[PDF] 3130908, Applied Mathematics for Electrical Engineering(AMEE)

 

   

3130908, Applied Mathematics for Electrical Engineering EBooks (AMEE) free pdf file & books related Applied Mathematics for Electrical Engineering syllabus are available. You can also download free AMEE books PDF file and it's syllabus are also upload in this  site

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Syllabus:-

Sr. No.	Content	Total Hrs	% Weightage
1	Numerical Solutions: Roots of Algebraic and Transcendental Equations : Bisection, false position, Secant and Newton-Raphson methods, Fixed Point Iteration, Rate of convergence,Applications to electrical engineering problems.	06	14 %
2	Interpolation: Finite Differences, Forward, Backward and Central operators, Interpolation by polynomials: Newton’s forward ,Backward interpolation formulae, Newton’s divided formulae and Lagrange’s interpolation formulae for unequal intervals, Applications to electrical engineering problems.	06	14 %
3	Numerical Integration: Newton-Cotes formula, Trapezoidal and Simpson’s formulae, error formulae, Gaussian quadrature formulae, Applications to electrical engineering problems	04	10%
4	Numerical solution of Ordinary Differential Equations: Picard, Taylor, Euler methods and Runge-Kutta methods, Applications to electrical engineering problems	04	10%
5	Curve fitting by the numerical method: Curve fitting by of method of least squares, fitting of straight lines, second degree parabola and more general curves.	04	10%
6	Basic Probability: Experiment, definition of probability,conditional probability, independent events, Bayes' rule, Bernoulli trials, Random variables, discrete random variable, probability mass function, continuous random variable, probability density function, cumulative distribution function, properties of cumulative distribution function, Applications to electrical engineering problems.	10	22 %
7	Basic Statistics: Measure of central tendency: Moments, Expectation, dispersion, skewness, kurtosis, Bounds on probability, Chebyshev‘s Inequality, Applications to electrical engineering problems.	08	20%

Suggested Specification table with Marks (Theory): 

Distribution of Theory Marks

R Level	U Level	A Level	N Level	E Level	C Level
15	35	35	0	0	0

Legends: R: Remembrance; U: Understanding; A: Application, N: Analyze and E: Evaluate C: Create and above Levels (Revised Bloom’s Taxonomy)

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 I N D E X

UNIT-1 » ROOTS OF NON-LINEAR EQUATION.................................................. 1

     

       1).            METHOD – 1: BISECTION METHOD (BOLZANO METHOD) ...................................................... 2

        2).             METHOD – 2: REGULA-FALSI METHOD ............................................................................................ 3

        3).             METHOD – 3: SECANT METHOD .......................................................................................................... 5

       4).             METHOD – 3: NEWTON-RAPHSON METHOD ................................................................................. 9

       5).             METHOD – 4: ITERATION METHOD ................................................................................................. 11

UNIT-2 » INTERPOLATION ............................................................................. 13

    6).            METHOD – 1: NEWTON’S FORWARD DIFFERENCE FORMULA ............................................ 16

    7).            METHOD – 2: NEWTON’S BACKWARD DIFFERENCE FORMULA ......................................... 18

    8).            METHOD – 3: NEWTON’S DIVIDED DIFFERENCE FORMULA ................................................ 22

      9).            METHOD – 4: LAGRANGE’S INTERPOLATION FORMULA ....................................................... 24

UNIT-3 » NUMERICAL INTEGRATION ............................................................. 27

      10).             METHOD – 1: TRAPEZOIDAL RULE .................................................................................................. 27

      11).             METHOD – 2: SIMPSON’S 1/3 RULE ................................................................................................. 29

      12).             METHOD – 3: SIMPSON’S 3/8 RULE ................................................................................................. 32

  13).            METHOD – 4: GAUSSIAN QUADRATURE (GAUSSIAN INTEGRATION) ............................... 35

UNIT- 4 » NUMERICAL METHODS FOR O.D.E. .............................................. 37

      14).             METHOD – 1: PICARD METHOD ........................................................................................................ 37

     15).             METHOD – 2: TAYLOR’S SERIES METHOD .................................................................................... 38

     16).             METHOD – 3: EULER’S METHOD ....................................................................................................... 39

    17).             METHOD – 4: IMPROVED EULER’S METHOD ............................................................................... 41

   18).             METHOD – 5: RK 4^TH ORDER METHOD ........................................................................................... 42

UNIT-5 » CURVE FITTING .............................................................................. 45

        19).             METHOD – 1: FITTING A STRAIGHT LINE 𝐲 = 𝐚 + 𝐛 𝐱............................................................. 47

        20).              METHOD – 2: FITTING A PARABOLA 𝐲 = 𝐚 + 𝐛𝐱 + 𝐜𝐱𝟐 ....................................................... 49                           

        21).            METHOD – 3: NON-LINEAR REGRESSION ..................................................................................... 51

UNIT 6 – BASIC PROBABILITY ....................................................................... 53

                 

22). METHOD – 1: BASIC EXAMPLES ON PROBABILITY ................................................................... 55

23). METHOD – 2: PROBABILITY OF EVENT ......................................................................................... 59

24). METHOD – 3: CONDITIONAL PROBABILITY ................................................................................ 62

25). METHOD-6: EXAMPLES ON TWO-DIMENSIONAL RANDOM VARIABLE ........................... 67

26). METHOD – 4: TOTAL PROBABILITY AND BAYE’S THEOREM ............................................... 72

27). METHOD – 5: PROBABILITY FUNCTION, EXPECTATION, VARIANCE ................................ 76

28). METHOD – 6: BINOMIAL DISTRIBUTION ...................................................................................... 81

29). METHOD – 7: CHEBYSHEV’S INEQUALITY .................................................................................... 84

 

UNIT-7 » BASIC STATISTICS .......................................................................... 85

30). METHOD – 1: EXAMPLES ON CENTRAL TENDENCY, DISPERSION AND SKEWNESS .. 91

31). METHOD – 2: EXAMPLES ON MOMEMNT (SKEWNESS AND KURTOSIS) ......................... 99

 

 

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