Numerical Analysis I

1. Apply Lagrange's and Newton's interpolation techniques to approximate function values.
2. Solve systems of linear algebraic equations using direct and iterative methods.
3. Determine eigenvalues and eigenvectors of matrices.
4. Apply numerical methods to find roots of non-linear equations.
5. Analyze and estimate errors in numerical computations.
6. Apply Taylor's theorem to approximate functions.

13 weeks, about 39 hours in total. Yours will differ.

1. Week 1Module 1: Interpolation

   • Unit 1: Interpolation (Lagrange's Form) · 3 hours

     Read the unit introduction to understand the concept of interpolation.. Study Lagrange's form of interpolation and work through examples.. Practice computing approximate values at non-tabular points.. Solve inverse interpolation problems..

2. Week 2Module 1: Interpolation

   • Unit 2: Newton's Form of the Interpolating Polynomial · 3 hours

     Study Newton's form of the interpolating polynomial.. Learn about divided differences and their tabular representation.. Practice computing interpolating polynomial errors.. Relate divided differences to derivatives of functions..

3. Week 3Module 1: Interpolation

   • Unit 3: Interpolation at Equally Spaced Points · 3 hours

     Study forward, backward, and central differences.. Learn about Newton's Forward-Difference and Backward-Difference formulas.. Practice applying difference formulas to solve interpolation problems.. Establish relationships between different types of differences..

4. Week 4Module 2: Solution of Linear Algebraic Equations

   • Unit 1: Direct Method · 3 hours

     Review preliminaries of linear algebraic equations.. Study Cramer's rule and its applications.. Learn about direct methods for solving linear algebraic equations.. Practice solving problems using Cramer's rule..

5. Week 5Module 2: Solution of Linear Algebraic Equations

   • Unit 2: Inverse of A Square Matrix · 3 hours

     Study the method of adjoints for finding the inverse of a square matrix.. Learn about the Gauss-Jordan reduction method.. Practice solving problems using the Gauss-Jordan method.. Study LU decomposition method..

6. Week 6Module 2: Solution of Linear Algebraic Equations

   • Unit 3: Iterative Methods · 3 hours

     Study the general iterative methods for solving linear equations.. Learn about the Jacobi's iteration method.. Practice solving problems using Jacobi's iteration method.. Study the Gauss-Seidel iteration method..

7. Week 7Module 2: Solution of Linear Algebraic Equations

   • Unit 4: Eigen-Values and Eigen-Vectors · 3 hours

     Study the Eigen value problem.. Learn about the power method for finding Eigen values.. Practice solving problems using power method.. Study the inverse power method..

8. Week 8Module 3: Solution of Non-Linear Equations in one Varibale

   • Unit 1: Review of Calculus · 3 hours

     Review the three fundamental theorems of calculus.. Study Taylor's theorem and its applications.. Learn about round-off and truncation errors.. Practice solving problems related to errors..

9. Week 9Module 3: Solution of Non-Linear Equations in one Varibale

   • Unit 2: Iteration Methods for Locating Root · 3 hours

     Study iteration methods for locating roots.. Learn about tabulation and graphical methods.. Practice solving problems using tabulation and graphical methods.. Study Bisection method and fixed point iteration method..

10. Week 10Module 3: Solution of Non-Linear Equations in one Varibale

    • Unit 3: Chord Methods for Finding Root · 3 hours

      Study chord methods for finding roots.. Learn about Repuler-Falsi method.. Practice solving problems using Repuler-Falsi method.. Study Newton – Raphson method and convergence criterion..

11. Week 11Module 3: Solution of Non-Linear Equations in one Varibale

    • Unit 4: Approximate Root of Polynomial Equation · 3 hours

      Study approximate root of polynomial equation.. Learn about some results on roots of polynomial equation.. Practice solving problems related to roots of polynomial equation.. Study Birge-Vieta method and Graeffe's Root squaring method..

12. Week 12Module 1: Interpolation

    • Unit 3: Interpolation at Equally Spaced Points · 3 hours

      Review Module 1: Interpolation. Solve additional exercises on Interpolation (Lagrange's Form).. Solve additional exercises on Newton's Form of the Interpolating Polynomial.. Solve additional exercises on Interpolation at Equally Spaced Points..

13. Week 13Module 2: Solution of Linear Algebraic Equations

    • Unit 4: Eigen-Values and Eigen-Vectors · 3 hours

      Review Module 2: Solution of Linear Algebraic Equations. Solve additional exercises on Direct Methods.. Solve additional exercises on Inverse of A Square Matrix.. Solve additional exercises on Iterative Methods.. Solve additional exercises on Eigen-Values and Eigen-Vectors..