<\/span><\/h2>\nCheck the latest syllabus for VTU Computer Science and Engineering 4th sem from below. All the computer science engineering 4th sem subjects are covered in this.\u00a0<\/span><\/p>\n\n\n\n\n<\/span>COMPLEX ANALYSIS, PROBABILITY AND STATISTICAL METHODS<\/span><\/h3>\n<\/td>\n<\/tr>\n\n| Course Code<\/td>\n | 18MAT41<\/strong><\/td>\n| CIE Marks<\/td>\n | 40<\/td>\n<\/tr>\n | \n| Teaching Hours\/Week (L:T:P)<\/td>\n | (2:2:0)<\/td>\n | SEE Marks<\/td>\n | 60<\/td>\n<\/tr>\n | \n| Credits<\/td>\n | 03<\/td>\n | Exam Hours<\/td>\n | 03<\/td>\n<\/tr>\n | \n| Course Learning Objectives:<\/strong>\n \u00a0<\/p>\n \u00b7 To provide an insight into applications of complex variables, conformal mapping, and special functions arising in potential theory, quantum mechanics, heat conduction, and field theory.<\/p>\n \u00b7 To develop probability distribution of discrete, continuous random variables and joint probability distribution occurring in digital signal processing, design engineering, and microwave engineering.<\/p>\n<\/td>\n<\/tr>\n \nModule-1<\/strong><\/td>\n<\/tr>\n\n| Calculus of complex functions: <\/strong>Review of the function of a complex variable, limits, continuity, and differentiability. Analytic functions: Cauchy-Riemann equations in Cartesian and polar forms and consequences.\n \u00a0<\/p>\n Construction of analytic functions: <\/strong>Milne-Thomson method-Problems.<\/p>\n<\/td>\n<\/tr>\n\nModule-2<\/strong><\/td>\n<\/tr>\n\n| Conformal transformations: <\/strong>Introduction. Discussion of transformations: = , = , = +\n \u00a0<\/p>\n , \u2260 0.Bilinear transformations- Problems.<\/p>\n Complex integration: <\/strong>Line integral of a complex function-Cauchy\u2019s theorem and Cauchy\u2019s integral formula<\/p>\nand problems.<\/p>\n<\/td>\n<\/tr>\n \nModule-3<\/strong><\/td>\n<\/tr>\n\nProbability Distributions: <\/strong>Review of basic probability theory. Random variables (discrete and continuous), probability mass\/density functions. Binomial, Poisson, exponential and normal distributions- problems (No derivation for mean and standard deviation)-Illustrative examples.<\/td>\n<\/tr>\n\nModule-4<\/strong><\/td>\n<\/tr>\n\n| Statistical Methods: <\/strong>Correlation and regression-Karl Pearson\u2019s coefficient of correlation and rank correlation\n \u00a0<\/p>\n -problems. Regression analysis- lines of regression \u2013problems.<\/p>\n Curve Fitting: <\/strong>Curve fitting by the method of least squares- fitting the curves of the form-<\/p>\n= + , = = + + .<\/p>\n<\/td>\n<\/tr>\n \nModule-5<\/strong><\/td>\n<\/tr>\n\n| Joint probability distribution: <\/strong>Joint Probability distribution for two discrete random variables, expectation and covariance.\n \u00a0<\/p>\n Sampling Theory: <\/strong>Introduction to sampling distributions, standard error, Type-I and Type-II errors. Test of hypothesis for means, student\u2019s t-distribution, and Chi-square distribution as a test of goodness of fit.<\/p>\n<\/td>\n<\/tr>\n\n| Course Outcomes: <\/strong>At the end of the course the student will be able to:\n \u00a0<\/p>\n \u00b7 Use the concepts of analytic function and complex potentials to solve the problems arising in electromagnetic field theory.<\/p>\n \u00b7 Utilize conformal transformation and complex integral arising in aerofoil theory, fluid flow visualization, and image processing.<\/p>\n \u00b7 Apply discrete and continuous probability distributions in analyzing the probability models arising in the engineering field.<\/p>\n \u00b7 Make use of the correlation and regression analysis to fit a suitable mathematical model for the statistical data.<\/p>\n<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n \n\n\n| \u00b7 Construct joint probability distributions and demonstrate the validity of testing the hypothesis.<\/td>\n<\/tr>\n | \n| Question paper pattern:<\/strong>\n \u00a0<\/p>\n \u00b7 The question paper will have ten full questions carrying equal marks.<\/p>\n \u00b7 Each full question will be for 20 marks.<\/p>\n \u00b7 There will be two full questions (with a maximum of four sub-questions) from each module.<\/p>\n<\/td>\n<\/tr>\n \nSl. No.<\/strong><\/td>\nTitle of the Book<\/strong><\/td>\nName of the Author\/s<\/strong><\/td>\nName of the Publisher<\/strong><\/td>\nEdition and Year<\/strong><\/td>\n<\/tr>\n\nTextbooks<\/strong><\/td>\n<\/tr>\n\n| 1<\/td>\n | Advanced Engineering Mathematics<\/td>\n | E. Kreyszig<\/td>\n | John Wiley & Sons<\/td>\n | 10th<\/sup> Edition,2016<\/td>\n<\/tr>\n\n| 2<\/td>\n | Higher Engineering Mathematics<\/td>\n | B. S. Grewal<\/td>\n | Khanna Publishers<\/td>\n | 44th<\/sup> Edition, 2017<\/td>\n<\/tr>\n\n| 3<\/td>\n | Engineering Mathematics<\/td>\n | Srimanta Pal et al<\/td>\n | Oxford University Press<\/td>\n | 3rd<\/sup> Edition,2016<\/td>\n<\/tr>\n\nReference Books<\/strong><\/td>\n<\/tr>\n\n| 1<\/td>\n | Advanced Engineering\n \u00a0<\/p>\n Mathematics<\/p>\n<\/td>\n | C. Ray Wylie,\n \u00a0<\/p>\n Louis C.Barrett<\/p>\n<\/td>\n | McGraw-Hill<\/td>\n | 6th<\/sup> Edition 1995<\/td>\n<\/tr>\n\n| 2<\/td>\n | Introductory Methods of\n \u00a0<\/p>\n Numerical Analysis<\/p>\n<\/td>\n | S.S.Sastry<\/td>\n | Prentice Hall of\n \u00a0<\/p>\n India<\/p>\n<\/td>\n | 4th<\/sup> Edition 2010<\/td>\n<\/tr>\n\n| 3<\/td>\n | Higher Engineering\n \u00a0<\/p>\n Mathematics<\/p>\n<\/td>\n | B. V. Ramana<\/td>\n | McGraw-Hill<\/td>\n | 11th<\/sup> Edition,2010<\/td>\n<\/tr>\n\n| 4<\/td>\n | A Text Book of Engineering\n \u00a0<\/p>\n Mathematics<\/p>\n<\/td>\n | N. P. Bali and\n \u00a0<\/p>\n Manish Goyal<\/p>\n<\/td>\n | Laxmi Publications<\/td>\n | 2014<\/td>\n<\/tr>\n | \n| 5<\/td>\n | Advanced Engineering\n \u00a0<\/p>\n Mathematics<\/p>\n<\/td>\n | Chandrika Prasad\n \u00a0<\/p>\n and Reena Garg<\/p>\n<\/td>\n | Khanna\n \u00a0<\/p>\n Publishing,<\/p>\n<\/td>\n | 2018<\/td>\n<\/tr>\n | \n| Web links and Video Lectures:<\/strong>\n \u00a0<\/p>\n 1. http:\/\/nptel.ac.in\/courses.php?disciplineID=111<\/a><\/p>\n2. http:\/\/www.class-central.com\/subject\/math(MOOCs)<\/a><\/p>\n3. http:\/\/academicearth.org\/<\/a><\/p>\n4. VTU EDUSAT PROGRAMME – 20<\/p>\n<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n \n\n\n\n<\/span>DESIGN AND ANALYSIS OF ALGORITHMS<\/span><\/h3>\n<\/td>\n<\/tr>\n\nCourse Code<\/strong><\/td>\n18CS42<\/strong><\/td>\nCIE Marks<\/strong><\/td>\n| 40<\/td>\n<\/tr>\n | \nNumber of Contact Hours\/Week<\/strong><\/td>\n| 3:2:0<\/td>\n | SEE Marks<\/strong><\/td>\n| 60<\/td>\n<\/tr>\n | \nTotal Number of Contact Hours<\/strong><\/td>\n| 50<\/td>\n | Exam Hours<\/strong><\/td>\n| 03<\/td>\n<\/tr>\n | \nCREDITS \u20134<\/strong><\/td>\n<\/tr>\n\nCourse Learning Objectives: <\/strong>This course (18CS42) will enable students to:<\/td>\n<\/tr>\n\n| \u00b7 Explain various computational problem-solving techniques.\n \u00a0<\/p>\n \u00b7 Apply appropriate methods to solve a given problem.<\/p>\n \u00b7 Describe various methods of algorithm analysis.<\/p>\n<\/td>\n<\/tr>\n | \nModule 1<\/strong><\/td>\nContact Hours<\/strong><\/td>\n<\/tr>\n\n| Introduction: <\/strong>What is an Algorithm? (T2:1.1), <\/strong>Algorithm Specification (T2:1.2), <\/strong>Analysis Framework (T1:2.1), Performance Analysis<\/strong>: Space complexity, Time complexity (T2:1.3)<\/strong>. Asymptotic Notations: <\/strong>Big-Oh notation (O<\/em>), Omega notation (\u2126<\/em>), Theta notation (Q<\/em>), and Little-oh notation (o<\/em>), Mathematical analysis of Non-Recursive and recursive Algorithms with Examples (T1:2.2, 2.3, 2.4). Important Problem Types: <\/strong>Sorting, Searching, String processing, Graph Problems, Combinatorial Problems. Fundamental Data Structures: <\/strong>Stacks, Queues, Graphs, Trees, Sets and Dictionaries. (T1:1.3,1.4).<\/strong>\n \u00a0<\/p>\n RBT: L1, L2, L3<\/strong><\/p>\n<\/td>\n| 10<\/td>\n<\/tr>\n | \nModule 2<\/strong><\/td>\n<\/tr>\n\n| Divide and Conquer<\/strong>: General method, Binary search, Recurrence equation for divide and conquer, Finding the maximum and minimum (T2:3.1, 3.3, 3.4)<\/strong>, Merge sort, Quick sort (T1:4.1, 4.2)<\/strong>, Strassen\u2019s matrix multiplication (T2:3.8)<\/strong>, Advantages and Disadvantages of divide and conquer. Decrease and Conquer Approach: <\/strong>Topological Sort. (T1:5.3).<\/strong>\n \u00a0<\/p>\n RBT: L1, L2, L3<\/strong><\/p>\n<\/td>\n| 10<\/td>\n<\/tr>\n | \nModule 3<\/strong><\/td>\n<\/tr>\n\n| Greedy Method: <\/strong>General method, Coin Change Problem, Knapsack Problem, Job sequencing with deadlines (T2:4.1, 4.3, 4.5). Minimum cost spanning trees: <\/strong>Prim\u2019s Algorithm, Kruskal\u2019s Algorithm (T1:9.1, 9.2)<\/strong>. Single source shortest paths: <\/strong>Dijkstra’s Algorithm (T1:9.3)<\/strong>. Optimal Tree problem: <\/strong>Huffman Trees and Codes (T1:9.4)<\/strong>. Transform and Conquer Approach: <\/strong>Heaps and Heap Sort (T1:6.4)<\/strong>.\n \u00a0<\/p>\n RBT: L1, L2, L3<\/strong><\/p>\n<\/td>\n| 10<\/td>\n<\/tr>\n | \nModule 4<\/strong><\/td>\n<\/tr>\n\n| Dynamic Programming: <\/strong>General method with Examples, Multistage Graphs (T2:5.1, 5.2)<\/strong>. Transitive Closure: <\/strong>Warshall\u2019s Algorithm, All Pairs Shortest Paths: <\/strong>Floyd’s Algorithm, Optimal Binary Search Trees, Knapsack problem ((T1:8.2, 8.3, 8.4)<\/strong>, Bellman-Ford Algorithm (T2:5.4)<\/strong>, Travelling Sales Person problem (T2:5.9)<\/strong>, Reliability design (T2:5.8)<\/strong>.\n \u00a0<\/p>\n RBT: L1, L2, L3<\/strong><\/p>\n<\/td>\n| 10<\/td>\n<\/tr>\n | \nModule 5<\/strong><\/td>\n<\/tr>\n\n | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
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