- To introduce various techniques for solving (i) linear, non-linear, and difference equations using various numerical methods and (ii) complex numbers and variables.
- To apply gained knowledge to solve practical problems.
COURSE LEARNING OUTCOMES (CLO)
CLO: 1. To solve problems of non-linear equations, interpolation, numerical differentiation/integration and linear simultaneous equations.
CLO: 2. To analyze complex numbers and variables.
CLO: 3. To justify his/her analysis of various engineering problems by concepts of Numerical Analysis.
CLO: 4. To perform simple calculations related to numerical analysis in software (Mat Lab or Mathematica).
- Solution of Non-Linear Equations
- Bisection method
- Newton’s method
- Secant method
- Method of false position
- Method of successive approximation
- Basic idea
- Taylor’s polynomial
- Lagrange’s formula of interpolation
- Numerical Differentiation and Integration
- Numerical differentiation
- Review of integration concept and their physical significance for Engineering
- Trapezoidal and Simpson’s rule numerical integration techniques
- Solution of Linear Simultaneous Equations
- Gaus Elimination and Gaus-Jordan methods
- Numerical solution of differential equations
- Euler and modified Euler methods
- Runge-Kutta methods
- Complex Numbers
- Basic operations
- Graphical representations
- Polar and exponential forms of complex numbers
- De’moivre’s theorem with applications
- Complex Variables
- Limit, continuity, zeros and poles
- Cauchy-Reimann Equations
- Use of Softwares