B.Tech II year Mathematics and Computing (IIIrd Semester) MATHEMATICS-III (MC - 201) L T P UNIT 1 Improper real Integrals of first and second kinds. Absolute convergence of Improper Integrals. Unit II Function of complex variables: Differentiability, Analytic functions. Cauchy- Riemann equations, Laplace equations, Harmonic functions, Elementary functions. Unit III Complex Integration, Line integral in the Complex Plane, Cauchy s integral theorem, Cauchy s integral formula, Derivatives of Analytic functions, Cauchy Goursat Theorem. Unit IV Power series, Taylor Series, Laurent Series, Removable singularities, zeros and poles, Residues, Residue Theorem and its applications to evaluate improper real integrals. Unit V Conformal Mappings (Conformal Mapping, Linear fractional transformations, Schwarz- Christoffel Transformations, Applications) Unit VI Introduction to difference equations, z- transforms, inverse z-transforms, convolution theorem, applications to difference equations. REFERENCES: 1. Kreyszig, Advanced Engineering Mathematics, JohnWiley. 2. Advanced engg. Mathematics, H. C. Taneja, IK International. 3. Churchill and Brown, Complex Analysis - Ed. V 4. A first course in Complex Analysis with applications, Dennis G. Zill & Shanahan, Jones & Bartlett (student edition) 2nd Edition. www.mcdtu.wordpress.com 1
DIFFERENTIAL EQUATIONS (MC - 202) L T P Unit I Introduction to two point boundary values problems, Green functions, Bessel functions: Generating function, Modified Bessel functions, Orthogonality of Bessel functions. Sturm-Liouville Problems, Eigen values and Eigen functions. Unit II Partial Differential Equations: First and second order partial differential equations. solution of first order non linear partial differential, Charpits method. Unit III Classification of second order PDE. Cauchy problems. Dirichlet and Neumann boundary value problems. Lagrange s method, Unit IV Boundary value problems involving wave equation, the heat equation, the Laplace equation. Solutions by the method of separation of variables. Solutions using Fourier transformations.. 1. Advanced Engg. Mathematics, O Neil, Cenage Learning. 2. Partial Differential Equation, I. N. Snnedon, Mc-Graw Hill 3. Kreyszig, Advanced Engineering Mathematics, JohnWiley. 4. An introduction to ordinary differential equations, Coddington, PHI. 5. Differential equations & their applications, Braun, Springer - Verleg. www.mcdtu.wordpress.com 2
DISCRETE MATHEMATICS (MC 203) L T P UNIT1 Set theory: Basic concepts of set theory, operations on sets, Cartesian products, relations, equivalence relation, equivalence classes, operations on relations, partial-orders, Hasse diagram, functions, recursive functions. UNIT-II Logic: Proposition, compound propositions, well-formed formulae, truth tables, tautology, contradiction, equivalence, algebra of proposition, normal forms, theory of inference, predicate logic: predicates, quantifiers, free and bound variables, theory of inference for predicates. UNIT-III Combinatorics: Permutations, combinations, recurrence relations, generating functions. Algebraic structures: Definition and their properties, introduction to semigroups, monoids and groups, homomorphisms. UNIT-IV Lattices and Boolean algebra: Definition of lattice, properties of lattices, bounded, complemented, distributive and complete lattice, Introduction, axioms and theorems of Boolean algebra, algebraic manipulation of Boolean expressions. UNIT-V Graph Theory: Graphs, digraphs, adjacency matrix, incidence matrix, connectivity, subgraphs, trees, spanning tree, complete graphs, walk, path, cycle. Texts: 1. J. P. Tremblay and R. Manohar, Discrete Mathematical Structures with Applications to Computer Science, Tata McGraw-Hill, 1997. 2. C. L. Liu, Elements of Discrete Mathematics, 2nd Edition, Tata McGraw-Hill, 2000. 3. Malic & Sen, Discrete Mathematics, Cenage Press. References: 1. B. Kolman, R. C. Busby and S. C. Ross, Discrete Mathematical Structures, Prentice Hall of India, 2004. 2. N. Deo, Graph Theory with Applications to Engineering and Computer Science, Prentice Hall of India, 1974. www.mcdtu.wordpress.com 3
DATA STRUCTURES (MC 204) L T P UNIT-I Introduction: Introduction to Algorithmic, Complexity- Time-Space Trade off. Introduction to abstract data types, design, implementation and applications. Introduction of data structure list. Arrays and Strings: Representation of Arrays in Memory: one dimensional, Two dimensional and Multidimensional, Accessing of elements of array,performing operations like Insertion, Deletion and Searching. Sorting elements of arrays. Strings and String Operations Stacks and Queues: Introduction to data structures like Stacks and Queues. Operations on Stacks and Queues, Array representation of Stacks, Applications of Stacks : recursion, Polish expression and their compilation conversion of infix expression to prefix and postfix expression, Operations of Queues, Representations of Queues Applications of Queues, Priority queues. UNIT-II Linked Lists: Singly linked lists, Representation of linked list, Operations of Linked list such as Traversing, Insertion and Deletion, Searching, Applications of Linked List.Concepts of Circular linked list and Doubly linked list and their Applications. Stacks and Queues as linked list. UNIT-III Trees: Basic Terminology, Binary Trees and their representation, binary search trees, various operations on Binary search trees like traversing, searching, Insertion and Deletion, Applications of Binary search Trees, Complete Binary trees, Extended binary trees,. General trees, AVL trees, Threaded trees, B- trees. UNIT-IV Sorting: Insertion Sort, Quick sort, Merge sort, Heap sort, sorting on different keys, External sorting. UNIT-V Graphs: Terminology and Representations, Graphs & Multi-graphs, Directed Graphs, Representation of graphs and their Transversal, Spanning trees, shortest path and Transitive Closure, Activity Networks, Topological Sort and Critical Paths. UNIT-VI File Structure: File Organization, Indexing & Hashing, Hashing Functions, Collision Resolution Techniques. [ Text Books: 1. Horowitz and Sahni, Fundamentals of Data structures, Galgotia publications 2. An introduction to data structures and application by Jean Paul Tremblay & Pal G. Sorenson (McGraw Hill). www.mcdtu.wordpress.com 4
PROBABILITY AND STATISTICS (MC - 205) L T P Unit I: Theory of probability Sample space, Probability axioms, Probability space, Theorems on probability of events, Addition and multiplication rules, Conditional probability and Baye s theorem, Independence of events. Unit II: Random variables and their probability distributions Random variables, Distribution function, Discrete random variable, Probability mass functions, Continuous random variables, Probability density functions, Functions of random variables, Joint distribution function, Joint probability mass function, Joint density function, Marginal distribution, Conditional distribution, Independence of random variables, Transformation of one-dimensional and two-dimensional random variables. Unit III: Moments and generating functions Mathematical expectation, Covariance, Variance, Correlation, Conditional expectation, Regression of mean, Conditional variance, Moment generating function, Some moment inequalities (Markov s inequality, Chebyshev s inequality), Order statistics and their distribution. Unit IV: Some special distributions Bernoulli, Binomial, Multinomial, Poisson, Geometric, Negative binomial, Hypergeometric, Uniform, Normal, Exponential and Exponential Family, Log normal, Gamma, Weibull, Beta, Cauchy. Unit V: Limit theorems Modes of convergence, weak law of large numbers, Strong law of large numbers, Central limit theorem. Unit VI: Sampling and Large sampling tests Sampling Introduction, Parameter and statistic, Sampling distribution, Hypothesis testing, Sampling of attributes and variables, Test of significance Unit VII: Exact sampling distributions Small sampling tests, Chi square dist., Student s t dist., Snedecor s F dist., Fisher s Z dist., One way and two way Analysis of variance (ANOVA). Books: 1. Vijay K. Rohtagi, An introduction to Probability and Statistics, Wiley. 2. Meyer, Introductory Probability and Statistical Application, Oxford and IBH publishing. 3. Kishor S. Trivedi, Probability and Statistics with Reliability, Queueing and Computer Science Application, Wiley. 4. Sheldon M. Ross, Introduction to Probability and Statistics for Engineers and Scientists, Academic Press. www.mcdtu.wordpress.com 5
ENGINEERING ECONOMICS L T P (MC-206) Unit 1: Introduction: Nature and significance of economics, Goods and Utility, Basic Concept of Demand and Supply, Elasticity of Demand- Price elasticity of Demand, Cross elasticity of Demand, Production - Production Function, Production Process and Factors of Production, Market Introduction to Monopoly, Perfect Competition, Oligopoly and Monopolistic Competition, Cost Concepts, E-commerce. Unit 2: Money- its evaluation and function, Bank- Commercial Bank and Central Bank and brief idea about function of banking system. Tax and Subsidy, Type of Tax- Direct and Indirect, Monetary and fiscal policy, Inflation and Business cycle, IPR & WTO, International trade, terms of Trade, Gain from International Trade, Free Trade vs. Protection, Dumping, Balance of Payment Unit 3: Role of Science, Engineering and Technology In economic Development: Some of the burning problems of rural and slum areas in India and how engineering and technology may be used to alleviate them, example of Green Revolution and White revolution. Reasons for their success and can we replicate them. Sustainable Development. Unit 4: Elementry Economic Analysis; Interest formulas and their Applications; Calculations of economic equivalence, Bases for Comparison of Alternatives: Present Worth Method, Future worth method, Annual equivalent, Internal Rate of return; Evaluating Production Operations, Business Risk Management. Suggested reading: G.J. Thuesen, & W.J. Fabrycky, Engineering Economy, Prentice-Hall of India Private Limited, New Delhi. William G. Sullivan, James A. Bontadelli & Elin M. Wicks, Engineering Economy, Pearson Education Asia, First Indian reprint. Donald G. Newnan, Jerome P. Lavelle & ted G. Eschenbach, Engineering Economic Analysis, Engineering press, Austin, Texas. Seema Singh, Economics for Engineering Students, IK International Publishing House Pvt. Ltd www.mcdtu.wordpress.com 6
MATHEMATICAL APPLICATIONS LAB (MC - 207) L T P 0 0 2 Lab based on the paper MC 201, MC-206. PROB. & STATISTICAL APPLICATIONS LAB (MC - 208) L T P 0 0 2 Lab based on the paper MC - 205 DATA STRUCTURE LAB (MC - 209) L T P 0 0 2 Lab based on the paper MC 204. SELF STUDY (MC - 210) L T P 0 0 1 www.mcdtu.wordpress.com 7