Savitribai Phule Pune University, Maharashtra (SPPU), Computer Engineering Semester 4, Mathematics III Syllabus

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Unit - 1 Linear Differential Equations (LDE)

1.1 LDE of nth order with constant coefficient Complementary functions Particular integral

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

2.1 Complex Exponential form of Fourier series

2.2 Fourier integral theorem

2.3 Fourier sine and cosine integrals and their inverses

2.4 Discrete Fourier transform

2.5 Z transform Introduction Definition standard properties

2.6 ZT of standard sequences and their inverses

2.7 Solution of difference equations

Unit - 3 Statistics

3.1 Measure of central tendency

3.2 Measures of dispersion

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

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 Sampling distributions

4.8 Test of Hypothesis ChiSquare test

4.9 tTest

Unit - 5 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

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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