__Advanced Engineering Mathematics Textbook Free Download__

__Main Contents: __

**Differential equations****Non-homogeneous linear differential equations of second and higher order****Curve tracing – Cartesian - Polar and Parametric curves.****Applications of Integration to Lengths, Volumes and Surface areas of revolution in Cartesian and Polar Coordinates.****Multiple integrals - double and triple integrals – change of variables – Change of order of Integration****Vector Differentiation: Gradient- Divergence- Curl and their related properties of sums-products- Laplacian and second order operators.****Inverse Laplace transforms– Convolution theorem - Application of Laplace transforms to ordinary differential equations Partial fractions.****Laplace transforms of standard functions –Shifting Theorems, Transforms of derivatives and integrals – Unit step function –Dirac’s delta function.****Fourier Series: Determination of Fourier coefficients – Fourier series – even and odd functions – Fourier series in an arbitrary interval– Half-range sine and cosine series.****Method of Separation of Variables - Applications to wave equation, heat equation and Laplace Equation.****Z-transform – properties – Damping rule – Shifting rule – Initial and final value theorems -Inverse z-transform -Convolution theorem – Solution of difference equation by z-transforms.****Gamma and Beta Functions – Properties – Evaluation of improper integrals.****Eigen values - Eigen vectors – Properties – Cayley-Hamilton Theorem - Inverse and powers of a matrix by using Cayley-Hamilton theorem.****Numerical Differentiation and Integration****Curve fitting: Fitting a straight line –Second degree curve-exponential curve-power curve by method of least squares.**

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