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# Engineering Mathematics IV pdf guide Pokhara University

Course Objectives:

1. To understand complex variables.
2. To apply concepts of Fourier and Z-transform in signal processing.
3. To study wave and diffusion equations in cartesian, cylindrical, and polar coordinates.
4. To provide basic knowledge of Linear Programming.

Course Contents:

1. Analytical Solid Geometry (4 hrs)

Curves in space, Tangent line, tangent plane, Ellipsoid, hyperboloids, and para boloids, Projection of area.

2. The Fourier Integral (8 hrs)

Review of the Fourier series. Fourier integral and inversion formula, Frequency and phase spectra, Fourier analysis of step and delta function.

3. Complex Variables (8 hrs)

Review the complex number system, Function of a complex variable, Taylor series and Laurent series. Singularities and poles, Complex integration, Residues.

4. Partial Differential Equations (10 hrs)

The diffusion equation in Cartesian coordinates, separation of variables, The wave equation in Cartesian coordinates, separation of variables, the Laplacian in cylindrical coordinates and Bessel's equation, The Laplacian in spherical coordinates and Legend's equation, Engineering applications.

5. The Z-Transform (8 hrs)

Region of convergence, relationship to causality, Properties of Z-transform, Single-sided and double-sided Z-transform and its applications, Convolution and the product of transforms, Inverse of Z-transform, Praseval's theorem, Solution of difference equations.

6. Linear Programming (7 hrs)

The simplex method, objective function and constraint conditions, changing inequalities to equalities, the conical form, of solution, optimal values of variables.