Nurimal Computations

1. Understand different types of errors in numerical computations
2. Apply curve-fitting techniques to experimental data
3. Solve systems of linear equations using various numerical methods
4. Find roots of algebraic and transcendental equations
5. Perform numerical integration using different quadrature rules
6. Solve initial value problems of ordinary differential equations
7. Write C++ programs to implement numerical methods

13 weeks, about 41 hours in total. Yours will differ.

1. Week 1Module 1:

   • Unit 1: Approximations and Errors in Numerical Computations · 3 hours

     Understand the importance of errors in numerical analysis.. Learn to round numbers to a specific number of significant figures.. Explore different types of errors and methods to reduce them..

2. Week 2Module 1:

   • Unit 2: Approximations and Errors in Numerical Computations · 3 hours

     Linearise a given equation to plot a linear graph.. Derive equations for least squares linear fit.. Fit a linear graph to a set of data..

3. Week 3Module 1:

   • Unit 3: Linear Systems of Equations · 3 hours

     Write a system of linear equations in an augmented matrix form.. Solve a system of linear equations using Gaussian elimination.. Apply Gauss-Jordan elimination and LU decomposition methods..

4. Week 4Module 1:

   • Unit 4: Roots of Algebraic and Transcendental Equations · 3 hours

     Find the root of an equation using the bisection method.. Apply the Newton-Raphson method to find roots.. Compare different methods for obtaining the zero of a function..

5. Week 5Module 1:

   • Unit 5: Finite Differences and Interpolation · 3 hours

     Deduce a polynomial from its difference table.. Derive Newton's forward and backward interpolation formulas.. Fit a polynomial to a given set of data..

6. Week 6Module 1:

   • Unit 6: Numerical Integration · 3 hours

     Numerically integrate a function using the Trapezoidal rule.. Apply Simpson's one-third and three-eighth rules.. Deduce the error involved in approximating an analytical integral with a numerical one..

7. Week 7Module 1:

   • Unit 7: Initial Value Problems of Ordinary Differential Equations · 3 hours

     Reduce a higher-order ODE to a system of first-order ODEs.. Solve a first-order ODE using Picard's method.. Apply the Euler method and Modified Euler method..

8. Week 8Module 1:

   • Review of Units 1 & 2 · 3 hours

     Practice problems on approximations and errors in numerical computations.. Review significant digits and arithmetic precision.. Complete Tutor-Marked Assignment (TMA) 1..

9. Week 9Module 1:

   • Review of Units 3 & 4 · 3 hours

     Practice problems on linear systems of equations.. Review Gaussian elimination and Gauss-Jordan elimination.. Complete Tutor-Marked Assignment (TMA) 2..

10. Week 10Module 1:

    • Review of Units 5 & 6 · 3 hours

      Practice problems on finite differences and interpolation.. Review Newton's forward and backward interpolation formulas.. Complete Tutor-Marked Assignment (TMA) 3..

11. Week 11Module 1:

    • Review of Unit 7 · 3 hours

      Practice problems on initial value problems of ordinary differential equations.. Review Picard's method and Runge-Kutta methods.. Complete Tutor-Marked Assignment (TMA) 4..

12. Week 12Module 1:

    • Final Revision: Numerical Methods · 4 hours

      Consolidate understanding of numerical methods.. Focus on key concepts and techniques.. Prepare for the final examination..

13. Week 13Module 1:

    • Final Revision: C++ Programming · 4 hours

      Consolidate understanding of C++ programming.. Focus on writing programs for solving numerical problems.. Final preparation for the examination..