syllabus for Mathematics IV

syllabus for Mathematics IV in an engineering program:

Unit I: Partial Differential Equations (PDE)

  • Formation of PDEs: By elimination of arbitrary constants and functions
  • First-Order PDEs: Linear and non-linear PDEs, Lagrange’s and Charpit’s methods
  • Higher-Order PDEs: Solutions of linear PDEs with constant coefficients, method of separation of variables

Unit II: Applications of PDEs

  • Classification: Second-order PDEs
  • Wave Equation: One-dimensional wave equation, D’Alembert’s solution
  • Heat Equation: One-dimensional heat conduction equation, solution by separation of variables
  • Laplace Equation: Two-dimensional Laplace equation, boundary value problems

Unit III: Probability and Statistics

  • Probability Concepts: Definitions, conditional probability, Bayes’ theorem
  • Random Variables: Discrete and continuous random variables, probability mass function (PMF), probability density function (PDF)
  • Expectation and Variance: Moments, moment generating functions

Unit IV: Probability Distributions

  • Discrete Distributions: Binomial, Poisson distributions
  • Continuous Distributions: Normal, exponential distributions
  • Applications: Fitting distributions to data, hypothesis testing

Unit V: Statistical Methods

  • Descriptive Statistics: Measures of central tendency (mean, median, mode), measures of dispersion (variance, standard deviation)
  • Correlation and Regression: Linear regression, correlation coefficients
  • Statistical Quality Control: Control charts, acceptance sampling

Unit VI: Numerical Methods

  • Solutions of Equations: Bisection method, Newton-Raphson method
  • Interpolation: Lagrange and Newton’s interpolating polynomials
  • Numerical Integration: Trapezoidal and Simpson’s rules
  • Numerical Solutions of ODEs: Euler’s method, Runge-Kutta methods

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