Numerical Methods and Computations
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Follow on Instagram for UpdatesNumerical Methods and Computations Syllabus — Unit-wise Content
The official GTU curriculum for Numerical Methods and Computations (subject code BE04041041) as prescribed for Robotics · Semester 4 divides the course into 7 units, covering 50 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 (BE04041041)Unit 1 Mathematical Modeling and Error Analysis
- Inherent error
- Round-off and truncation errors
- Absolute error
- True percentage relative error
- Approximate percentage relative error
Unit 2 Systems of Linear Equations
- Numerical simulation: Using Gauss Elimination Method
- Gauss Jordan Method and matrix inversion
- techniques for improving solutions
- Gauss- SeidelMethod
- Case Studies
Unit 3 Solution of Nonlinear Equations
- Bisection Method
- Iteration methods based on first degree – Secant and Regula-Falsi methods
- Newton- Raphson Method
- modified Newton-Raphson Method
- Iteration methods based on second degree equation– Muller’s method
- Chebyshev method
- Roots of polynomials
- Computing with polynomials
- Bairstow’s method to extract a quadratic factor
- Case studies applicable to robotics
Unit 4 Principles of Least-Squares
- Fitting a straight line
- fitting asecond-degree curve
- fitting an exponential curve
- calculation of the sum of the squares of the residuals for the line fit and a parabolic fit
- Linearization of nonlinear relationships (Exponential Model
- Power Law, Saturation-growth-rate equation)
- Polynomial regression
- Multiple linear regression
- Case studies
Unit 5 Polynomial Interpolation
- Introduction to interpolation
- Trajectory generation using Cubic interpolation
- Newton interpolating Polynomial
- Lagrange interpolating Polynomial
- Inverse Interpolation
- Error and approximation properties
- Estimation of deviation between actual and interpolated motion
Unit 6 Spline and Piecewise Interpolation
- Introduction to splines
- Linear splines
- Quadratic splines
- Cubic splines
- multi-dimensional interpolation
Unit 7 Iterative method for Eigen values
- Eigne value problem
- The polynomial method
- The power method
- Ordinary Differential Equations & Eigen values
- Jacobi’s method for finding eigen values
- Case studies. 07 8* Numerical solution of 2D and 3D robotic arms: Forward and inverse kinematic solutions
- Numerical solution to minimize the error between the forward kinematic solution and the desired end effector pose
- To be dealt in the Lab
- Total Hrs
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