Savitribai Phule Pune University, Maharashtra, Information Technology Semester 4, Engineering Mathematics- III Syllabus

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Unit - 1 Linear Differential Equations
Unit1
Linear differential equations
1.1 LDE of nth order with constant coefficient
1.2 The general method and Short methods
1.3 Methods of variation of parameters
1.4 Cauchy’s and Legendre’s Different1ial Equation
1.5 Simultaneous and symmetric simultaneous differential equations
Unit - 2 Transforms
Unit2
Transforms
2.1 Complex Exponential form of Fourier series
2.2 Fourier integral theorem
2.3 Fourier sine and cosine integrals
2.4 Fourier transform
2.5 Fourier sine and cosine transforms and their inverses
2.6 Discrete Fourier transform
2.7 Z transform Introduction Definition standard properties
2.8 ZT of standard sequences and their inverses
2.9 Solution of difference equations
Unit - 3 Statistics
Unit3
Statistics
3.1 Measure of central tendency
3.2 Measures of dispersion and Standard Deviation
3.3 Coefficient of variation
3.4 Moments Skewness and Kurtosis
3.5 Curve fitting of a straight line
3.6 Fitting Parabola and related curves
3.7 Correlation and regression
3.8 Reliability of regression estimates
Unit - 4 Probability and Probability Distributions
Unit4
Probability and Probability Distribution
4.1 Theorems on Probability
4.2 Bayes theorem
4.3 Random variables
4.4 Mathematical expectation
4.5 Probability density function
4.6 Probability distributions Binomial Poisson and Normal distributions hypergeometric distribution
4.7 Test of Hypothesis ChiSquare test tdistribution.
4.8 ChiSquare test
4.9 tdistribution Test
Unit - 5 Numerical Methods
Unit5
Numerical Methods
5.1 Bisection
5.2 Secant
5.3 RegulaFalsi
5.4 Newton Raphson and successive approximation method convergence and stability
5.5 Numerical Solutions of System of linear equations Gauss elimination method
5.6 LU Decomposition Cholesky
5.7 Jacobi and GaussSiedel methods
Unit - 6 Numerical Methods
Unit6
Numerical Methods
6.1 Interpolation Finite differences
6.2 Newton’s and Lagrange interpolation formulae
6.3 Numerical differentiation
6.4 Numerical integration Trapezoidal and Simpson’s Rules Bound of truncation error
6.5 Solution of ordinary differential equations Euler’s method
6.6 Modified Euler’s method
6.7 RungeKutta 4th order method Predicator and corrector
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Other Subjects of Semester-2
Computer graphics
Software engineering
Processor architecture
Database management system
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