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NUMERICAL TECHNIQUES &
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2141703
Code: 2141703
Credits: 5
Semester 4
Biomed
Numerical Techniques & Statistical Methods
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GTU Previous Year Papers
Numerical Techniques & Statistical Methods Syllabus — Unit-wise Content
The official GTU curriculum for Numerical Techniques & Statistical Methods (subject code 2141703) as prescribed for Biomed · Semester 4 divides the course into 10 units, covering 57 listed topics. The unit-wise breakdown below is read from the GTU syllabus document for this subject code, so you can check what the course actually covers before deciding which papers to attempt.
Download the official syllabus PDF (2141703)Unit 1 ERROR ANALYSIS
- Round-off errors and truncation errors in numerical computation
- error propagation, and numerical instability
Unit 2 SOLUTION OF EQUATIONS AND EIGENVALUE
- PROBLEMS Linear interpolation (method of false position) – Newton’s method - Statement of fixed point theorem – Fixed point iteration: x=g(x) method – Solution of linear system by Gaussian elimination and Gauss-Jordon method – Iterative methods: Gauss Jacobi and Gauss-Seidel methods – Inverse of matrix by Gauss Jordon method – Eigen value of matrix by power method
Unit 3 INTERPOLATION AND APPROXIMATION
- Lagrangian Polynomials – Divided differences – Interpolating with a cubic spline – Newton’s forward difference formulas
Unit 4 NUMERICAL DIFFERENTION AND INTEGRATION
- Derivatives from difference tables – Divided differences and finite differences – numerical integration by trapezoidal and Simpson’s 1/3 and 3/8 rules – Romberg’s method – Two and Three point Gaussian quadrature formulas – Double integrals using trapezoidal and Simpson’s rules
Unit 5 INITIAL VALUE PROBLEMS FOR ORDINARY
- DIFFERINTIAL EQUATIONS Single step methods: Taylor series method – Euler and modified Euler methods – Fourth order Runge-Kutta method for solving first and second order equations – Multistep methods: Milne’s and Adam’s predictor and corrector methods
Unit 6 INTRODUCTION TO STATISCTICAL PARAMETERS
- Significant figures
- scientific notations
- average- Mean
- geometric mean
- harmonic mean
- root- mean-square and root-sum-squares average
- Logarithmic representation of signal levels
- Data classes
- Variation – Gaussian curve
- standard deviation
Unit 7 PROBABILITY AND PROBABILITY DISTRIBUTIONS
- Introduction to probability
- Random Experiments
- Sample Space
- Events and their probabilities
- Some basic results of probability
- Conditional probability
- Random variables: Probability distributions
- Expected value & variance of a probability distribution
- Discrete probability distributions: Binomial
- Continuous probability distributions: Exponential
Unit 8 SAMPLING, SAMPLING DISTRIBUTION &
- INTERVAL ESTIMATION Simple random sampling
- point estimation
- introduction to sampling distributions
- sampling distributions of, Sampling distribution of sample proportion
- Properties of point estimation
- Other sampling methods
- Interval estimation: Population mean: σ known
- Determining the sample size
- Sampling distribution of variance
Unit 9 STATISTICAL INFERENCES, TESTING OF
- -TEST Introduction
- Test of significance for large samples: Difference between small & large samples
- Two-tailed test for difference between the means of two samples
- Standard error of the difference between two standard deviations
- Test of significance for small samples: The assumption of normality
- properties and application of t-distribution
- testing difference between means of two samples (Independent samples
- Dependent samples) Definition of chi-square
- degrees of freedom
- chi- square distribution
- Conditions for applying chi-square test
- Uses of chi-square test
- Misuse of chi-square test
Unit 10 NETWORK ANALYSIS
- Network definition
- Minimal spanning tree problem
- Shortest route problem
- Maximum flow problem concepts and solution algorithm as applied to problems
- Project planning and control by CPM network
- Probability assessment in PERT network
- PROJECT MANAGEMENT AND SCHEDULING Project management (CPM & PERT) Network concepts
- rules for network construction
- critical path method (CPM) and Project evaluation and review Techniques (PERT)
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