstrass’s M-test, Continuity, Differentiability and integrability of limit functions of sequences and series of functions.
5.Euclidean n-space: Norms in Rn, Distance in Rn, Convergence and completeness, Compactness, Continuous functions and their properties, Implicit function theorem, Multiple Integrals, Jacobian, Fubini’s Theorem.
MTH-222: Ordinary Differential Equations II
3 Credits 100 Marks
1.Existence and uniqueness theory: Fundamental Existence and uniqueness theorem. Dependence od solutions on initial conditions and equation parameters. Existence and uniqueness theorem for systems of equations and higher order equations.
2.Series solutions of second order linear equations: Taylor’s series solutions about an ordinary point, Frobenious series solutions about regular singular points, Series solution of Legendre, Bessel, Laguerre and Hermite equations. Hypergeometric equations.
3.Systems of linear first order differential equations: Elimination method, Matrix method for homogeneous linear systems with constant coefficients, Variation of parameters, Matrix exponential.
4.Eigenvalue problems and Strum-Liouvlle boundary value problems: Regular Strum-Liouville boundary value problems, Nonhomogeneous boundary value problems and the Fredholm alternative, Solution by eigen function expansion, Green’s functions, Singular Strum-Liouville boundary value problems/Oscillation and comparison theory.
MTH-223: Linear Algebra II
3 Credits 100 Marks
1.Matrices: Canonical forms of matrices, symmemtric, orthogonal and Hermitian matrices, Normal and Unitary matrices.
2.Linear Functionals and Dual Space: Linear Functionals and Dual Space, Dual basis, Second dual space, Annihilators, Transpose of a linear transformation.
3.Inner Product space: Inner products, Inner product spaces, Complex inner product space, Orthogonal and orthonormal sests, Orthonormal basis, Gram-Schmidt orthogonalization process, Linear functions and adjoints, Positive operators, Unitary operators, normal operators, the spectral theorem.
4.Nillinear, quadratic and Hermitian forms: Matrix form, transformations, canonical forms, reduction forms, definite and semi-definite forms, principal minors and factorable forms.
5.Complex vector spaces, Complex Inner Product Spaces, Unitary, Normal and Hermittian Matrices.
MTH-224: Programming with FORTRAN
3 Credits 100 Marks
1.Introduction to personal computers.
2.Disk operating systems: MS DOS, WINDOWS
3.Problem solving techniques using computers: Flowcharts, Algorithms, Pseudo codes.
4.Programming in FORTRAN: Syntax and semantics, Data types and structures, Input/Output, Loops, Decision statements, Arrays, User-defined functions, Subprograms and recursion.
5.Computing using FORTRAN: Construction and implementation of FORTRAN programs for solving problems in mathematics and sciences.
Classes: Theory (2 hours/week), Lab (At least 10 assignments).
MTH-225: Math Lab I: MATHEMATICA I
3 Credits 100 Marks
Problem-solving using MATHEMATICA: Solving problems in Calculus, Algebra, Geometry (Three shall be at least 10 lab assignments).
MTH-229: Comprehensive Viva
2 Credits 100 Marks
Comprehensive Viva on courses taught in Second year.
3rd Year 1st Semister
Session:2015-16, 2016-17, 2017-18.
MTH-311: Complex Analysis I
3 Credits 100 Marks
1.Complex number and properties, Geometric representation of complex numbers, Properties of Modulii and arguments, Polar faorm Exponential form, Power and roots, Region in the Complex plane.
2.Function ofa complex variable, Mappings, Limits, Theorems on limits, Continuity and Uniform Continuity.
3.Derivatives, Analytic functions, Cauchy-Riemann Equations, Harmonic functions, Geometric interpretation of the derivatives, Differentials, Rules for diferentation, Derivatives of elementary functions, Higher order derivatives, L’Hospital”s Rules, Singular points, Orthogonal families, Curves, Applications, Gradient, Divergence, Curl and Laplacian, Identities involving gradient, Divergence and Curl.
4.Complex Line Integrals, Real Line Integrals, Connection between real and complex line Integrals, Properties of Integrals, Change of variables, Simply and Multi-Connected Regions, Jordan Curves, Complex form of Green’s Theorem, Cauchy’s theorem, Extension of Cauchy’s Theorems, The Cauchy-Goursat theorems, Morera’s theorem, Related problems.
MTH-312: Abstract Algebra I
3 Credits 100 Marks
1.Equivalence relations and equivalence classes, Permutations of a set and associated problems, Congruence and residue classes modulo n, Binary operations, Identity element, Inverse elements.
2.Groupoids, Monoids and semigroups.
3.Groups and subgroups, Order of group, order of an element in a group, Permutation groups, symmetric group, alternating group, Cyclic groups, Multiplication of subgroups.
4.Cosets, Larange’s theorem, Product of cosets, Frobenius’s counting formula.
5.Normal subgroups, Quotient groups, Centre of a group, Homomorphisms and isomorphisms, The isomorphisms theorems.
6.Application of Groups.
MTH-313: Mathematical Methods
3 Credits 100 Marks
1.Fourier series: Fourier series and its convergence, Fourier sine and cosine series, properties of Fourier series, Operations on Fourier series, Complex form, Applications of Fourier series.
2.Special Functions: Gamma function, Error function, Hyper geometric function (Hyper geometric equation, special hyper geometric function, generalized hyper geometric function, special confluent hyperbolic functions).
3.Laplace transforms: Laplace transforms, basic definations and properties. Existence theorem, Transforms of derivatives, Relations involving integrals, Transforms of periodic functions, Convoluations properties, Inverse Laplace transform, Calculation of inverse transforms, Applications to solutions of ordinary differential equation, solution of initial value and boundary value problems.
4.Fourier transforms: Fourier transforms, Inversion theorem, sine and cosine transforms, Transform of derivatives, Transforms of rational function, Convolution theorem, Parseval’s theorem, Applications to boundary value problems and integral equation.
MTH-314: Numerical Analysis I
3 Credits 100 Marks
1.Solution of equation in one variable: Error, Bisection method, Method of False position, Fixed point iteration, Newton-Raphson method, Error analysis for iterative method, Accelerating limit of convergence.
2.Interpolation and polynomial approximation: Taylor polynomials, Interpolation, Lagrance’s interpolations and Divided difference interpolation, iterated interpolation, Central difference interpolation formula and extrapolation.
3.Differentiation and Integration: Numerical differentiation, Richardson’s extrapolation, Numerical integration, Trapezoidal rule, Simpson’s rules, Weddle’s rule, Adaptive quadrature method, Romberg’s integration, Gaussian quadrature.
4.Solutions of linear systems: Gaussian elimination and backword substitution, Linear algebra and matrix inversion, Determinant of a matrix, Pivoting strategies, Direct factorization of matrices, LU decomposition method.
MTH-315: Partial Differential Equation
3 Credits 100 Marks
1.First Order Equations: Complete integral, General solution, Cauchy problems, Method of characteristics for linear and quasilinear equations, Lagrance’s method, Charpit’s method for finding complete integrals, Methods for finding general solutions.
2.Second order equations: Classifications, Reduction to canonical forms, Characteristics curves, Boundary value problems related to linear equations, Applications of Fourier methods (Coordinate systems and and separability, Homogeneous equations, Non-homogeneous boundary conditions, Inhomogeneous equations), Problems involving cylindrical and spherical symmetry, Boundary value problems involving special functions, Transform methods for boundary value problems (Applications of the Laplace transforms, Application of Fourier sine and cosine transforms), Inhomogeneous equations.
MTH-316: Discrete Mathematics
3 Credits 100 Marks
1.Mathematical reasoning: Inference and fallacies, Methods of proof, Recursive definitions, Program verification.
2.Combinatorics: Counting principles, Inclusion-exclusion principle, Pigeonhole principle, Generating functions, Recurrence relations, Applications to computer operations.
3.Algorithms on graphs: Introduction to graphs, Paths and trees, Shortest path problems (Dijkstra’s algorithm, Floyd-Warshall algorithm and their comparisons), Spanning tree problems (Kruskal’s greedy algorithm, Prim’s greedy algorithm and their comparisons).
4.Network flows: Flows and cuts, Flow augmentation algorithm, Application of a Max-flow min-cut theorem.
3rd Year 2nd Semister
Session: 2015-16, 2017-18, 2017-18.
MTH-321: Complex Analysis II
3 Credits 100 Marks
1.Cauchy’s integral formulae, Extension of Cauchy’s Integral formulae, Some Related theorems Cauchy’s Inequality, Liouvolie’s Theorem, Fundamental theorem of algebra, Guss mean value theorem, Maximum Modulus Theorem And Minimum Modulus Theorem.
2.Sequences of functions, Series of functions, Convergences, Power Series, Some related theorems, Taylor’s theorem, Some special series, Laurent’s Theorem.
3.Zero of a function, Singular points, Different types of singularities, Poles and zeros are Isolated, Limit points of Zero and Poles, Memomorphic functions, Working rules for poles and singularities, The argument theorems and its Extension. Weirstrass Theorem, Rouche’s theorem.
4.Residues, Cauchy’s residue theorem, Evaluation of Definite integrals, Theorems used in evaluating Integrals, Integration round the cut circle, Improper integration involving sines and cosines, Integrals by contour integrations, Branch points, Branch lines and cuts. Integration through branch cut and Related contours.
5.Transformations, Jacobian of a Transformation, Conformal mappings, Simple functions, some general transformation, The Linear transformation, Successive Transformation, Bilinear transformations, Mapping of a half plane onto a circle, The Schwarz-Christoffel Transformation, Physical applications of conformal Mapping.
MTH-322: Abstract Algebra II
3 Credits 100 Marks
1.Rings, Various types of rings, Properties of rings, Subrings, Ideals, Principle ideals, Prime ideals and Maximal ideals.
2.Integral domains, Division rings, Fields, Quotient rings, Homomorphism and isomorphism of rings, Isomorphism theorems on rings.
3.Principal ideal domains, Euclidean domains, Unique factorization domains. Divisibility, Units, Associates, HCF/GCD and LCM, Polynomial rings.Factorizations in polynomial rings, Primitive polynomials, Division algorithm, Gauss’s theorem, Einstein’s irreducibility criterion.
4.Characteristic of a ring or integral domain. Prime Fields, Structure of prime fields.
MTH-323: Linear Programming
3 Credits 100 Marks
1.Convex sets and related theorem.
2.Introduction to linear programming and related theorems of feasibility and optimality.
3.Formulation of Linear Programming problems.
4.Graphical solutions.
5.Simplex method.
6.Duality of linear programming and related theorems.
7.Sensitivity analysis in linear programming.
8.Applications of Linear Programming.
MTH-324: Numerical Analysis II
3 Credits 100 Marks
1.Iterative techniques of Matrix algebra: Iterative technique for solving linear systems of equations, Error estimates and iterative refinement, eigenvalues and eigenvectors, the power method, Householder’s method, Q-R method.
2.Numerical solution of Non-linear system: Fixed point method for functions of several variables, Newton’s method, Quasi-Newton’s method.
3.Initial value problem for O.D.E.: Euler’s method and modified Euler’s method, Higher order Taylor’s method, Single-step method (Runge-Kutta methods, extrapolation methods-higher order differential equations and system of differential equations), Multi-step methods (Adams-Bashforth, Adams-Moulton, Predictor-Corrector and Hybrid methods, variable step-size multi-step methods, error and stability analysis).
4.Boundary Value problem for ODE: Shooting method for Linear and nonlinear problems.
5.Programs: Construction of FORTRAN programs for numerical methods.
MTH-325: Math Lab II: MATHEMATICA
3 Credits 100 Marks
Problem-solving using MATHEMATICA: Solving problems in Calculus, Algebra, Geometry and Numerical Analysis-I. (There shall be at least 10 lab [Laboratory Works] assignments.)
MTH-329: Comprehensive Viva
2 Credits 100 Marks
Comprehensive Viva on courses taught in the third year second semester.
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Mathematics-10 Batch, Comilla University. 