Probability and complex function

Probability and complex function - Engineering Subject

Probability and complex function - MA3303 3rd Semester EEE Dept | 2021 Regulation | Anna University Engineering Subject Paper

Unit I: Probability and random variables

1. Probability and random variables - Introduction

2. Some important terms of probability

3. Axioms of probability - Theorem, Proof, Solved Example Problems

4. Exercises 1.1 (Axioms of probability) - Problems with Answer

5. Conditional Probability - Theorem, Proof, Solved Example Problems

6. Baye's Theorem - Solved Example Problems | Probability

7. Exercise 1.2 and Exercise 1.3 (Conditional Probability, Baye's Theorem) - Problems with Answer

8. Random Variable - Types

9. (i) Discrete random variable

10. Discrete random variable: Formula, Solved Example Problems

11. (ii) Continuous random variables - Formula, Solved Example Problems

12. Exercises 1.4 and 1.5 (Discrete and Continuous random variable) - Problems with Answer

13. Moments - moment generating functions and their properties - Formula, Solved Example Problems | Random variables

14. Exercises 1.6 (Moments - moment generating functions) - Problems with Answer | Random variables

15. Binomial distribution - Random variables

16. Binomial distribution: Examples Solved Problems - Random variables

17. Exercise 1.7 (Binomial distribution) - Problems with Answer | Random variables

18. Poisson distribution - Random variables

19. Poisson distribution: Solved Example Problems - Random variables

20. Exercise 1.8 (Poisson distribution) - Problems with Answer | Random variables

21. Geometric Distribution - Formula, Solved Example Problems | Random variables

22. Exercise 1.9 (Geometric Distribution) - Problems with Answer | Random variables

23. Uniform distribution (or) Rectangular Distribution - Random variables

24. Uniform distribution (or) Rectangular Distribution: Example Solved Problems - Random variables

25. Exercise 1.10 (Uniform distribution or Rectangular Distribution) - Problems with Answer | Random variables

26. Exponential distribution - Formula, Solved Example Problems | Random variables

27. Exercise 1.11 (Exponential distribution) - Problems with Answer | Random variables

28. Normal distributions - Random variables

29. Normal distributions: Solved Example Problems - Random variables

30. Exercise 1.12 (Normal distributions) - Problems with Answer | Random variables

31. 2 Marks Questions and Answers - Probability and random variables | Probability and complex function

32. Part B Questions and Answer - Probability and random variables | Probability and complex function

Unit II: Two dimensional random variables

1. Discrete and Continuous Random Variable - Two dimensional random variables

2. Two dimensional random variables - Introduction

3. Joint distributions - marginal and conditional distributions - Two dimensional random variables

4. Problems under discrete random variables - Two dimensional random variables

5. Problems under continuous random variables - Two dimensional random variables

6. Exercise 2.1 (Discrete and Continuous Random Variable) - Two dimensional random variables

7. Covariance, correlation and regression - Two dimensional random variables

8. Covariance, correlation and regression: Example Solved Problems - Two dimensional random variables

9. Exercise 2.2 (Covariance, correlation and regression) - Problems with Answer | Two dimensional random variables

10. Regression - Two dimensional random variables

11. Regression: Example Solved Problems - Two dimensional random variables

12. Exercise 2.3 (Regression) - Problems with Answer | Two dimensional random variables

13. Transformation of random variables - Solved Example Problems | Two dimensional random variables

14. Exercise 2.4 (Transformation of random variables) - Problems with Answer | Two dimensional random variables

15. Central limit theorem - Two dimensional random variables

16. Central limit theorem: Example Solved Problems - Two dimensional random variables

17. Exercise 2.5 (Central limit theorem) - Problems with Answer | Two dimensional random variables

18. 2 Marks Questions and Answers - Two dimensional random variables | Probability and complex function

Unit III: Analytic functions

1. Analytic functions

2. Analytic functions - necessary and sufficient conditions for analyticity in cartesian and polar co-ordinates

3. Problems based on analytic function necessary conditions – cauchy - riemann equations - Solved Example Problems

4. Exercise 3.1 (Analytic function necessary conditions - Cauchy - Riemann equations) - Problems with Answer

5. Properties harmonic conjugates - Analytic functions

6. Example Solved Problems based on Properties harmonic conjugates - Analytic functions

7. Example Solved Problems based on harmonic conjugate - Analytic functions

8. Construction of analytic function

9. Problems based on construction of analytic functions

10. Exercise 3.3 (Construction of Analytic functions) - Problems with Answer

11. Conformal mappings, w = z+k, w = kz, - Solved Example Problems | Analytic functions

12. Some standard transformation - Solved Example Problems | Analytic functions

13. Exercise 3.4 (Conformal mappings, Transformation) - Problems with Answer | Analytic functions

14. Bilinear transformation - Theorem, Proof, Definition | Analytic functions

15. Problems based on fixed points or invariant points - Analytic functions

16. Problems based on bilinear transformation - Analytic functions

17. Exercise 3.5 (Bilinear transformation) - Problems with Answer | Analytic functions

Unit IV: Complex integration

1. Complex integration - Line integral, Cauchy's integral theorem

2. Contour Integral - Statement, Proof | Complex integration

3. Problems based on cauchy's integral theorem

4. Problems based on cauchy's integral formula - Complex integration

5. Exercise 4.1 (Cauchy's integral theorem) - Formula, Problems with Answer | Complex integration

6. Taylor's and laurent's series - Some important Results | Complex integration

7. Problems based on Taylor's and laurent's series - Solved Example Problems

8. Exercise : 4.2 (Taylor's and laurent's series) - Problems with Answer | Complex integration

9. Singularities - residues residue theorem - Complex integration

10. Problems based on singularities and residues - Solved Example Problems | Complex integration

11. Singular points (or) Singularity of f(z) - Complex integration

12. Singularities - residues residue theorem: Solved Example Problems - Complex integration

13. Cauchy's residue theorem - Statement, Proof, Formula, Solved Example Problems

14. Example Problems Based on Cauchy's Residue Theorem

15. Exercise 4.3 (Singularities residues residue theorem) - Problems with Answer | Complex integration

16. Application of residue theorem for evaluation of real integrals as use of circular and semi-circular contour

17. Problems based on contour integration - Example Solved Problems

18. Problems based on contour integration (Method 2) - Solved Example Problems

19. Exercise 4.4 (Contour Integration) - Problems with Answer

Unit V: Ordinary Differential Equations

1. Ordinary Differential Equations - Introduction

2. Higher order linear differential equations with constant coefficients

3. (a) Problems based on r.h.s. of the given differential equation is zero - Solved Example Problems | Ordinary Differential Equations

4. (b) Problems based on P.I.= 1/f(D) eax ⇒ Replace D by a - Solved Example Problems | Ordinary Differential Equations

5. (c) Problems based on P.I = 1 / f(D) sin ax or 1 / f(D) cos ax ⇒ Replace D2 by -a2 - Solved Example Problems | Ordinary Differential Equations

6. (d) problems based on R.H.S = eax + sin ax(or) eax + cos ax - Solved Example Problems | Ordinary Differential Equations

7. (e) problems based on R.H.S = xn - Solved Example Problems | Ordinary Differential Equations

8. (f) Problems based on R.H.S. = eax X - Solved Example Problems | Ordinary Differential Equations

9. (g) problems based on f(x) = x V type - Solved Example Problems | Ordinary Differential Equations

10. (h) problems based on eax integral e-ax - Solved Example Problems | Ordinary Differential Equations

11. (i) General ode problems - Solved Example Problems | Ordinary Differential Equations

12. (i) Problems based on R.H.S = eax + xn + cos ax - Solved Example Problems | Ordinary Differential Equations

13. Exercise 5.1 (Ordinary Differential Equations) - Problems with Answer

14. Method of variation of parameters - Ordinary Differential Equations

15. Problems based on method of variation of parameters - Solved Example Problems | Ordinary Differential Equations

16. Exercise 5.2 (method of variation of parameters) - Problems with Answer | Ordinary Differential Equations

17. Homogeneous equation of euler's and legendre's type - Ordinary Differential Equations

18. (a) Problems based on cauchy-euler - Solved Example Problems | Ordinary Differential Equations

19. (b) problems based on legendre's linear differential equation - Solved Example Problems | Ordinary Differential Equations

20. Exercise 5.3. (a) cauchy-euler - Problems with Answer | Ordinary Differential Equations

21. Exercise 5.3. (b) Legendre's linear differential equation - Problems with Answer | Ordinary Differential Equations

22. System of simultaneous linear differential equations with constant co-efficients

23. Problems based on system of simultaneous linear differential equations with constant co-efficients - Solved Example Problems

24. Exercise 5.4 (System of simultaneous linear differential equations with constant co-efficients) - Problems with Answer | Ordinary Differential Equations

25. Method of undetermined coefficients - Ordinary Differential Equations

26. Problems based on, to find the particular integral by the method of undetermined coefficients - Solved Example Problems | Ordinary Differential Equations

27. Exercise 5.5 (Method of undetermined coefficients) - Problems with Answer | Ordinary Differential Equations