This course provides the basic definition of Laplace transform and their theorems: First shift theorem, transform of differentiation and integration, unit step function, second shift theorem and convolution theorem. Inverse of Laplace transform. Fourier analysis: Definition of Fourier series, Fourier series of functions of period 2P, Fourier series for even and odd functions, half-Range expansions and Fourier series for harmonic functions. Then the student should also study Fourier integrals, Fourier cosine and sine transforms and Fourier transform. Also, this course provides an introduction to linear programming, including its basic concepts, unconstrained optimization, and solving system of linear inequalities using the simplex method. Vector spaces are studied in an abstract setting, examining the concepts of linear independence, span, bases, subspaces, and dimension. There follows a discussion of the association between linear transformations and matrices.
Software Engineering bachelor`s degree Program
Erwin Kreyszig, Advanced Engineering Mathematics, John Wiley and Sons Inc.
| content serial | Description |
|---|---|
| 1 | First order D.E. (i) Separation of variables |
| 2 | First order D.E. (ii) Homogeneous equation |
| 3 | First order D.E. (iii) Exact equation |
| 4 | First order D.E. (iv) Linear equations , (v) Bernoulli’s equation – Revision on First order D.E. 5 Second order D.E. with constant coeff. ( Homogeneous equations) |
| 5 | Method of undermined coefficients. Second order D.E. with constant coeff. (Non-homogeneous equations) |
| 6 | Method of variation of parameters |
| 7 | Laplace transform |
| 8 | Laplace transform: Basic definition – First shifting theorem |
| 9 | Laplace transform: Transform differentiation- Transform integration |
| 10 | Unit step function- Second shifting theorem |
| 11 | Inverse Laplace transforms |
| 12 | Inverse Laplace transforms |
| 13 | Solution of D.E. and integral equations using Laplace transform- Application: Solve R-L circuit using Laplace transform |
| 14 | Linear programming and simplex method |
| 15 | General Revision |
| 1 | First order D.E. (i) Separation of variables |
| 2 | First order D.E. (ii) Homogeneous equation |
| 3 | First order D.E. (iii) Exact equation |
| 4 | First order D.E. (iv) Linear equations , (v) Bernoulli’s equation – Revision on First order D.E. 5 Second order D.E. with constant coeff. ( Homogeneous equations) |
| 5 | Method of undermined coefficients. Second order D.E. with constant coeff. (Non-homogeneous equations) |
| 6 | Method of variation of parameters |
| 7 | Laplace transform |
| 8 | Laplace transform: Basic definition – First shifting theorem |
| 9 | Laplace transform: Transform differentiation- Transform integration |
| 10 | Unit step function- Second shifting theorem |
| 11 | Inverse Laplace transforms |
| 12 | Inverse Laplace transforms |
| 13 | Solution of D.E. and integral equations using Laplace transform- Application: Solve R-L circuit using Laplace transform |
| 14 | Linear programming and simplex method |
| 15 | General Revision |
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