| Weeks | Topics |
| 1 |
Mathematical Foundations and Error Analysis
|
| 2 |
Roots of nonlinear algebraic equations: Implicit Methods (Bisection Method, False Position Method)
|
| 3 |
Roots of nonlinear algebraic equations: Explicit Methods (Fixed Point Iteration, Newton-Raphson Method, Secant Method)
|
| 4 |
Curve Fitting: Least squares regression (Linear regression, Polynomial regression, Multiple linear regression)
|
| 5 |
Curve Fitting: Linearization of nonlinear relations
|
| 6 |
Interpolation (Newton and Lagrange interpolation polynomials)
|
| 7 |
Extrapolation, Inverse Interpolation
|
| 8 |
Numerical Differentiation and Integration (Introduction): Numerical Integration (Trapezoidal Rule)
|
| 9 |
Numerical Integration (Simpson's Rules, Integration with unequal segments)
|
| 10 |
Numerical Differentiation (Finite divided difference formulas)
|
| 11 |
Numerical Solution of Ordinary Differential Equations (Introduction): Euler's Method, Heun's method
|
| 12 |
Numerical Solution of Ordinary Differential Equations: Runge-Kutta Methods, Systems of ODE's
|
| 13 |
Boundary-Value Problems for ODEs
|
| 14 |
Numerical Analysis Applications in Chemical Engineering
|