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Savitribai Phule Pune University, Maharashtra (SPPU), Mechanical Engineering Semester 5, Numerical & Statistical Methods Syllabus
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Unit - 1 Roots of Equation and Simultaneous Equations
Unit 1
Roots of Equation and Simultaneous Equations
1.1 Roots of Equation Bracketing method
1.2 NewtonRaphson method
1.3 Solution of simultaneous equations Gauss Elimination Method with Partial pivoting
1.4 GaussSeidel method
1.5 Thomas algorithm for Tridiagonal Matrix
Unit - 2 Numerical Solution of Differential Equations
Unit 2
Numerical Solution of Differential Equation
2.1 Ordinary Differential Equation Taylor’s Series method
2.2 Euler’s Method
2.3 Runge Kutta Method fourth order
2.4 Simultaneous equation using Runge Kutta 2nd order method
2.5 Partial Differential Equation The finite Difference Method
2.6 Simple Laplace’s Method
2.7 Elliptic explicit solution
2.8 PDEs parabolic explicit solution
Unit - 3 Numerical Integration
Unit 3
Numerical Integration
3.1 Numerical Integration 1D Trapezoidal rule
3.2 Simpson’s 13rd Rule
3.3 Simpson’s 38 rule
3.4 Gauss Quadrature 2point and 3point method
3.5 Double Integration Trapezoidal rule
3.6 Simpson’s 13rd rule
Unit - 4 Curve Fitting And Regression Analysis
Unit 4
Curve Fitting and Regression Analysis
4.1 Curve Fitting Least square technique first order Power exponential and quadratic equation
4.2 Regression Analysis Linear regression
4.3 Nonlinear regression multiple regressions
4.4 Polynomial regression
4.5 Lagrange’s Interpolation
4.6 Numerical interpolation and differentiation using Newton’s forward method
4.7 Inverse Interpolation Lagrange’s Method only
Unit - 5 Statistics
Unit 5
Statistics
5.1 Measures of central tendency mean
5.2 Median
5.3 Mode
5.4 Measurement of variability and dispersion Standard deviation and variance
5.5 Standard error
5.6 Range
5.7 Measure of shape skewness kurtosis
5.8 Statistical diagram scattered diagram histogram pie charts
5.9 Measure of association between two variables
5.10 Correlation Karl Pearson’s Coefficient of correlation and its mathematical properties
5.11 Spearman’s Rank correlation and its interpretations
Unit - 6 Probability And Linear Algebra
Unit 6
Probability and Linear Algebra
6.1 Probability Joint
6.2 Conditional probability
6.3 Marginal probability
6.4 Bayes’ theorem
6.5 Independence
6.6 Theorem of total probability
6.7 Expectation and variance
6.8 Random variables
6.9 Probability distributions Binomial Poisson Geometric Uniform Exponential Gamma Normal and Chi square
6.10 Linear algebra Review of matrix operations
6.11 Vector and vector spaces
6.12 Linear mapping
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