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

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

## Topics with syllabus and resources

100.00 Complex Variable and Mapping
• 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.
200.00 Laplace Transform
• 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.
300.00 Fourier Series
• 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.
400.00 Vector Algebra and Calculus
• 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).
500.00 Z Transform
• 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.
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