## BCA Bachelor of Computer Applications Part 2

*University Syllabus Course For BCA Part 2 ( Second Year )*

Atlanta Computer Institute Nagpur conducts Tuition Classes for BCA First Year ( Part 1 ) , BCA Second Year ( Part 2 ) and BCA Final Year ( Part 3 ) for all universities in India . The Following syllabus is of Nagpur University. Final Year Projects Training is also given to BCA Students. The Tuition Classes are also conducted for syllabus of BCA of all universities in India.

#### BCA Part 2 ( Second Year )

#### C) COMPUTATIONAL METHODLOGY ------ BCA Second year

__SUBJECT – III __

__PAPTER – 1 THEORY OF COMPUTER __

__ __

UNIT – 1 : Finite Automata & Regular Expression Preliminaries : (String, Alphabets and languages, Graphs & Trees, Inductive Proofs, Set notation, Relations), Finite state system, Non-deterministic finite automata with E-moves, Regular expressions, Two way finite automata with output, application on Finite automata.

UNIT – 2 :Regular sets & Context Free Grammar

Properties of Regular Sets : The pumping lemma for regular sets, closure properties of regular sets, decision Algorithm for sets.

Context Free Grammar : Motivation and Introduction, Context Free Grammar, Derivation Trees, Simplification of Context Free Grammars, Chomsky Normal Form, Greibach Normal form, Inherently ambiguous context free languages and its existence.

UNIT – 3 Automata & Context Free Language

Push Down Automata : informal Description, definitions, pushdown Automata and Context Free Language.

UNIT – 4 TURNING MACHINE

Introduction, The turning Machine Model, Computable languages and functions, Techniques for Turning Machine construction, Modification of turning Machines as enumerators, Restricted Turning Machine as enumerators, Restricted Turning equivalent to basic model.

UNIT – 5 The Chomsky Hierarchy

The Chomsky Hierarchy ; Normal Forms for DPDA’s Closure of DCFL’s under complementation, Predication Machines, Additional Closure Properties of DCD’s, LR(0) grammars’ and DPDA’s.

Closure properties of families of languages : Trios and full trios, Generalized Sequential Machine Mapping. Other Closure properties of Trios, Abstract families of Languages Independent of AFL’s operations.

__PAPER – 2 DATA STRUCTURE __

Unit – 1 : introduction of Data structures

About Data structure – Information and meaning, binary and decimal integer, concept of data types, data structure data representation / implementation, Abstract Data Type, Sequences of Value definition, ADT for varying length Data string.

Arrays, Records & Pointers – About arrays, records, & Pointers; their implementation in memory Arrays as an ADT, Using One dimensional Array & two dimensional, about records & pointers.

Linked List – Concept of singly Linked list, Operations on linked list, inserting and removing nodes from a list, array implementation of lists, limitation of the Array implementation over Linked List concept of Doubly Linked list, generalized List.

Unit – 2 Stack & Queues

Stacks – definition and example, primitive operations, stack as an ADT Implementation of stacks as any Array and Linked List, operations on stacks, stacks stored as a Lined List, Arithmetic expressions – Infix, Postfix and Prefix, Evaluating postfix expression, converting an expression from infix to postfix.

Queues – Definition and example of queues, Queues as an Abstract Data Type, Queues Stored as a Linked List, Circular Queue, Implementation of queues as an Array and Linked list, operations on Queues, Priority Queue & Desuetude.

UNIT – 3 Recursion

Recursive definition and process, Factorial function, Multiplication of natural Numbers, Fabonacci sequence, Properties of recursive definition writing recursive programs (The tower of Hanoi problem converting prefix to postfix using recursion), Simulation recursion(Return from a function, implementing recursive function, simulation of factorial).

UNIT – 4 Trees & Graphs

Trees – Definition of trees, Basic Terminology of trees, Binary Tree, Binary tree traversal, Threaded Binary tree, Height Balance Tree, B-trees, General Trees.

Graphs : Basic terminology of Graphs, Implementation of Graphs as an arrays & linked list, Operations of Graphs, Graphs Travels.

UNIT - 5 : Sorting and Searching

Sorting – Definition of sorting, Classification of sorting, Classification of sorting Techniques, different sorting techniques Bubble sort, Quick Sort, Efficiency of quick sort, insertion sort, Selection sort, Merge sort, Efficiency of quick sort, insertion sort, Selection sort, merge sort, Heap sort.

Searching – Basic search techniques (Dictionary as an ADT, sequential searching, efficiency of sequential searching). Searching an ordered Table Binary search.

__PAPER – 3 NUMERICAL METHODS & ERROR ANALYSIS __

Unit – 1 Approximation & Error in Computing

Significant digits, Data Error, Conversion Error, Round off Error, Chopping, Symmetric Round off, truncation Error, Modeling Error, Absolute and Relative Error, Error propagation, Conditioning & stability, Convergence of Iterative process, Error Estimation, Minimizing the total Error.

UNIT – 2 Roots of Non – Linear Equations

Algebraic equation, Polynomial equation, transcendental equation, Iterative method, starting & Stopping Iterative method, Iterative method, Bisection Method, False position method, Newton Raphson Method, Secant method, Determining all possible roots, Multiple roots of polynomial, Complex Roots using muller’s Method.

UNIT – 3 Solution to Linear Equations

Existence of Solution Gauss Elimination method, Gauss elimination with pivoting, Gauss Jordan Method, Round off errors and refinement, III conditioned system Matrix inversion method

UNIT – 4 Curve Fitting

Linear interpolation Lagrange Interpolation, Spline Interpolation, Interpolation with equidistant points, Least Square regression, Fitting Transcendental equations, Multiple linear reression, Ill conditioning in Least square Method.

UNIT – 5 : Integration & Differentiation

Trapezoidal Rule, Simpson 1/3 Rules, Simpson 3/8 Rules, Gaussian Integration, Solution to differential equation (using Runge-Kutta second and fourth order methods, Multistep method for differential equations. (milne – simpson method, adams –bashforth moulton method.)

BCA Part 2 Group A Computer Science ( COMPUTER SOFTWARE )

BCA Part 2 Group B Electronics ( Computer Hardware )

BCA Part 2 Group COMPUTATIONAL METHODOLOGY

BCA Bachelor Of Computer Application, BCCA, Bachelor of Commerce & Computer Application BE IT/CS, Information technology/Computer Science MCA, Master of Computer Application MCM, Master of Computer Management Diploma , Polytechnic Others,