YMA001 APPLIED MATHEMATICS - I SYLLABUS | ANNA UNIVERSITY BCA 1ST SEM SYLLABUS REGULATION 2010 2011 2012-2013 BELOW IS THE ANNA UNIVERSITY FIRST SEMESTER B.C.A. (BACHELOR OF COMPUTER APPLICATIONS) DEPARTMENT SYLLABUS, TEXTBOOKS, REFERENCE BOOKS,EXAM PORTIONS,QUESTION BANK,PREVIOUS YEAR QUESTION PAPERS,MODEL QUESTION PAPERS, CLASS NOTES, IMPORTANT 2 MARKS, 8 MARKS, 16 MARKS TOPICS. IT IS APPLICABLE FOR ALL STUDENTS ADMITTED IN THE YEAR 2011 2012-2013 (ANNA UNIVERSITY CHENNAI,TRICHY,MADURAI,TIRUNELVELI,COIMBATORE), 2010 REGULATION OF ANNA UNIVERSITY CHENNAI AND STUDENTS ADMITTED IN ANNA UNIVERSITY CHENNAI DURING 2010
YMA001 APPLIED MATHEMATICS - I L T P C
3 1 0 4
UNIT I COMPLEX NUMBERS
12
Expansion of Sin n Cos n in terms of Sin and Cos - Expansion of Sinn ; Cosn in
terms of sines and cosines of multiples of , hyperbolic functions. Inverse hyperbolic functions.
UNIT II MATRICES 12
Rank of matrix - consistency and inconsistency of a system of linear equations – Eigen values
and Eigen vectors – Properties - Cayley Hamilton theorem – Reduction of Quadratic form to
Canonical form by Orthogonal reduction.
UNIT III DEFINITE INTEGRALS 12
Reduction form ula for integral of sinnx, cosn x, tann x – Definite integrals –P rope rties – Are a of
Cartesian Curves -– volumes of Revolution.
UNIT IV ORDINARY DIFFERENTIAL EQUATIONS
12
Solution of second order with constant coefficients and Variable coefficients - complimentary
function – particular integrals – simultaneous linear equations with constant coefficients of first
order.
UNIT V APPLICATION OF DIFFERENTIATION 12
Curvature of a curve – Radius of a curvature in Cartesian form - Centre of curvature – Circle of
curvature – Evolutes and Envelopes.
LECTURE: 45 TUTORIALS: 15 TOTAL : 60
REFERENCES :
1 Veerarajan.T., “Engineering Mathematics”, TMH Pub. Co. Ltd., New Delhi 1999.
2 Kandasamy.P., Thilagavathy.K. and Gunavathy.K. – “Engineering Mathematics, Volume –
I”, S.Chand & Co., New Delhi, 2001.
YMA001 APPLIED MATHEMATICS - I L T P C
3 1 0 4
UNIT I COMPLEX NUMBERS
12
Expansion of Sin n Cos n in terms of Sin and Cos - Expansion of Sinn ; Cosn in
terms of sines and cosines of multiples of , hyperbolic functions. Inverse hyperbolic functions.
UNIT II MATRICES 12
Rank of matrix - consistency and inconsistency of a system of linear equations – Eigen values
and Eigen vectors – Properties - Cayley Hamilton theorem – Reduction of Quadratic form to
Canonical form by Orthogonal reduction.
UNIT III DEFINITE INTEGRALS 12
Reduction form ula for integral of sinnx, cosn x, tann x – Definite integrals –P rope rties – Are a of
Cartesian Curves -– volumes of Revolution.
UNIT IV ORDINARY DIFFERENTIAL EQUATIONS
12
Solution of second order with constant coefficients and Variable coefficients - complimentary
function – particular integrals – simultaneous linear equations with constant coefficients of first
order.
UNIT V APPLICATION OF DIFFERENTIATION 12
Curvature of a curve – Radius of a curvature in Cartesian form - Centre of curvature – Circle of
curvature – Evolutes and Envelopes.
LECTURE: 45 TUTORIALS: 15 TOTAL : 60
REFERENCES :
1 Veerarajan.T., “Engineering Mathematics”, TMH Pub. Co. Ltd., New Delhi 1999.
2 Kandasamy.P., Thilagavathy.K. and Gunavathy.K. – “Engineering Mathematics, Volume –
I”, S.Chand & Co., New Delhi, 2001.
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