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Tribhuvan university BIT BIT 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 BIT department. Aligned with the BIT Curriculum, this course (BIT203) 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 different concepts of numerical techniques of solving non-linear equations, system of linear equations, integration and differentiation, and ordinary and partial differential equations.

Course Objective: The main objective of this course is to provide concepts of numerical techniques for solving different types of equations and developing algorithms for solving scientific problems.

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.

  • Boundary Value Problems
    SO-10

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

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.

  • Types of E-commerce
    IN-7

    Overview of different types of E-commerce including B2C, B2B, C2B, C2C, M-Commerce, U-commerce, Social-Ecommerce, and Local E-commerce.

Key Topics

  • Numerical Differentiation
    NU-1

    Concept of differentiation, differentiating continuous functions using two-point forward and backward difference formulae, and three-point formula. Also, differentiating tabulated functions using Newton's differences.

  • Maxima and Minima of Tabulated Functions
    NU-2

    Finding maxima and minima of tabulated functions using numerical differentiation methods.

  • Numerical Integration
    NU-3

    Concept of integration, Newton-Cote's quadrature formulae including trapezoidal rule, Simpson's 1/3 rule, and Simpson's 3/8 rule.

  • Trapezoidal Rule
    NU-4

    Approximating definite integrals using the trapezoidal rule, including single-segment and multi-segment trapezoidal rule.

  • Simpson's Rules
    NU-5

    Approximating definite integrals using Simpson's 1/3 rule and Simpson's 3/8 rule, including single-segment and multi-segment Simpson's rules.

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.

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.

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.

Lab works