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# Applied Mathematics 3 Semester 3 (SE Second Year) BE Instrumentation Engineering University of Mumbai Topics and Syllabus

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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.

CBCGS [2017 - current]
CBGS [2013 - 2016]
Old [2000 - 2012]

## 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

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## Syllabus

C Module 1
101 Laplace Transform (Lt) of Standard Functions
• 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.
102 Properties of Laplace Transform
• 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.
103 Inverse Laplace Transform
• Partial fraction method
• long division method
• residue method.
104 Applications of Laplace Transform
• Solution of ordinary differential equations.
CC Module 2
201 Introduction
• Definition
• Dirichlet‘s conditions
• Euler‘s formulae.
202 Fourier Series of Functions
• 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.
CCC Module 3
301 Solution of Bessel Differential Equation
• Series method, recurrence relation, properties of Bessel function of order +1/2 and -1/2 Generating function, orthogonality property.
• Bessel Fourier series of functions.
CD Module 4
401 Scalar and Vector Product
• Scalar and vector product of three and four vectors and their properties.
402 Vector Differentiation
• Gradient of scalar point function
• divergence and curl of vector point function.
403 Properties
• Solenoidal and irrotational vector fields
• conservative vector field.
404 Vector Integral
• Line integral
• Green‘s theorem in a plane
• Gauss‘ divergence theorem
• Stokes‘ theorem.
D Module 5
501 Complex Variable
• Analytic Function: Necessary and sufficient conditions, Cauchy.
• Reiman equation in polar form.
• Harmonic function, orthogonal trajectories.
502 Mapping
• Conformal mapping.
• bilinear transformations.
• cross ratio.
• fixed points.
• bilinear transformation of straight lines and circles.
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