AKTU Mathematics-IV (BAS303 / BAS403) Syllabus PDF – B.Tech 2nd Year

Course Outcomes

The objective of this course is to familiarize the students with partial differential equation, their application and statistical 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 differential equation and its different types of solution.
• The concept ofmethod of separation of variables and Fourier transform to solve partial differential equations.
• The basic ideas of statistics including measures of central tendency, correlation, regression and their properties.
• The idea of probability, random variables, discrete and continuous probability distributions and their properties.
• The statistical methods of studying data samples, hypothesis testing and statistical quality control.

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 Transformto solve partial differential equation.

Module III: Statistical Techniques I 8

Overview of Measures of central tendency, Moments, Skewness, Kurtosis, Curve Fitting, Method of least squares, Fitting of straight lines, Fitting of second degree parabola, Exponential curves,Correlation and Rank correlation, Regression Analysis: Regression lines of y on x and x on y.

Module IV: Statistical Techniques II 8

Overview of Probability Random variables (Discrete and Continuous Random variable) Probability mass function and Probability density function, Expectation and variance, Discrete and Continuous Probability distribution: Binomial, Poission and Normal distributions.

Module V: Statistical Techniques III 8

Introduction of Sampling Theory, Hypothesis, Null hypothesis, Alternative hypothesis, Testing a Hypothesis, Level of significance, Confidence limits, Test of significance of difference of means, t-test, Z-test and Chi-square test, Statistical Quality Control (SQC) , Control Charts, Control Charts for variables ( X and R Charts), Control Charts for Variables (p, np and C charts).

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; https://perhuaman.files.wordpress.com/2014/07/metodos-numericos.pdf