### MA6151 M1 2marks-16marks

Anna University Regulation 2013 Computer Science & M1ineering (CSE) MA6151 M1 2marks & 16marks for all 5 units are provided below. Download link for CSE 1st SEM MA6151 MATHEMATICS I Short answers, Question Bank are listed down for students to make perfect utilization and score maximum marks with our study materials.

MA6151- MATHEMATICS I

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.UNIT I MATRICES 9+3Eigenvalues 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+3Sequences: 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.

**MA6151 M1 Unit 1 notes – Download Here**

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:

- Bali N. P and Manish Goyal, “A Text book of Engineering Mathematics”, Eighth Edition, Laxmi Publications Pvt Ltd., 2011.
- Grewal. B.S, “Higher Engineering Mathematics”, 41st Edition, Khanna Publications, Delhi, 2011.

REFERENCES:

- Dass, H.K., and Er. Rajnish Verma,” Higher Engineering Mathematics”, S. Chand Private Ltd., 2011.
- Glyn James, “Advanced Modern Engineering Mathematics”, 3rd Edition, Pearson Education, 2012.
- Peter V. O‟Neil,” Advanced Engineering Mathematics”, 7th Edition, Cengage learning, (2012).
- Ramana B.V, “Higher Engineering Mathematics”, Tata McGraw Hill PublishingCompany, New Delhi, 2008.
- Sivarama Krishna Das P. and Rukmangadachari E., “Engineering Mathematics”, Volume I,Second Edition, PEARSON Publishing, 2011.

**MA6151 M1 Unit 1 notes – Download Here**

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MA6151 2marks, M1 Unit wise short answers – CSE 1st Semester