UNIVERSITY OF MADRAS
B.Sc. DEGREE COURSE IN Nautical Science
SEMESTER SYSTEM WITH CREDITS
(Effective from the Academic Year 2003-2004)

SYLLABUS

Semester III - Paper V - Nautical Mathematics II

Duration of Examination: 3 hrs
Maximum Marks: 100
Credits: 4

1. Integral Calculus

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, Applications of integration to the evaluation of first and second moments of areas and volumes.

2. Beta & Gama Functions

a) Beta & Garna functions & their properties, relation between Beta & Gama functions.
b) Error functions
c) Differentiation under integral sign.

3. Infinite Series and Fourier Series

Convergence, of infinite series, uniform convergence, properties of uniformly convergent series, power series and their properties, expansion of a function as power series. Exponential and logarithmic series, definition of Trigonometric and Fourier series, Fourier coefficients, Dirichiet's conditions, statement of Dirichiet's theorem, expansion of functions in Fourier series, Even and Odd functions, half range Fourier series, Complex form of 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].

4. Spherical Trigonometry

Properties of a spherical triangle and oblique spherical triangle. Cosine formula, Haversine formula, Sine formula and four part formula and their application to Navigational problems. Polar triangle and application of their properties. Right angle and quadrantal triangles. Napier's Rules and their application to Navigational problems. Area of a spherical triangle. Inequalities, Derivation of formula by supplemental theorem. 'Half angle' formula, ‘Hlaf side' formula, Identities. Delambre's Analogies, Napier's Analogies, Legendre's theorem.

5. Simpson's Rule

Derivation of Simpson's first, second and five-eighth rules and their use in the computation of areas, volumes and centroids.

Books Recommended For Reference

1. Higher Mathematics for Engineers, and Physicists Sokolnikoff, I.S & Sokohikoff .E.S.
2. Advanced Calculus Wilfred Kaplan
3. Spherical Trigonometry Capt. H. Subramaniam
4. An introduction to Spherical Trigonometry Clough - Smith J.H.
5. Ship Stability for Masters and Mates Derret D.R.
6. Higher Engineering Mathematics Grewal B.S.
7. Integral Calculus Shanti Narayan
8. Text Book of Applied Mathematics Wartikar P.N. & Wartikar J.N.