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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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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