BIT · Semester III
Numerical Methods syllabus
Official TU syllabus for Numerical Methods (BIT203): 10 units, 59 topics. Every unit links to its notes and solved questions.
1
Errors and Approximations
2 Q- True error and relative error definitions
- Sources of errors in numerical computation
- Round-off error and truncation error
- Error precision and convergence criteria
- Effect of errors on numerical computations
2
Root Finding Methods
8 Q- Bisection method derivation and application
- Newton Raphson method formula and convergence
- Secant method formula and derivation
- Comparison of root finding methods
- Horner's method for polynomial evaluation
- Algorithm and implementation of root finding methods
3
Interpolation and Approximation
8 Q- Lagrange interpolation formula and algorithm
- Newton's divided difference method
- Newton's forward difference formula
- Newton's backward difference table construction
- Interpolation versus regression
- Applications of interpolation
- Derivative estimation using interpolation formulas
4
Curve Fitting and Regression
5 Q- Least squares method for function fitting
- Quadratic polynomial fitting
- Exponential curve fitting
- Regression versus interpolation
- Fitting algorithms and applications
5
Numerical Differentiation
4 Q- Derivatives of continuous functions
- Two point forward difference formula
- Two point backward difference formula
- Divided difference table for derivatives
- First and second order derivatives
- Algorithm and program for numerical differentiation
6
Numerical Integration
8 Q- Trapezoidal rule and composite trapezoidal rule
- Simpson's 1/3 rule and composite Simpson's 1/3 rule
- Simpson's 3/8 rule and composite Simpson's 3/8 rule
- Double integration using Simpson's rules
- Applications of numerical integration
- Algorithm and program for numerical integration
7
Systems of Linear Equations
8 Q- Gaussian elimination method
- Gaussian elimination with partial pivoting
- Jacobi iteration method
- Gauss-Seidel iteration method
- Comparison of iterative methods
- LU decomposition and Doolittle method
- Cholesky decomposition method
- Applications of linear equation systems
8
Eigenvalues and Eigenvectors
4 Q- Eigenvalue and eigenvector definitions
- Characteristic equation and determinant method
- Computing eigenvalues and eigenvectors
- Applications of eigenvalue problems
9
Ordinary Differential Equations
9 Q- Initial value problems and solution methods
- Euler's method for ODE solving
- Heun's method for ODE solving
- Runge-Kutta fourth order method
- Boundary value problems and initial value problems
- Shooting method for boundary value problems
- Higher order differential equation solving
10
Partial Differential Equations
4 Q- Poisson's equation and finite difference method
- Laplace equation and steady state problems
- Grid discretization and boundary conditions
- Iterative solution of PDE systems
- Heat conduction and temperature distribution problems
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