Higher Engineering Mathematics 40th Edition notes

EMPIRICAL AND CURVE FITTING.

The unit covers following points - Types of correlation: positive, negative, and zero correlations indicate relationships between variables. - Regression and linear regression analyze the relationship between dependent and independent variables. - Random variables represent outcomes of random events, with specific probability distributions. - The normal distribution is characterized by its bell-shaped curve and mean-variance properties. - The Poisson distribution models the number of event...

Calculus,diffrential equation,linear algebra,probability complex analysis,vector calculus,numerical methods,laplace transform.

The unit covers following points - Introduction to linear differential equations and their significance in mathematics and engineering - Explanation of basic concepts such as order, linearity, and homogeneity - Overview of methods for solving first-order linear differential equations, including separation of variables and integrating factors - Discussion on solving higher-order linear differential equations using techniques like the method of undetermined coefficients and variation of param...

The unit covers following points - Introduction to vectors and their significance in mathematics and physics - Explanation of linear integral, involving the integration of vector fields along curves or paths - Discussion on surface integrals, focusing on the integration of vector fields over surfaces - Overview of volume integrals, used to calculate properties within three-dimensional regions - Introduction to Stokes' theorem, relating line integrals of vector fields to surface integrals ...

The unit covers following points - Introduction to linear differential equations and their importance in various fields of mathematics and physics - Explanation of Cauchy's equations, fundamental in understanding the behavior of linear differential equations - Overview of legendary equations and their significance in solving specific types of linear differential equations - Application of linear differential equations to practical problems in engineering, physics, and other disciplines - I...

The unit covers following points - Introduction to vectors and their role in mathematics and physics - Explanation of curl as a measure of rotational behavior in vector fields - Discussion on directional derivatives, indicating how a function changes along a given direction - Overview of gradients, representing the rate of change of a scalar function in space - Application of vectors in solving numerical problems involving normal surfaces and vector fields - Illustrative examples and exer...

The unit covers following points - Introduction to numerical methods for solving ordinary differential equations (ODEs) using vectors - Explanation of Picard's method, an iterative approach for approximating solutions to initial value problems - Overview of Taylor's series expansion method, which provides a systematic way to approximate solutions near a given point - Introduction to Runge-Kutta methods, including Runga's method and the popular fourth-order Runge-Kutta method, for solving...