Numerical Methods - Engineering Mathematics

ANANTH PAI S

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Why do you enroll

This course assumes a strong foundation in calculus, linear algebra, and basic programming skills. Prior exposure to mathematical modeling and differential equations is beneficial but not mandatory.

By the end of this course, students should be able to:

- Apply numerical methods to solve a wide range of engineering and scientific problems.

- Analyze the accuracy and stability of numerical algorithms.

- Implement numerical solutions using programming languages like MATLAB, Python, or C/C++.

- Prepare for GATE examinations by mastering the numerical methods portion of the syllabus.

This course is designed to help students not only excel in their GATE exams but also to develop practical problem-solving skills that are highly valuable in engineering and scientific research and practice.

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Key topics covered

This course is designed to equip students with the fundamental concepts and techniques of numerical methods, which are essential for solving engineering and scientific problems. The course focuses on both theoretical understanding and practical implementation of numerical algorithms. It is tailored to meet the requirements of GATE examinations in various engineering disciplines.

1. **Introduction to Numerical Methods**:

- Role of numerical methods in engineering and science.

- Sources of error in numerical computations.

2. **Root Finding Methods**:

- Bisection method.

- Newton-Raphson method.

- Secant method.

3. **Linear Systems of Equations**:

- Gaussian elimination.

- LU decomposition.

- Iterative methods (Jacobi, Gauss-Seidel).

4. **Interpolation and Approximation**:

- Lagrange interpolation.

- Newton's divided difference interpolation.

- Curve fitting using least squares.

5. **Numerical Differentiation and Integration**:

- Numerical differentiation methods.

- Numerical integration methods (Trapezoidal rule, Simpson's rule).

6. **Numerical Solutions of Ordinary Differential Equations (ODEs)**:

- Euler's method.

- Runge-Kutta methods.

- Multistep methods (e.g., Adams-Bashforth).

7. **Partial Differential Equations (PDEs)**:

- Finite difference methods for PDEs.

- Boundary value problems (e.g., Laplace and Poisson equations).

8. **Numerical Techniques for Optimization**:

- Gradient descent method.

- Conjugate gradient method.

9. **Error Analysis and Stability**:

- Analysis of errors in numerical methods.

- Stability and convergence of numerical algorithms.

10. **Applications**:

- Practical engineering and scientific problems solved using numerical methods.

- Case studies from various engineering disciplines.

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Course Details

The Graduate Aptitude Test in Engineering (GATE) is a competitive examination in India for students seeking admission to postgraduate programs in various engineering and science disciplines. Numerical Methods may be a part of the syllabus for certain GATE papers, such as Computer Science and Engineering, Mechanical Engineering, Civil Engineering, and others, depending on the specific paper's syllabus. Below is a general description of what you might expect in a Numerical Methods course for GATE preparation: