(A0001201) LINEAR ALGEBRA AND ADVANCED CALCULUS
For Branches: CE, EEE, ME, CSE, CSE (DS), CSE&BS
COURSE OBJECTIVES:
- To familiarize the concepts of matrices and mean value theorems and their applications in engineering.
- To equip the students to solve various application problems in engineering through evaluation of Gamma, Beta functions and multiple integrals etc., COURSE OUTCOMES:
After completion of the course the student will be able to: - Understand the use of matrices and linear system of equations in solving Network analysis, encoding and decoding in Cryptography and Quantum mechanics problems. - Apply the concept of Gamma and Beta functions in digital signal processing, discrete Fourier transform, digital filters and Oscillatory theory in engineering. - Analyze differential and integral calculus to solve improper integrals and its applications in many engineering disciplines. - Determine the process to evaluate double and triple integrals and understand its usage to find surface area and volumes of various bodies in engineering. - Identify the applications of advanced calculus & Linear algebra in electro-magnetic theory and in telecommunication engineering.
MAPPING OF COs & POs:
| PO1 | PO2 | PO3 | PO4 | PO5 | PO6 | PO7 | PO8 | PO9 | PO10 | PO11 | PO12 |
|---|---|---|---|---|---|---|---|---|---|---|---|
| CO1 | 3 | 2 | 2 | 2 | 2 | - | - | - | - | - | - |
| CO2 | 3 | 2 | 2 | 2 | 3 | - | - | - | - | - | - |
| CO3 | 2 | 2 | 2 | 2 | 3 | - | - | - | - | - | - |
| CO4 | 3 | 2 | 3 | 3 | 2 | - | - | - | - | - | - |
| CO5 | 2 | 3 | 2 | 2 | 2 | - | - | - | - | - | - |
UNIT – I
Matrices: Elementary row transformations – Rank – Echelon form, Normal form – Solutions of Linear System of Homogenous and Non Homogeneous equations.
UNIT – II
Eigen Values, Eigen vectors – Properties – Cayley – Hamilton Theorem – Inverse and Power of a matrix by Cayley – Hamilton theorem.
UNIT – III
Quadratic forms: Linear Transformation – Reduction of quadratic form to canonical form and their nature (Rank, Signature and Index).
UNIT – IV
Mean value theorems: Rolle‟s Theorem – Lagrange‟s Mean Value Theorem – (excluding proof). Simple examples of Taylor‟s and Maclaurin‟s Series. Functions of several variables – Jacobian – Maxima and Minima of functions of two variables - Lagrange method of Multipliers with three variables only.
UNIT – V
Multiple integrals: – Evaluation of Double integrals (Cartesian and Polar) – Change of Variables – Change of order of Integration – Changing into Polar coordinates – Evaluation of triple integrals. RGM-R-2020 R G M COLLEGE OF ENGINEERING AND TECHNOLOGY AUTONOMOUS COMPUTER SCIENCE AND ENGINEERING (DATA SCIENCE)
UNIT – VI
Special functions: Gamma function – Properties – Beta function – properties – Relation between Gamma and Beta functions – Evaluation of Integrals using Gamma & Beta functions.
TEXTBOOKS:
1) B. S. Grewal, Higher Engineering Mathematics, Khanna Publications. 2) R. K. Jain, S. R .K. Iyengar, Advanced Engineering Mathematics, Alpha Science. 3) T.K.V. Iyengar, B. Krishna Gandhi, A Text Book of Engineering Mathematics, Vol – I, S. Chand & Company. REFERENCES: 1) G.B. Thomas and R.L. Finney, Calculus and Analytic geometry, 9th Edition, Pearson, Reprint, 2002. 2) Erwin kreyszig, Advanced Engineering Mathematics, 10th Edition, John Wiley & Sons,2011. 3) Veerarajan T., Engineering Mathematics for first year, Tata McGraw-Hill, New Delhi, 2008. 4) Ramana B.V., Higher Engineering Mathematics, Tata McGraw Hill New Delhi, 11thReprint, 2010. 5) N.P. Bali and Manish Goyal, A text book of Engineering Mathematics, Laxmi Publications, Reprint, 2008.