University of Mumbai Syllabus For Semester 3 (SE Second Year) Applied Mathematics 3: Knowing the Syllabus is very important for the students of Semester 3 (SE Second Year). Shaalaa has also provided a list of topics that every student needs to understand.
The University of Mumbai Semester 3 (SE Second Year) Applied Mathematics 3 syllabus for the academic year 2021-2022 is based on the Board's guidelines. Students should read the Semester 3 (SE Second Year) Applied Mathematics 3 Syllabus to learn about the subject's subjects and subtopics.
Students will discover the unit names, chapters under each unit, and subtopics under each chapter in the University of Mumbai Semester 3 (SE Second Year) Applied Mathematics 3 Syllabus pdf 2021-2022. They will also receive a complete practical syllabus for Semester 3 (SE Second Year) Applied Mathematics 3 in addition to this.
University of Mumbai Semester 3 (SE Second Year) Applied Mathematics 3 Revised Syllabus
University of Mumbai Semester 3 (SE Second Year) Applied Mathematics 3 and their Unit wise marks distribution
University of Mumbai Semester 3 (SE Second Year) Applied Mathematics 3 Course Structure 2021-2022 With Marking Scheme
| # | Unit/Topic | Marks |
|---|---|---|
| 100 | Complex Variable and Mapping | |
| 200 | Laplace Transform | |
| 300 | Fourier Series | |
| 400 | Vector Algebra and Calculus | |
| 500 | Z Transform | |
| Total | - |
Syllabus
- Functions of a complex variable, Analytic functions, Cauchy-Riemann equations in Cartesian co-ordinates, Polar co-ordinates.
- Harmonic functions, Analytic method and Milne Thomson methods to find f(z), Orthogonal trajectories.
- Conformal Mapping, Linear, Bilinear transformations, Cross ratio, fixed points and standard transformation such as rotation and magnification, invertion, translation.
- Introduction, Definition of Laplace transform, Laplace transform of constant, trigonometrical, exponential functions.
- Important properties of Laplace transform:- First shifting theorem, Laplace transform without proof.
- Unit step function, Heavi side function, Dirac-delta function, Periodic function and their Laplace transforms, Second shifting theorem.
- Inverse Laplace transform with Partial fraction and Convolution theorem (without proof).
- Application to solve initial and boundary value problem involving ordinary differential equations with one dependent variable and constant coefficients.
- Dirichlet’s conditions, Fourier series of periodic functions with period 2π and 2L.
- Fourier series for even and odd functions.
- Half range sine and cosine Fourier series, Parsevel’s identities (without proof).
- Orthogonal and Ortho-normal functions, Complex form of Fourier series.
- Fourier Integral Representation.
- Vector Algebra:- Scalar and vector product of three and four Vectors and their properties.
- Vector Calculus:- Vector differential operator, Gradient of a scalar point function, Diversions and Curl of Vector point function.
- Vector Integration:- Line integral; conservative vector field, Green’s theorem in a plane (Without proof)
- Gauss-Divergence theorem & Stokes’ theorem (Without proof and no problems on verification of above theorems).
- Z-transform of standard functions such as Z(an), Z(np).
- Properties of Z-transform:- Linearity, Change of scale, Shifting property, Multiplication of K, Initial and final value, Convolution theorem (all without proof)
- Inverse Z transform:- Binomial Expansion and Method of Partial fraction.
