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• 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
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.
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: 60 PERIODS
* 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", 41 Edition, Khanna Publications, Delhi, (2011).
* 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 Publishing Company, New Delhi, (2008).