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# Applied Mathematics 4 Semester 4 (SE Second Year) BE Biotechnology University of Mumbai Topics and Syllabus

SubjectApplied Mathematics 4
CBCGS [2017 - current]
CBGS [2013 - 2016]
Old [2000 - 2012]

## Topics with syllabus and resources

100.00 Fourier Series
• Expansion of functions in any interval (a, b).
• Half range expansion;
• Complex form;
• Parseval’s identity theorem;
• Orthogonal and Orthonormal functions. (NO PROOFS REQUIRED)
200.00 Fourier Integrals and Fourier Transform
• sine & cosine Integrals,
• sine & cosine transforms,
• complex transforms. (NO PROOFS REQUIRED)
300.00 Partial Differential Equations
• Elliptic, Parabolic & Hyperbolic Equations;
• Laplace’s equation;
• One dimensional Heat & Wave Equation, Two Dimensional wave equation. (ONLY NUMERICAL PROBLEMS. NO PROOFS REQUIRED)
400.00 Vector Integration
• Green’s Theorem in the plain;
• Conservative & Solenoidal Fields.
• Gauss Divergence Theorem,
• Stokes’ Theorem. (ONLY NUMERICAL PROBLEMS. NO PROOFS REQUIRED)
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