Numerical Methods for Engineers
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Follow on Instagram for UpdatesNumerical Methods for Engineers Syllabus — Unit-wise Content
The official GTU curriculum for Numerical Methods for Engineers (subject code 3162424) as prescribed for PE · Semester 6 divides the course into 8 units, covering 63 listed topics. The unit-wise breakdown below is read from the GTU syllabus document for this subject code, so you can check what the course actually covers before deciding which papers to attempt.
Download the official syllabus PDF (3162424)Unit 1 Introduction
- • Mathematical modelling and problem solving • Approximations and errors
- significant figure
- error definition
- round off error etc. • Taylor’s series
- error propagation
- total numerical error
- Truncation error
- formulation errors, and data uncertainty
Unit 2 Roots of Equations
- • Introduction • bracketing methods like bisection method
- false position method
- incremental searches and determining initial guesses • Open methods like simple fixed-point iteration
- Newton-Raphson method
- Secant method
- Brent’s method
- multiple roots • Roots of polynomials
- polynomials in engineering
- computing with polynomials
- methods for finding roots of polynomials like Muller’s method
- Bairstow’s method etc. • Preparing algorithms for finding roots of equations
Unit 3 Linear Algebraic Equations
- Linear equations
- solving set of linear equations using Gauss Elimination method
- pitfalls of elimination method and improving solution
- LU Decomposition
- matrix inversion
- error analysis
- Special matrices
- Gauss-Seidel method etc. • Preparing algorithms for solution of linear algebraic equations
Unit 4 Nonlinear Equations
- solution of nonlinear equations
- methods like Bisection method
- regula falsie method
- Secant method etc
- Subject Code: 3162424 w.e.f
- Content Teaching Hours % Weightage
Unit 5 Optimization
- non-computer methods
- optimization, and engineering practices • One dimensional unconstrained optimization
- Golden section search
- parabolic interpolation
- Newton’s method
- Brent’s method • Multi-dimensional unconstrained optimization
- direct methods
- Gradient methods • Constrained optimization
- Linear programming
- nonlinear constrained optimization
Unit 6 Curve Fitting
- noncomputer methods
- curve fitting and engineering practice. • Least Square regressions
- linear regression
- polynomial regression
- multiple linear regression
- general linear least squares
- nonlinear regressions • Interpolation
- different methods used for interpolation
- Fourier Approximation etc. • Preparing algorithms for curve fitting problems
Unit 7 Numerical differentiation and integration
- • Introduction • Numerical differentiation
- high accuracy differentiation formula
- Richardson Extrapolation
- derivatives of unequally spaced data
- • integration methods like Trapezoidal rule
- Simpson’s rule etc.
- Concept of integration of equations. • Derivatives and integrals of data with errors
- Partial derivatives • Preparing algorithms for integration and differentiation
Unit 8 Differential Equations
- • Ordinary Differential Equations • Euler’s methods
- Runge Kutta Methods
- Systems of equations • Preparing algorithms for solution of differential equations
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