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Get the syllabus for MA6151 Engineering mathematics – I or M – I Syllabus from here.MA6151 SEMESTER – I Syllabus Regulation 2013 syllabus.Check anna university result nov/dec 2017 here.
MA6151 MATHEMATICS – I L T P C 3 1 0 4
OBJECTIVES:
Eigen values and Eigenvectors of a real matrix – Characteristic equation – Properties of eigenvalues and eigenvectors – Statement and applications of Cayley-Hamilton Theorem – Diagonalization of matrices – Reduction of a quadratic form to canonical form by orthogonal transformation – Nature of quadratic forms.
UNIT II SEQUENCES AND SERIES 9+3
Sequences: Definition and examples – Series: Types and Convergence – Series of positive terms – Tests of convergence: Comparison test, Integral test and D‟Alembert‟s ratio test – Alternating series – Leibnitz‟s test – Series of positive and negative terms – Absolute and conditional convergence.
UNIT III APPLICATIONS OF DIFFERENTIAL CALCULUS 9+3
Curvature in Cartesian co-ordinates – Centre and radius of curvature – Circle of curvature – Evolutes – Envelopes - Evolute as envelope of normals.
UNIT IV DIFFERENTIAL CALCULUS OF SEVERAL VARIABLES 9+3
Limits and Continuity – Partial derivatives – Total derivative – Differentiation of implicit functions – Jacobian and properties – Taylor‟s series for functions of two variables – Maxima and minima of functions of two variables – Lagrange‟s method of undetermined multipliers.
UNIT V MULTIPLE INTEGRALS 9+3
Double integrals in cartesian and polar coordinates – Change of order of integration – Area enclosed by plane curves – Change of variables in double integrals – Area of a curved surface - Triple integrals – Volume of Solids. TOTAL (L:45+T:15): 60
PERIODS OUTCOMES:
This course equips students to have basic knowledge and understanding in one fields of materials, integral and differential calculus.
TEXT BOOKS:
1. Bali N. P and Manish Goyal, “A Text book of Engineering Mathematics”, Eighth Edition, Laxmi Publications Pvt Ltd., 2011.
2. Grewal. B.S, “Higher Engineering Mathematics”, 41st Edition, Khanna Publications, Delhi, 2011.
REFERENCES:
1 Dass, H.K., and Er. Rajnish Verma,” Higher Engineering Mathematics”, S. Chand Private Ltd., 2011.
2 Glyn James, “Advanced Modern Engineering Mathematics”, 3rd Edition, Pearson Education, 2012.
3 Peter V. O‟Neil,” Advanced Engineering Mathematics”, 7th Edition, Cengage learning, 2012.
4 Ramana B.V, “Higher Engineering Mathematics”, Tata McGraw Hill Publishing Company, New Delhi, 2008.
5 Sivarama Krishna Das P. and Rukmangadachari E., “Engineering Mathematics”, Volume I, Second Edition, PEARSON Publishing, 2011.
Get the syllabus for MA6151 Engineering mathematics – I or M – I Syllabus from here.MA6151 SEMESTER – I Syllabus Regulation 2013 syllabus.Check anna university result nov/dec 2017 here.
MA6151 Syllabus
OBJECTIVES:
- To develop the use of matrix algebra techniques this is needed by engineers for practical applications.
- To make the student knowledgeable in the area of infinite series and their convergence so that he/ she will be familiar with limitations of using infinite series approximations for solutions arising in mathematical modeling.
- To familiarize the student with functions of several variables. This is needed in many branches of engineering.
- To introduce the concepts of improper integrals, Gamma, Beta and Error functions which are needed in engineering applications.
- To acquaint the student with mathematical tools needed in evaluating multiple integrals and their usage.
Eigen values and Eigenvectors of a real matrix – Characteristic equation – Properties of eigenvalues and eigenvectors – Statement and applications of Cayley-Hamilton Theorem – Diagonalization of matrices – Reduction of a quadratic form to canonical form by orthogonal transformation – Nature of quadratic forms.
UNIT II SEQUENCES AND SERIES 9+3
Sequences: Definition and examples – Series: Types and Convergence – Series of positive terms – Tests of convergence: Comparison test, Integral test and D‟Alembert‟s ratio test – Alternating series – Leibnitz‟s test – Series of positive and negative terms – Absolute and conditional convergence.
UNIT III APPLICATIONS OF DIFFERENTIAL CALCULUS 9+3
Curvature in Cartesian co-ordinates – Centre and radius of curvature – Circle of curvature – Evolutes – Envelopes - Evolute as envelope of normals.
UNIT IV DIFFERENTIAL CALCULUS OF SEVERAL VARIABLES 9+3
Limits and Continuity – Partial derivatives – Total derivative – Differentiation of implicit functions – Jacobian and properties – Taylor‟s series for functions of two variables – Maxima and minima of functions of two variables – Lagrange‟s method of undetermined multipliers.
UNIT V MULTIPLE INTEGRALS 9+3
Double integrals in cartesian and polar coordinates – Change of order of integration – Area enclosed by plane curves – Change of variables in double integrals – Area of a curved surface - Triple integrals – Volume of Solids. TOTAL (L:45+T:15): 60
PERIODS OUTCOMES:
This course equips students to have basic knowledge and understanding in one fields of materials, integral and differential calculus.
TEXT BOOKS:
1. Bali N. P and Manish Goyal, “A Text book of Engineering Mathematics”, Eighth Edition, Laxmi Publications Pvt Ltd., 2011.
2. Grewal. B.S, “Higher Engineering Mathematics”, 41st Edition, Khanna Publications, Delhi, 2011.
REFERENCES:
1 Dass, H.K., and Er. Rajnish Verma,” Higher Engineering Mathematics”, S. Chand Private Ltd., 2011.
2 Glyn James, “Advanced Modern Engineering Mathematics”, 3rd Edition, Pearson Education, 2012.
3 Peter V. O‟Neil,” Advanced Engineering Mathematics”, 7th Edition, Cengage learning, 2012.
4 Ramana B.V, “Higher Engineering Mathematics”, Tata McGraw Hill Publishing Company, New Delhi, 2008.
5 Sivarama Krishna Das P. and Rukmangadachari E., “Engineering Mathematics”, Volume I, Second Edition, PEARSON Publishing, 2011.
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