AKTU Mathematics-III (BAS302 / BAS402) Syllabus PDF – B.Tech 2nd Year

Course Outcomes

The objective of this course is to familiarize the students with partial differential equation, their application, statistical and numerical techniques. It aims to present the students with standard concepts and tools at an intermediate to superior level that will provide them well towards undertaking a variety of problems in the discipline.

• The idea of partial differentiation, its types and their solution.
• The concept of Fourier transform and method of separation of variables to solve partial differential equations.
• To apply the basic ideas of statistics including measures of central tendency, correlation, regression and their properties.
• To apply numerical techniques in solving algebraic equations and data interpolation.
• To apply numerical techniques in solving linear equations, numerical differentiation and numerical integration.

Module I: Partial Differential Equations 8

Origin of Partial Differential Equations, Linear and Non-Linear Partial Differential Equations of first order, Lagrange’s Equations method to solve Linear Partial Differential Equations, Charpit’s method to solve Non-Linear Partial Differential Equations, Solution of Linear Partial Differential Equation of Higher order with constant coefficients, Equations reducible to linear partial differential equations with constant coefficients.

Module II: Applications of Partial Differential Equations and Fourier Transform 8

Method of separation of variables, Solution of one dimensional heat equation, wave equation, Two dimensional heat equation (only Laplace Equation)and their application, Complex Fourier transform, Fourier sine transform, Fourier cosine transform, Inverse transform, convolution theorem, Application of Fourier Transform to solve partial differential equation.

Module III: Statistical Techniques 8

Moments, Skewness, Kurtosis, Curve fitting, Method of least squares, Fitting of straight lines, Polynomials, Exponential curves, Correlation and regression, Binomial, Poisson and Normal distributions, Tests of significations: Sampling theory (small & large), Null hypothesis, Alternative hypothesis, testing of hypothesis: Chi-square test, t-test, z-test.

Module IV: Numerical Techniques–I 8

Zeroes of transcendental and polynomial equations using Bisection method, Regula-falsi method and Newton-Raphson method, Rate of convergence of above methods. Interpolation:

Finite differences, Newton’s forward and backward interpolation, Lagrange’s and Newton’s divided difference formula for unequal intervals.

Module V: Numerical Techniques–II: 8

Solution of system of linear equations, Matrix Decomposition method, Jacobi method, Gauss- Seidel method. Numerical differentiation, Numerical integration, Trapezoidal rule, Simpson’s one third and three-eight rules, Solution of ordinary differential equations by Picard’s and fourth-order Runge-Kutta methods.

Text Books

1. Dr. B.S. Grewal, “Higher Engineering Mathematics”, 44 th Edition, Khanna Publishers, New Dehli.

Reference Books

1. Peter V. O’Neil, “Advance Engineering Mathematics”, SI Edition 8 th Edition, Cengage Learning, 2017.
2. B. V. Ramana, Higher Engineering Mathematics, McGraw-Hill Publishing Company Ltd., 2017.
3. S. S. Sastry, “Introductory methods of Numerical solutions”, 4th Edition , Prentice Hall of India.
4. Erwin Kreyszig , “Advanced Engineering Mathematics”, John Wiley Publications, 1999.
5. R.K.Jain & S.R.K.Iyengar, “Numerical Methods” , New Age International ( P ) Limited
6. James F. Epperson Mathematical Reviews “An Introduction To Numerical Methods And Analysis” Second Edition, Wiley;