MA6151-Mathematics – I

General info:          MA6151-Mathematics – I	University – Anna university,  Tamilnadu, India Marks: UNIT 1 to 5 – 9+3 each unit  Period - TOTAL (L:45+T:15): 60 PERIODS
Objectives: 1)    To develop the use of matrix algebra techniques this is needed by engineers for practical applications. 2)    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. 3)    To familiarize the student with functions of several variables. This is needed in many branches of engineering. 4)    To introduce the concepts of improper integrals, Gamma, Beta and Error functions which are needed in engineering applications. 5)    To acquaint the student with mathematical tools needed in evaluating multiple integrals and their usage.
Syllabus - UNIT I : MATRICES - Marks – 9 + 3  Eigenvalues 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. Notes:
Syllabus - UNIT II :  SEQUENCES AND SERIES Marks – 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.
Syllabus - Unit III: APPLICATIONS OF  DIFFERENTIAL CALCULUS Marks – 9 + 3  Curvature in Cartesian co-ordinates – Centre and radius of curvature – Circle of curvature – Evolutes – Envelopes - Evolute as envelope of normals.
Syllabus - Unit- IV : DIFFERENTIAL CALCULUS OF SEVERAL VARIABLES Marks – 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.
Syllabus - 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.
University Recommended 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 ublications, Delhi, 2011.
Other 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. Notes from Vidhyarthi – Click here…
You can download our  notes here … Thanks to Mrs.Kanakalakshmi, Lecturer
Contact Me: Parthasarathy.poovendran@gmail.com Ppartha.blogspot.com