# Engineering Mathematics Hand Written Note

Here, We provided to Engineering Mathematics Hand Written Note. Engineering mathematics is a branch of applied mathematics concerning mathematical methods and techniques that are typically used in engineering and industry. Along with fields like engineering physics and engineering geology, both of which may belong in the wider category engineering science, engineering mathematics is an interdisciplinary subject motivated by engineers’ needs both for practical, theoretical and other considerations outwith their specialization, and to deal with constraints to be effective in their work. Students see the application of the maths they are learning to their engineering degree through the book’s applications-focussed introduction to engineering mathematics, which integrates the two disciplines.

Provides the foundation and advanced mathematical techniques most appropriate to students of electrical, electronic, systems and communications engineering, including algebra, trigonometry, and calculus, as well as set theory, sequences, and series, Boolean algebra, logic and difference equations integral transform methods, including the Laplace, z and Fourier transforms are fully covered. Students learn and test their understanding of mathematical theory and the application to engineering with a huge number of examples and exercises with solutions.

#### BOOK INFO

BOOK NAMEENGINEERING MATHEMATICS HAND WRITTEN NOTE

AUTHOR –

SIZE2MB

PAGES9

### Linear Algebra:

Algebra of matrices; Inverse and rank of a matrix; System of linear equations; Symmetric, skew-symmetric and orthogonal matrices; Determinants; Eigenvalues and eigenvectors; Diagonalisation of matrices; Cayley-Hamilton Theorem.

### Calculus:

Functions of a single variable: Limit, continuity, and differentiability; Mean value theorems; Indeterminate forms and L’Hospital’s rule; Maxima and minima; Taylor’s theorem; Fundamental theorem and mean value-theorems of integral calculus; Evaluation of definite and improper integrals; Applications of definite integrals to evaluate areas and volumes.

Functions of two variables: Limit, continuity, and partial derivatives; Directional derivative; Total derivative; Tangent plane and normal line; Maxima, minima and saddle points; Method of Lagrange multipliers; Double and triple integrals, and their applications.

Sequence and series: Convergence of sequence and series; Tests for convergence; Power series; Taylor’s series; Fourier Series; Half range sine and cosine series.

### Vector Calculus:

Gradient, divergence, and curl; Line and surface integrals; Green’s theorem, Stokes theorem and Gauss divergence theorem (without proofs)

### Complex variables:

Analytic functions; Cauchy-Riemann equations; Line integral, Cauchy’s integral theorem and integral formula (without proof); Taylor’s series and Laurent series; Residue theorem (without proof) and its applications.  ### Ordinary Differential Equations:

First-order equations (linear and nonlinear); Higher order linear differential equations with constant coefficients; Second-order linear differential equations with variable coefficients; Method of variation of parameters; Cauchy-Euler equation; Power series solutions; Legendre polynomials, Bessel functions of the first kind, and their properties.

### Partial Differential Equations:

Classification of second-order linear partial differential equations; Method of separation of variables; Laplace equation; Solutions of one-dimensional heat and wave equations.

### Probability and Statistics:

Axioms of probability; Conditional probability; Bayes’ Theorem; Discrete and continuous random variables: Binomial, Poisson and normal distributions; Correlation and linear regression.

### Numerical Methods:

The solution of systems of linear equations using LU decomposition, Gauss elimination and gauss-Seidel methods; Lagrange and Newton’s interpolations, Solution of polynomial and transcendental equations by Newton-Raphson method; Numerical integration by trapezoidal rule, Simpson’s rule, and Gaussian quadrature rule; Numerical solutions of first-order differential equations by Euler’s method and 4th order Runge-Kutta method.

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