BSc Nautical Sciences APPLIED MATHEMATICS II Syllabus - Mumbai University 2026
This degree runs on the Choice Based Credit System throughout, items 4.69, 4.70 and 4.71 of the Academic Council of 23 July 2020, in force from the academic year 2020-21. The University’s earlier Credit Based Semester and Grading System syllabus is what her older third-year timetables name, so check which scheme your exam form names before you revise.
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Syllabus for APPLIED MATHEMATICS - II
Module I: Integral Calculus and Beta & Gama Functions
- Rectification of plane curves. Double & Triple integrals, their geometrical interpretation and evaluation. Evaluation of double integrals by change of order and change to polar form. Applications of double & triple integrals to areas and volumes Centre of mass, Moment of Inertia. Beta & Gama functions & their properties, relations between Beta & Gama functions. Error functions
Module II: Infinite Series and Fourier Series
- Convergence of infinite series, uniform convergence, properties of uniformly convergent series, Exponential and logarithmic series, definition of Trigonometric and Fourier series, Fourier coefficients, expansion of functions in Fourier series, Even and Odd functions, half range Fourier series, Differentiation and Integration of Fourier Series, Fourier series with respect to a set of orthogonal functions over (a,b). [Fourier series over (- π, π), (0, 2π) and for arbitrary range (a, a+2L) must be treated.
Module III: Differential Calculus
- Indeterminate forms. L’Hospital’s rule, Expansion of function in power series (all types), Partial derivatives of first and higher orders. Total differential. Euler’s theorem on homogeneous functions. Deduction from Euler theorems. Errors & approximations. Maxima & Minima the functions of two variables. Differential equations
- a Exact differential equations and those which can be made exact by use integrating factors by inspection. (i) Linear Equations and reducible to linear (Bernoulli) equations, (ii) Method of substitution to reduce the equations to one of the above forms.
- b Linear Differential Equations of the nth order with constant coefficients. Complimentary function and Particular integral when the function of the independent variable R.H.S. is e ax , x n , e ax V(x), Sin (ax+b), Cos (ax+b). Cauchy’s Linear equation (homogeneous). Legendre’s Linear equation. Variation of parameters and method of indeterminate coefficients.
- c Elementary applications of above differential equations in solving engineering problems such as Electrical Engg., Mech. Engg.
Reference Books
- 1 An introduction to Spherical Trigonometry Clough-Smith J.H
- 2 Spherical Trigonometry Capt. H. Subramaniam
- 3 Higher engineering Mathematics Dr. B.S. Grewal
- 4 A Text book of applied mathematics Wartikar P.N. & Wartikar J.N.
- 5 Integral Calculus Shanti Narayan
Reproduced from the University of Mumbai syllabus for B.Sc. (Nautical Science) under the Choice Based Credit and Grading System, in force from the academic year 2020-21. Wording is as printed in that syllabus. Module numbering is as printed there too.
The complete syllabus
This subject is cut from the University circular for its year. Open a document here if you want the whole thing rather than a single subject.