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Tribhuvan university BCA BCA Curriculum Numerical Methods

Numerical Methods - Syllabus

Course Overview and Structure
Syllabus Notes Old Questions Unit Wise Questions Question Bank

Embark on a profound academic exploration as you delve into the Numerical Methods course (NM) within the distinguished Tribhuvan university's BCA department. Aligned with the BCA Curriculum, this course (CACS252) seamlessly merges theoretical frameworks with practical sessions, ensuring a comprehensive understanding of the subject. Rigorous assessment based on a 60 + 20 + 20 marks system, coupled with a challenging passing threshold of , propels students to strive for excellence, fostering a deeper grasp of the course content.

This 3 credit-hour journey unfolds as a holistic learning experience, bridging theory and application. Beyond theoretical comprehension, students actively engage in practical sessions, acquiring valuable skills for real-world scenarios. Immerse yourself in this well-structured course, where each element, from the course description to interactive sessions, is meticulously crafted to shape a well-rounded and insightful academic experience.


Course Description 

This course covers solution of nonlinear equations, interpolation and approximation, numerical differentiation and integration and solution of linear algebraic equation, ordinary differential equations and partial difrential equations. it provides knowledge for numerical analysis.

Course Objectives 

The general objectives of this subject are to make students familiar with the 

theory of numerical analysis for solving algebraic and transcendental equations, 

solution of ordinary and partial differential equations, numerical di fferentiation 

and integration.


Units

Key Topics

  • Errors in Numerical Calculations
    SO-1

    This topic covers the sources of errors in numerical calculations, propagation of errors, and a review of Taylor's Theorem.

  • Trial and Error Method
    SO-2

    This topic explains the trial and error method for solving non-linear equations, including its convergence.

  • Half-Interval Method
    SO-3

    This topic covers the half-interval method for solving non-linear equations, including its convergence.

  • Newton's Method
    SO-4

    This topic explains Newton's method for solving non-linear equations, including its convergence and application to calculating multiple roots.

  • Secant Method
    SO-5

    This topic covers the secant method for solving non-linear equations, including its convergence.

  • Fixed Point Iteration
    SO-6

    This topic explains the fixed point iteration method for solving non-linear equations, including its convergence.

  • Horner's Method
    SO-7

    This topic covers Horner's method for solving non-linear equations.

  • Solving System of Ordinary Differential Equations
    SO-8

    Methods for solving systems of ODEs, including numerical and analytical approaches.

  • Solution of Higher Order Equations
    SO-9

    Methods for solving higher order ODEs, including reduction of order and numerical methods.

Key Topics

  • Introduction to E-commerce
    IN-1

    Overview of E-commerce and its significance in the digital age.

  • E-business vs E-commerce
    IN-2

    Understanding the differences between E-business and E-commerce.

  • Features of E-commerce
    IN-3

    Key characteristics and benefits of E-commerce.

  • Pure vs Partial E-commerce
    IN-4

    Types of E-commerce models and their applications.

  • History of E-commerce
    IN-5

    Evolution and development of E-commerce over time.

  • E-commerce Framework
    IN-6

    Understanding the components of E-commerce framework including People, Public Policy, Marketing and Advertisement, Support Services, and Business Partnerships.

Key Topics

  • History of Number Systems
    NU-01

    Introduction to the historical development of number systems and their significance.

  • Introduction to Number Systems
    NU-02

    Overview of positional and non-positional number systems, including their characteristics and applications.

  • Decimal Number System
    NU-03

    In-depth study of the decimal number system, including its representation and operations.

  • Binary Number System
    NU-04

    In-depth study of the binary number system, including its representation and operations.

  • Octal and Hexadecimal Number Systems
    NU-05

    In-depth study of the octal and hexadecimal number systems, including their representation and operations.

Key Topics

  • Errors in Numerical Calculations
    SO-1

    This topic covers the sources of errors in numerical calculations, propagation of errors, and a review of Taylor's Theorem.

  • Trial and Error Method
    SO-2

    This topic explains the trial and error method for solving non-linear equations, including its convergence.

  • Half-Interval Method
    SO-3

    This topic covers the half-interval method for solving non-linear equations, including its convergence.

  • Newton's Method
    SO-4

    This topic explains Newton's method for solving non-linear equations, including its convergence and application to calculating multiple roots.

  • Secant Method
    SO-5

    This topic covers the secant method for solving non-linear equations, including its convergence.

  • Fixed Point Iteration
    SO-6

    This topic explains the fixed point iteration method for solving non-linear equations, including its convergence.

  • Horner's Method
    SO-7

    This topic covers Horner's method for solving non-linear equations.

  • Solving System of Ordinary Differential Equations
    SO-8

    Methods for solving systems of ODEs, including numerical and analytical approaches.

  • Solution of Higher Order Equations
    SO-9

    Methods for solving higher order ODEs, including reduction of order and numerical methods.

Key Topics

  • Errors in Numerical Calculations
    SO-1

    This topic covers the sources of errors in numerical calculations, propagation of errors, and a review of Taylor's Theorem.

  • Trial and Error Method
    SO-2

    This topic explains the trial and error method for solving non-linear equations, including its convergence.

  • Half-Interval Method
    SO-3

    This topic covers the half-interval method for solving non-linear equations, including its convergence.

  • Newton's Method
    SO-4

    This topic explains Newton's method for solving non-linear equations, including its convergence and application to calculating multiple roots.

  • Secant Method
    SO-5

    This topic covers the secant method for solving non-linear equations, including its convergence.

  • Fixed Point Iteration
    SO-6

    This topic explains the fixed point iteration method for solving non-linear equations, including its convergence.

  • Horner's Method
    SO-7

    This topic covers Horner's method for solving non-linear equations.

  • Solving System of Ordinary Differential Equations
    SO-8

    Methods for solving systems of ODEs, including numerical and analytical approaches.

  • Solution of Higher Order Equations
    SO-9

    Methods for solving higher order ODEs, including reduction of order and numerical methods.

  • Boundary Value Problems
    SO-10

    Introduction to boundary value problems, including their definition and importance in ODEs.

Introduction to Partial Differential Equations, Deriving Differences Equations, Laplacian Equation and Poisson's Equation.

Lab works

Laboratory Works 

Laboratory works will consist of program development and testing of Non-linear Equations, Interpolation, Numerical Differentiation and Integration, Linear Algebraic Equations, Ordinary and Partial Differential Equations using C or C+ I Builder.