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Precize Computer Oriented Numerical Methods for BCA 3rd Semester PU

₹245.00

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Precize Computer Oriented Numerical Methods is an essential textbook for BCA 2nd year students at Punjab University, Chandigarh. Authored by G.S. Sandhu, Sukhpal Singh, Daljit Kaur, and Gulshan Kumar, this comprehensive guide covers critical topics in numerical methods, including data representation, solving non-linear and linear equations, interpolation, numerical integration, and more. With clear explanations and practical examples, it equips students with valuable skills essential for their academic and professional journeys. 

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  • Q1
    What is "Precize Computer Oriented Numerical Methods"?
    A1

    This book is a comprehensive textbook designed for BCA 2nd year (Semester 3) students at Punjab University, Chandigarh. It covers various numerical computation methods used in computer science.

  • Q2
    Who are the authors of this textbook?
    A2

    The textbook is authored by G.S. Sandhu, Sukhpal Singh, Daljit Kaur, and Gulshan Kumar, who have substantial expertise in the field of numerical methods and computer science.

  • Q3
    What topics are included in the textbook?
    A3

    The book includes topics such as data representation and computer arithmetic, solution methods for non-linear and simultaneous linear equations, interpolation, numerical integration, function approximation, and solutions for ordinary differential equations.

  • Q4
    How is the content organized?
    A4

    The content is structured into four units, each focusing on key aspects of numerical methods. The chapters build on one another, enabling a progressive learning approach.

  • Q5
    What is the format of the examination based on this textbook?
    A5

    The question paper will consist of four units with a total of nine questions: two questions from each unit and one compulsory short answer question that covers the entire syllabus.

  • Q6
    Are calculators permitted during exams?
    A6

    Yes, students can use basic type calculators, and log tables may also be provided for computation purposes.

  • Q7
    What types of errors are discussed in this textbook?
    A7

    The book discusses several types of errors, including data errors, truncation errors, round-off errors, and computational errors, along with measures of accuracy and error propagation techniques.

  • Q8
    What iterative methods for solving non-linear equations does the book cover?
    A8

    The book covers several iterative methods, such as the bisection method, false-position method, secant method, and Newton-Raphson method, as well as methods for finding polynomial zeros using the Birge-Vieta approach.

  • Q9
    How does the book address interpolation and numerical integration?
    A9

    The book provides in-depth discussions on interpolation techniques like Lagrange interpolation, and methods for numerical integration including the trapezoidal rule and Simpson's rules.

  • Q10
    What is the significance of function approximation in this textbook?
    A10

    Function approximation is essential for simplifying complex problems. The book discusses Taylor series representation and Chebyshev polynomials, which are critical for more advanced numerical computations.

  • Q11
    Are there practical examples included in the book?
    A11

    Yes, the textbook includes clear explanations and practical examples throughout each chapter to help illustrate the concepts in a practical context.

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0.Preliminaries
1.Data Representation and computer arithmetic 
2.Solution of Non-Linear equations 
3.Simultaneous linear equations
4.Interpolation 
5.Numerical Integration 
6.Appproximation of functions 
7.Solution of Ordinary Differential equations 
Note : 
i. The Questions paper will consist of four Units.
ii. Examiner will set total of NINE questions comprising TWO questions from each Unit and ONE compulsory question of short answer type covering whole syllabi.
iii. The students are required to attempt ONE question from each unit and compulsory question.
iv. All questions carry equal marks unless specified.
v.The students can use only basic type of calculator.
vi.Log tables are allowed. The same may be provided to the students for computation.


Unit - 1 
Introduction to differentiation, intergration and matrix algebra.
Data representation and computer arithmetic : Introduction, Concept of Exact and approximate numbers, concept of significant digits, Representation of numbers in Memory, strorage of interger numbers: signed representation, 1's Complement Representatio, 2's complement representation,floating point numbers and their storage, floating point arithmetic normalization and their consequences, errors, measures of accuracy: Absolute error, relatives error and percentage error, error types: Data errors, Truncation errors, Round-off errors, Computational error, Rules, Computational error propagation: Error Propagation in Addition Operation, Subtration operation, Multipilication operation and Division Operation.


Unit - 2
Solution of non-linear equations : introduction, types of non-linear equations: polynomial equations, Transcendental equations, methods of finding solutions of non-iterative methods: Direct method, Iterative method.
Iterative methods : Bisection method, false-position method, Secant method, newton - rasphson methods, Zeros of a polynomial using birge - vieta method. Convergence of iterative methods, Comparison between iterative methods. 

Simultaneous Linear equations : Solution of Simultaneaus linear equations using direct and iterative methods: Direct methods : Gauss - Elimination method, gauss-Jordan method, Concept of Pivoting, Iterative method : Gauss - Seidal method.


Unit - 3
Interpolation : Introduction, lagrange interpolation, inverse interpolation, Finite differences: Forward differences, Backward difference table, divided difference table, observations regarding difference tables, Newton's method of interpolation : newton's forward difference interpolation formula, Newton's backward difference interpolation formula, newton's divided difference interpolation formula.

Numerical integration : introduction, newton-cotes intergration formulae: trapezoidal rule, simpson's 1/3rd rule, Simpson's 3/8th rule. 


Unit - 4
Approximation : Approximation of Functions: Taylor series representation, Chebyshev polynomials.
Solution of Ordinary differential equations : Introduction, Euler's method, Runga-kutta methods: 2nd order & 4th order, Predictor corrector methods: Euler's method. 

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