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 |
|---|---|---|
| C | Module 1 | |
| 101 | Laplace Transform (Lt) of Standard Functions | |
| 102 | Properties of Laplace Transform | |
| 103 | Inverse Laplace Transform | |
| 104 | Applications of Laplace Transform | |
| CC | Module 2 | |
| 201 | Introduction | |
| 202 | Fourier Series of Functions | |
| CCC | Module 3 | |
| 301 | Solution of Bessel Differential Equation | |
| CD | Module 4 | |
| 401 | Scalar and Vector Product | |
| 402 | Vector Differentiation | |
| 403 | Properties | |
| 404 | Vector Integral | |
| D | Module 5 | |
| 501 | Complex Variable | |
| 502 | Mapping | |
| Total | - |
Syllabus
- Definition. unilateral and bilateral Laplace Transform
- LT of sin(at), cos(at), eat ,tn , sinh(at), cosh(at), erf(t)
- Heavi-side unit step
- dirac-delta function
- LT of periodic function.
- Linearity,
- first shifting theorem,
- second shifting theorem,
- multiplication by tn , division by t ,
- Laplace Transform of derivatives and integrals,
- change of scale,
- convolution theorem,
- initial and final value theorem,
- Parsavel‘s identity.
- Partial fraction method
- long division method
- residue method.
- Solution of ordinary differential equations.
- Definition
- Dirichlet‘s conditions
- Euler‘s formulae.
- Exponential, trigonometric functions, even and odd functions, half range sine and cosine series.
- Complex form of Fourier series, orthogonal and orthonormal set of functions, Fourier integral representation.
- Series method, recurrence relation, properties of Bessel function of order +1/2 and -1/2 Generating function, orthogonality property.
- Bessel Fourier series of functions.
- Scalar and vector product of three and four vectors and their properties.
- Gradient of scalar point function
- divergence and curl of vector point function.
- Solenoidal and irrotational vector fields
- conservative vector field.
- Line integral
- Green‘s theorem in a plane
- Gauss‘ divergence theorem
- Stokes‘ theorem.
- Analytic Function: Necessary and sufficient conditions, Cauchy.
- Reiman equation in polar form.
- Harmonic function, orthogonal trajectories.
- Conformal mapping.
- bilinear transformations.
- cross ratio.
- fixed points.
- bilinear transformation of straight lines and circles.
