ANDHRA UNIVERSITY, WALTAIR
M.Sc. APPLIED MATHEMATICS, SECOND SEMSTER
AM-202 : TECHNIQUES OF APPLIED MATHEMATICS - II
[ A total of seven questions are to be set. All questions carry equal marks. The first question which is compulsory carries 20 marks. It consists of 4 short answer sub questions each of five marks covering the entire syllabus. The remaining six questions each carrying 20 marks are to be set as suggested in the body of the syllabi.]
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Partial differential equations : Equations of the form dx / P = dy/Q = dz /R , orthogonal trajectories, Pfaffian differential equations, 1st order partial differential equations; Charpit’s method and some special methods. Jacobi’s method. Second order constant and variable coefficients. Partial differential equations : canonical forms, separation of variables method, Monge’s method (Chapater I (excluding sections 7 & 8), chapter-II (excluding section 14), Chapter III (excluding section 10) of Ref.1). (Three questions are to be set)
Integral equations : Classification of integral equations, connection with differential equations, Integral equations of the convolution type, method of successive approximations. The resolvent, Fredholm theory (Chapters 1,2,3,4,8,9 (excluding 9.3.1) of ref.2). (One question is to be set)].
Fourier and Laplace Transforms with applications to ordinary , partial differential equations and Integral equations (2.2 to 2.10, 2.15 ,2.16 and 3.1 to 3.11, 3.14 to 3.16 (Two questions are to be set)
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References :
- I.N.Sneddon, Elements of partial differential equations, McGraw Hill , International student edition, 1964.
- B.L.Moiseiwitsch, ‘Integral equations’ Longman Inc., New york 1977.
- The use of Integral transforms by IAN . N. Sneedon by TMH, Edition.
