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MATHEMATICS COURSES FOR B. TECH. IT PROGRAM, SEMESTER I, MAD1181, , R 2021, ALGEBRA AND DIFFERENTIAL CALCULUS, , L, 3, , T, 1, , P, 0, , C, 4, , SDG: 4, COURSE OBJECTIVES:, COB1: To introduce matrix algebra techniques for engineers to apply in practical, problems, COB2:To find the roots of polynomial equations using different techniques, COB3:To demonstrate the concepts of limits, continuity and application of differential, calculus., COB4: To familiarize the students with the functions of several variables, COB5: To develop the use of differential equations necessary for engineering, applications, MODULE I, , MATRICES, , 9+3, , Characteristic Equation- Eigenvalues and Eigenvectors of a real matrix –Properties of, Eigenvalues and Eigenvectors – Cayley-Hamilton Theorem (without proof) – Orthogonal, matrices – orthogonal transformations of a symmetric matrix to diagonal form – Reduction of, quadratic form to canonical form by orthogonal transformation, MODULE II, , THEORY OF EQUATIONS, , 9+3, , Introduction - Surds and irrational roots – simple problems – Equations whose roots are in, A.P,G.P and in H.P – Relations between the roots and coefficients – symmetric functions –, Formation of equations – Decreasing and Increasing the roots – transformation of equation –, Reciprocal equations, MODULE III, , DIFFERENTIAL CALCULUS, , 9+3, , Limits of functions - one sided limits – Continuity - Curvature – Cartesian and polar, coordinates – center and radius of curvature – Circle of curvature – Involutes and evolutes –, Envelopes, MODULE IV, , DIFFERENTIAL CALCULUS OF SEVERAL VARIABLES, , 9+3, , Laws of limits –Functions of two variables – partial derivatives – total differential – Implicit, Functions – Jacobian - Taylor’s series expansion – Optima of two variables – Lagrange’s, multiplier method, MODULE V, , ORDINARY DIFFERENTIAL EQUATIONS, , 9+3, , Linear equations of second order with constant and variable coefficients – Simultaneous first, order linear equations with constant coefficients – homogeneous equations of Euler’s type –, method of undetermined coefficients- method of variation of parameters, L –45 ; T-15; TOTAL HOURS – 60

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TEXT BOOKS:, 1. Ramana, B.V, “Higher Engineering Mathematics” Tata McGraw Hill Publishing, Co. New Delhi, 2010., 2. Grewal B.S., “Higher Engineering Mathematics” 44th edition, Khanna Publishers,, New Delhi, 2017., 3. Kreyszig, E., “Advanced Engineering Mathematics”, 10th edition, John Wiley and, Sons (Asia) Pvt Ltd., Singapore, 2011, REFERENCES:, 1.Veerarajan.T., “Engineering Mathematics” (5th edition) Tata Mc Graw Hill, Publishing Co. New Delhi, 2012, 2. Jain, R.K. & Iyengar, S. R. K., “Advanced Engineering Mathematics”, Narosa, Publishers, 5th edition, 2016., 3. Peter V. O'Neil, “Advanced Engineering Mathematics”, 7th edition, Cengage, Learning, 2011., 4. Venkataraman, M.K., “Engineering Mathematics”, Volume I, 2nd edition, National, Publishing Co., Chennai, 2003., 5. James Stewart ,“ Calculus” 7th edition, Brooks/Cole Cengagelearning, UK, COURSE OUTCOMES: At the end of the course students will be able to, CO1: Use the matrix algebra methods for finding eigenvalues, eigenvectors and, diagonalization, CO2: Solve equations using the relations between roots and coefficients, CO3: Apply differential calculus in various engineering problems, CO4: Able to use differential calculus on several variable functions, CO5: solve various types of differential equations that arise in many applications, Board of Studies (BoS) :, , Academic Council:, , th, , 17th AC held on 15.07.2021, , 12 BOS of Mathematics & AS held on, 23.06.2021, , CO, 1, CO, 2, CO, 3, CO, 4, CO, 5, , PO, , PO, , PO, , PO, , PO, , PO, , PO, , PO, , PO, , PO, , PO, , PO, , PSO, , PSO, , PSO, , 1, , 2, , 3, , 4, , 5, , 6, , 7, , 8, , 9, , 10, , 11, , 12, , 1, , 2, , 3, , M, M, H, M, M

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SDG 4 : Ensure inclusive and equitable, , quality education and promote, , lifelong opportunities for all, Learning of various mathematical techniques like matrices and calculus will, lead to knowledge of applications in Computer Science