Statistics and Numerical Methods

Statistics and Numerical Methods - Engineering Subject

Statistics and Numerical Methods - MA3251 2nd Semester 2021 Regulation M2 Engineering Mathematics 2 | Anna University Engineering Subject Paper

Unit I: Testing of Hypothesis

1. Testing of Hypothesis

2. Sampling Distributions - Theorem | Testing of Hypothesis | Statistics

3. Large sample test (Normal distribution) for single mean - Solved Example Problems | Testing of Hypothesis | Statistics

4. Large sample test (Normal distribution) for difference of means - Working Procedure, Steps, Solved Example Problems | Testing of Hypothesis | Statistics

5. Large sample test for Single proportion - Solved Example Problems | Testing of Hypothesis | Statistics

6. Large sample test for difference of proportions - Solved Example Problems | Testing of Hypothesis | Statistics

7. Small Sample Tests - Solved Example Problems | Testing of Hypothesis | Statistics

8. Small sample test for difference of means - Solved Example Problems | Testing of Hypothesis | Statistics

9. Test Based on x2- Distribution - Solved Example Problems | Testing of Hypothesis | Statistics

10. x2-test to test the goodness of fit - Solved Example Problems | Testing of Hypothesis | Statistics

11. x2-test to test the independence of attributes - Solved Example Problems | Testing of Hypothesis | Statistics

12. F-distribution [Test for equality of variances] - Solved Example Problems | Testing of Hypothesis | Statistics

13. Two Marks Questions and Answers - Testing of Hypothesis | Statistics

Unit II: Design of Experiments

1. Design of Experiments - Statistics

2. Analysis of Variance - Definition, Assumptions | Design of Experiments | Statistics

3. One Way Classification - Merits, Demerits, Applications, Solved Example Problems | Design of Experiments | Statistics

4. Two - Way Classification - Merits, Demerits, Solved Example Problems | Design of Experiments | Statistics

5. EXERCISE 2.3 [Two-way classification] [RBD] - Solved Example Problems | Design of Experiments | Statistics

6. Latin Square Design - Solved Example Problems | Design of Experiments | Statistics

7. Exercise 2.4 [Latin Square Design] - Solved Example Problems | Design of Experiments | Statistics

8. 22 factorial design - Solved Example Problems | Design of Experiments | Statistics

9. Exercise 2.5 [22 factorial design] - Solved Example Problems | Design of Experiments | Statistics

10. Two Marks Questions with Answers - Design of Experiments | Statistics

Unit III: Solution of Equations and Eigenvalue Problems

1. Solution of Equations and Eigenvalue Problems

2. (a) statement of fixed point theorem lein- fixed point iteration fixed point iteration x = g(x) method. - Solved Example Problems

3. Short Questions and Answers - Fixed point Iteration x = g(x) method

4. Exercise 3.1 (a) [Fixed point Iteration x = g(x) method] - Solved Example Problems | Solution of Equations and Eigenvalue Problems

5. 3.1 (b) newton's method [or Newton-Raphson method] - Solved Example Problems | Solution of Equations and Eigenvalue Problems

6. Short Questions and Answers - Newton's Method

7. Exercise 3.1(b) [Newton's Method] - Solution of Equations and Eigenvalue Problems

8. Solution of linear system of equations by gaussian elimination and gauss-jordon methods - Solved Example Problems

9. Short Questions and Answers - Gaussian Elimination and Gauss-Jordan

10. Exercise 3.2 [Gaussian Elimination and Gauss- Jordan] - Solution of Equations and Eigenvalue Problems

11. Iterative Methods - Types, Solved Example Problems | Solution of Equations and Eigenvalue Problems

12. Short Questions and Answers - Gauss-Jocobi method & Gauss-Seidel method

13. Exercise 3.3 [Gauss-Jocobi method & Gauss-Seidel method] - Solved Example Problems | Solution of Equations and Eigenvalue Problems

14. Eigen values of a Matrix by Power Method - Solved Example Problems | Solution of Equations and Eigenvalue Problems

15. Short Questions and Answers - Eigenvalue of a matrix by power method

16. Exercise 3.4 [Eigenvalue of a matrix by power method] - Solution of Equations and Eigenvalue Problems

17. Eigenvalue of a matrix by jacobi method for symmetric matrix - Solved Example Problems | Solution of Equations and Eigenvalue Problems

18. Exercise 3.5 - Solution of Equations and Eigenvalue Problems

Unit IV: Interpolation, Numerical Differentiation and Numerical Integration

1. Interpolation, numerical differentiation and numerical integration

2. Lagrange's Interpolation - Solved Example Problems

3. Lagrange's Inverse interpolation - Solved Example Problems

4. Short Questions and Answers - Lagrange's Interpolation

5. Exercise 4.1 [Lagrange's Interpolation] - Solved Example Problems

6. Newton's divided difference interpolations - Solved Example Problems

7. Short Questions and Answers - Newton's Divided Differences interpolation

8. Exercise 4.2 [Newton's Divided Differences interpolation] - Solved Example Problems

9. Newton's forward and backward difference interpolation - Solved Example Problems

10. Short Questions and Answers - Newton forward and backward difference

11. Exercise 4.3 - [Newton forward and backward difference W 1- eros MA U.A][010S (MU.A] formula] - Solved Example Problems

12. Approximation of derivatives using interpolation polynomials - Solved Example Problems

13. Short Questions and Answers - Approximation of derivatives using interpolation polynomials

14. Exercise 4.4 [Approximation of derivatives using interpolation polynomials] - Solved Example Problems

15. (a) numerical single integration by Trapezoidal and simpson's 1rd / 3 Rules - Solved Example Problems

16. Short Questions and Answers - Trapezoidal and Simpson's 1/3rd rule

17. Exercise 4.5 (a) [Trapezoidal and Simpson's 1/3rd rule] - Solved Example Problems

18. (b) numerical double integrals by trapezoidal and simpson's 1/3rd Rules - Solved Example Problems

19. Short Questions and Answers - Double integrals using Tapezoidal and Simpson's 1/3rd rules

20. Exercise 4.5 (b) [Double integrals using Tapezoidal and Simpson's 1/3rd rules] - Solved Example Problems

Unit V: Numerical Solution of Ordinary Differential Equations

1. Taylor's series method - Solved Example Problems

2. Taylor's series method for simultaneous first order differential equations - Solved Example Problems

3. Solving higher order linear differential equations - Taylor's Series Method | Solved Example Problems

4. Short Questions and Answers - Taylors Series Method

5. Exercise 5.1 [Taylor's Series Method] - Solved Example Problems

6. Euler and Modified Euler Method - Solved Example Problems

7. Short Questions and Answers - Euler and Modified Euler

8. Exercise 5.2 [Euler and Modified Euler] - Solved Example Problems

9. Fourth order runge-kutta method for solving first order equations - Solved Example Problems

10. R-k method for simultaneous first order differential equation - Solved Example Problems

11. Short Questions and Answers - Fourth order R-K Method

12. Exercise 5.3 [Fourth order R-K Method] - Solved Example Problems

13. Milne's predictor and corrector methods for solving first order equations - Solved Example Problems

14. Short Questions and Answers - Milne's Predictor and Corrector method

15. Exercise 5.4 [Milne's Predictor and Corrector method] - Solved Example Problems

16. Adams-bash forth predictor and corrector methods - Solved Example Problems

17. Short Questions and Answers - Adam's Predictor and Corrector Method

18. Exercise 5.5 [Adam's Predictor and Corrector Method] - Solved Example Problems

19. Standard Normal Distribution Function - Solved Example Problems

20. Values of tɑ (one tail) - Solved Example Problems