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Tribhuvan university CSIT 2074 Syllabus Numerical Method

Numerical Method - 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 Method course (NM) within the distinguished Tribhuvan university's CSIT department. Aligned with the 2074 Syllabus, this course (CSC207) 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 contains the concepts of numerical method techniques for

solving linear and nonlinear equations, interpolation and regression, differentiation and

integration, and partial differential equations.


Course Objectives: The main objective of the course is to provide the knowledge of numerical

method techniques for mathematical modeling.


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.

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.

  • Challenges in E-commerce
    IN-8

    Common obstacles and difficulties faced in E-commerce.

  • Status of E-commerce in Nepal
    IN-9

    Current state and trends of E-commerce in Nepal.

Key Topics

  • Error Detection Codes
    NU-10

    Introduction to error detection codes and their applications in digital systems.

  • 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.

  • Primality Testing
    NU-6

    Introduction to primality testing, including the Miller-Rabin randomized primality test and its analysis.

  • Miller-Rabin Randomized Primality Test
    NU-7

    The Miller-Rabin randomized primality test, including its algorithm, analysis, and applications.

  • Simpson's 3/8 Rule
    NU-8

    This topic covers Simpson's 3/8 rule for numerical integration.

  • Multi-Segment Simpson's 3/8 Rule
    NU-9

    This topic covers the multi-segment Simpson's 3/8 rule for numerical integration.

  • Romberg Integration
    NU-11

    This topic covers Romberg integration for numerical integration.

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.

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.

  • Shooting Method
    SO-11

    Numerical method for solving boundary value problems, including its algorithm and applications.

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.

Lab works

Laboratory Works:

The laboratory exercise should consists of program development and testing of non-linear

equations, interpolation, numerical integration and differentation, linear algebraic equations,

ordinary and partial differential equations numerical solutions using appropriate languages like

C, C++ or Matlab.

List topics to be included in Laboratory Exercises:

  •  Solution of non-linear equations using Bisection Method and Secant Method
  •  Solution of non-linear equations using Newton’s Raphson Method and Fixed Point

Iteration Method

  •  Solution of polynomial using Newton’s Method and Horner’s Rule to evaluate

polynomial

  •  Polynomial interpolation using Lagrange’s Interpolation and Newton’s Divided Difference   Interpolation, Newton’s forward and backward difference interpolation
  •  Fitting of linear (straight line , y=ax + b) and non-linear (exponential y=aebx,   quadraticy=ax2+bx+c) function using least square method
  •  Derivatives from divided difference table
  •  Integration using Trapezoidal rule, Simpson’s 1/3 rule and Simpson’s 3/8 rule, Line and

Double Integration.

  •  Solution of system of linear equations using Gauss Elimination method and Gauss Jordan

Method

  •  Gauss Seidel Method, Jacobi Method and Power Method
  •  Solution of ordinary differential equation using Euler’s Method, Heun’s Method and 4th   order Runge-Kutta Method
  •  Boundary value problems using Shooting Method
  •  Laplacian Equation, Poison’s Equation