Hello Students,
Mathematics-4 is a second-year subject for B.Tech students in AKTU that focuses on advanced mathematical concepts such as complex analysis, partial differential equations, and transforms. This subject builds on the foundation laid in the previous mathematics courses and aims to equip students with the knowledge and skills needed to solve more complex mathematical problems that arise in engineering and other technical fields. The course covers topics such as conformal mapping, analytic functions, Laplace transforms, Fourier transforms, and their applications. Mathematics-4 provides a strong mathematical background for students pursuing careers in fields such as electrical engineering, mechanical engineering, civil engineering, and computer science.
I am sharing Mathematics-4 question bank with answers and solutions in Q&A format for engineering/BTech second year. This is available as a PDF file for free download below.
List of topics covered in Mathematics-4 question bank with solutions (Q&A) for engineering/BTech second year:
Unit 1: Complex Analysis
Unit 3: Numerical Methods
Mathematics-4 is a second-year subject for B.Tech students in AKTU that focuses on advanced mathematical concepts such as complex analysis, partial differential equations, and transforms. This subject builds on the foundation laid in the previous mathematics courses and aims to equip students with the knowledge and skills needed to solve more complex mathematical problems that arise in engineering and other technical fields. The course covers topics such as conformal mapping, analytic functions, Laplace transforms, Fourier transforms, and their applications. Mathematics-4 provides a strong mathematical background for students pursuing careers in fields such as electrical engineering, mechanical engineering, civil engineering, and computer science.
I am sharing Mathematics-4 question bank with answers and solutions in Q&A format for engineering/BTech second year. This is available as a PDF file for free download below.
List of topics covered in Mathematics-4 question bank with solutions (Q&A) for engineering/BTech second year:
Unit 1: Complex Analysis
- Complex numbers and their algebra
- Analytic functions and Cauchy-Riemann equations
- Elementary functions such as exponential, trigonometric, and logarithmic functions
- Complex integration and Cauchy's integral theorem and formula
- Singularities and Laurent series
- Residues and poles
- Applications to evaluation of real integrals
- Probability: Sample space, events, probability measures, conditional probability, Bayes’ theorem, independent events, random variables, distribution functions, probability density functions, probability mass functions, expectation, variance, covariance, correlation coefficient, moments, and moment generating functions
- Statistical Inference: Sampling distributions, estimation, testing of hypotheses, confidence intervals, and chi-square tests
Unit 3: Numerical Methods
- Interpolation: Finite differences, Newton's divided differences, Lagrange’s interpolation formula, and inverse interpolation
- Numerical Differentiation and Integration: Numerical differentiation using forward, backward and central differences, numerical integration using Trapezoidal rule, Simpson's 1/3 and 3/8 rules, and Gaussian quadrature formula
- Solution of Equations: Bisection method, Regula-Falsi method, Newton-Raphson method, and Secant method
- Laplace Transform: Definition and properties, inverse Laplace transforms, transforms of derivatives and integrals, convolution theorem, and application to solve ordinary differential equations
- Fourier Series: Periodic functions, Fourier series, half-range expansions, complex form of Fourier series, and applications
- Fourier Transform: Fourier integral theorem and Fourier transforms, properties of Fourier transforms, convolution theorem, and applications
- Linear Programming: Formulation of linear programming problems, simplex method, duality theory, and sensitivity analysis
- Non-linear Programming: Unconstrained optimization, Newton's method, and conjugate gradient method, Constrained optimization, Kuhn-Tucker conditions, and Lagrange multipliers.