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

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SubjectApplied Mathematics 3
CBCGS [2017 - current]
CBGS [2013 - 2016]
Old [2000 - 2012]

## Topics with syllabus and resources

1 Module 1
1.01 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.
1.02 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.
1.03 Inverse Laplace Transform
• Partial fraction method
• long division method
• residue method.
1.04 Applications of Laplace Transform
• Solution of ordinary differential equations.
2 Module 2
2.01 Introduction
• Definition
• Dirichlet‘s conditions
• Euler‘s formulae.
2.02 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.
3 Module 3
3.01 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.
4 Module 4
4.01 Scalar and Vector Product
• Scalar and vector product of three and four vectors and their properties.
4.02 Vector Differentiation
• Gradient of scalar point function
• divergence and curl of vector point function.
4.03 Properties
• Solenoidal and irrotational vector fields
• conservative vector field.
4.04 Vector Integral
• Line integral
• Green‘s theorem in a plane
• Gauss‘ divergence theorem
• Stokes‘ theorem.
5 Module 5
5.01 Complex Variable
• Analytic Function: Necessary and sufficient conditions, Cauchy.
• Reiman equation in polar form.
• Harmonic function, orthogonal trajectories.
5.02 Mapping
• Conformal mapping.
• bilinear transformations.
• cross ratio.
• fixed points.
• bilinear transformation of straight lines and circles.

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