This course provides the first order ordinary differential equations (Separable, Homogeneous, Exact, Linear and Bernoulli’s equations) –Second order ordinary differential equations with constant coefficients (General solution of homogeneous and Non-homogeneous equations: Method of undetermined coefficients– The Method of variation of parameters)–Second order ordinary differential equations with variable coefficients:[Cauchy- Euler Equation] – Laplace transforms(First Shifting Theorem – Derivatives of Transforms – Transform Integration – Unit Step Function – Second Shifting Theorem – Inverse Laplace Transforms – Applications(Solution of ODEs using Laplace Transforms–Solution of R-L circuit using the Laplace Transforms)–Fourier series of functions of period 2P, Fourier series for even and odd functions, half range expansions and for harmonic functions. 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.
Software Engineering 144 CRs
Erwin Kreyszig, Advanced Engineering Mathematics, John Wiley and Sons Inc
| content serial | Description |
|---|---|
| 1 | First order ordinary differential equations |
| 2 | Separable equations – Initial value problems- Homogeneous equations |
| 3 | Linear equations and Bernoulli’s equations |
| 4 | Exact equations |
| 5 | Second order ordinary differential equations with constant coefficients: Fundamental set of solutions - Linear independence of solutions: Wronskian- General solution of homogeneous equations |
| 6 | Second order ordinary differential equations with constant coefficients: non-homogeneous equations (Method of undetermined coefficients) |
| 7 | Second order ordinary differential equations with constant coefficients: The method of variation of parameters + 7th Week Examination |
| 8 | Laplace transforms: Basic definition- First shifting theorem (s-shifting) |
| 9 | Laplace transform : Derivatives of Transforms - Transform integration |
| 10 | Laplace transforms: Unit Step Function - Second Shifting Theorem (t-shifting) |
| 11 | Inverse Laplace transforms |
| 12 | Applications: Solution of ODEs using Laplace transforms Solution of R-L circuit using the + 12th Week Examination |
| 13 | Fourier series: Fourier series for functions of period 2P |
| 14 | Fourier series: Fourier series for even and odd functions |
| 15 | Linear programming and simplex method |
| 16 | Final Examination |
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