# Computer Engineering Semester 3

 Applied Mathematics III Complex Variable & mapping 1.1 Functions of a complex variable, Analytic functions, Cauchy-Riemann equations in Cartesian co-ordinates, Polar co-ordinates. 1.2 Harmonic functions, Analytic method and Milne Thomson methods to find f(z), Orthogonal trajectories. 1.3 Conformal Mapping, Linear, Bilinear transformations, Cross ratio, fixed points and standard transformation such as rotation and magnification, invertion, translation. Laplace Transform 2.1 Introduction, Definition of Laplace transform, Laplace transform of constant, trigonometrical, exponential functions. 2.2 Important properties of Laplace transform: First shifting theorem, Laplace transform of L{tn f(t)}, L{ f(t)/t}, , , L{f(at)} without proof. 2.2Unit step function, Heavi side function, Dirac-delta function, Periodic function and their Laplace transforms, Second shifting theorem. 2.3Inverse Laplace transform with Partial fraction and Convolution theorem (without proof). 2.4 Application to solve initial and boundary value problem involving ordinary differential equations with one dependent variable and constant coefficients. Fourier series 3.1 Dirichlet’s conditions, Fourier series of periodic functions with period 2? and 2L. 3.2 Fourier series for even and odd functions. 3.3 Half range sine and cosine Fourier series, Parsevel’s identities (without proof). 3.4Orthogonal and Ortho-normal functions, Complex form of Fourier series. 3.5 Fourier Integral Representation. Vector Algebra and Calculus 4.1 Vector Algebra: Scalar and vector product of three and four Vectors and their properties. 4.2 Vector Calculus: Vector differential operator ?, Gradient of a scalar point function, Diversions and Curl of Vector point function, ? (u v), 4.3 Vector Integration: Line integral; conservative vector field,Green’s theorem in a plane (Without proof) 4.4 GaussDivergence theorem & Stokes’ theorem (Without proof and no problemson above verifications Z transform 5.1 Z-transform of standard functions such as Z(an), Z(np). 5.2 Properties of Z-transform :Linearity, Change of scale, Shifting property, Multiplication of K, Initial and final value, Convolution theorem (all without proof) 5.3 Inverse Z transform: Binomial Expansion and Method of Partial fraction. Term work: Term work shall consist of minimum four SCILAB practicals and six tutorials. SCILAB practicals : 10 marks Tutorials : 10 marks Attendance : 05 marks Total : 25 marks Text Books: • Higher Engineering Mathematics by Grewal B. S. 38th edition, Khanna Publication 2005. • Advanced Engineering Mathematics by Kreyszig E. 9th edition, John Wiley. • A Text Book of Applied Mathematics Vol. I & II by P.N.Wartilar & J.N.Wartikar, Pune, Vidyarthi Griha Prakashan., Pune. • Discrete and Combinational Mathematics by Ralph P. Crimaldi, B Y Ramana. Theory Examination: 1. Question paper will comprise of total 6 questions, each of 20 Marks. 2. Only 4 questions need to be solved. 3. Question 1 will be compulsory and based on maximum part of the syllabus. 4. Remaining questions will be mixed in nature (for example suppose Q.2 has part (a) from module 3 then part (b) will be from any module other than module 3) In question paper, weightage of each module will be proportional to number of respective lecture hours as mentioned in the syllabus.

 Object Oriented Programming Methodology (OOPM)* Programming Approach from proceduaral to Object Orientation OO methodologies: Grady Booch Methodology of OO developmentOO Concepts: Object, Class, Encapsulation or information hiding, Inheritance, Polymorphism, Message communication, Abstraction, Reuse, Coupling and Cohesion, Sufficiency Completeness and Primitiveness, Meta Class Object Oriented Programming: Java Evolution: History, How java differs from others Overview of Java language: Introduction, Installing and implementing Java, JVMConstants, variables and data types Operators and Expressions Revision of Branching and loopingClass Object and Method: member, method, Modifier, Selector, constructer, destructor, iterator, State of an object, Method Overloading, Inheritance, Method Overriding ,Final class, abstract class and method Classes and Relationships : Implementation of Association and Aggegation using simple scenariosArray, String, Vector Interfaces : variables in Interfaces, Extending an Interface, Difference between an Abstarct class and an InterfaceMultithread programming Grouping of classes for deployment and reuse: Built-in Packages: java.lang: wrapper classes java.util: ArrayList and LinkedList Creating and using User defined packagesManaging Error and Exception Applet programming TermWork: Students will submit Term Work in the form of a journal that will include at least 15 programming assignments. Each programming assignment will consist of an algorithm or class diagram/sequence diagram (if applicable), program listing with proper documentation and snapshot of the output. Practical Examination will be based on the term work and questions will be asked to judge understanding of the assignments at the time of the examination. The final certification and acceptance of term work ensures that satisfactory performance of laboratory work and minimum passing marks in term work. Term Work: 25 Marks ( total marks ) = 15 Marks ( Experiment ) + 5 Marks ( Assignment ) + 5 (Attendance (theory+practical)) Practical Exam will based on above syllabus Theory Examination: 1. Question paper will comprise of total 6 questions, each of 20 Marks. 2. Only 4 questions need to be solved. 3. Question 1 will be compulsory and based on maximum part of the syllabus. 4. Remaining questions will be mixed in nature (for example suppose Q.2 has part (a) from module 3 then part (b) will be from any module other than module 3) In question paper, weightage of each module will be proportional to number of respective lecture hours as mentioned in the syllabus. Text Books: 1. Ralph Bravaco , Shai Simoson , “Java Programing From the Group Up” ,Tata McGraw-Hill 2. Grady Booch, Object Oriented Analysis and Design ; 3. Jaime Nino, Frederick A. Hosch, ‘An introduction to Programming and Object Oriented Design using Java’, Wiley Student Edition.