BAS103 : ENGINEERING MATHEMATICS-I
Course Objectives:
The objective of this course is to familiarize the graduate engineers with techniques in matrix, calculus,
multivariate analysis and vector calculus. It aims to equip the students with standard concepts and tools from
intermediate to advanced level that will enable them to tackle more advanced level of mathematics and
applications that they would find useful in their disciplines.
The students will learn:
• The essential tools of matrices, Eigen values and its application in a Comprehensive-manner.
• To apply the knowledge of differential calculus in the field of engineering.
• To deal with functions of several variables that is essential in optimizing the results ofreal life
problems.
• To apply integral calculus in various field of engineering and have a basicunderstanding of Beta and
Gamma functions and application of Dirichlet’s integral.
• To deal with vector calculus that is required in different branches of Engineering tograduate
engineer.
Contact
Content
Hours
Unit-1: Matrices 8
Elementary transformations, Inverse of a matrix, Rank of matrix, Solution of system of
linear equations, Characteristic equation, Cayley-Hamilton Theorem and its application,
Linear Dependence and Independence of vectors, Eigen values and Eigen vectors, Complex
Matrices, Hermitian, Skew-Hermitian and Unitary Matrices, Applications to Engineering
problems.
Unit-2: Differential Calculus- I 8
Successive Differentiation (nth order derivatives), Leibnitz theorem, Curve tracing,
Partial derivatives, Euler’s Theorem for homogeneous functions, Total derivative, Change
of variables.
Unit-3: Differential Calculus-II 8
Expansion of functions by Taylor’s and Maclaurin’s theorems for functions of one and two
variables, Maxima and Minima of functions of several variables, Lagrange’s method of
multipliers, Jacobians, Approximation of errors.
Unit-4: Multiple integration 8
Double integral, Triple integral, Change oforder of integration, Change of variables, Beta and
Gama function and their properties, Dirichlet’s integral and its applications to area and
volume, Liouville’s extensions of Dirichlet’s integral.
Unit-5: Vector Calculus 8
Vector differentiation: Gradient, Curl and Divergence and their Physical interpretation,
Directional derivatives.
Vector Integration: Line integral, Surface integral, Volume integral, Gauss’s Divergence
theorem, Green’s theorem and Stoke’s theorem (without proof) and their applications.
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Course Outcomes:
Course Outcome (CO) Bloom’s
Level
At the end of this course, the students will be able to:
CO 1 Understand the concept of complex matrices, Eigen values, Eigen vectors and apply K2 & K5
the concept of rank to evaluate linear simultaneous equations
CO 2 Remember the concept of differentiation to find successive differentiation, K1,K6 & K5
Leibnitz Theorem, and create curve tracing, and find partial and total derivatives
CO 3 Applying the concept of partial differentiation to evaluate extrema, series expansion, K3 &K5
error approximation offunctions and Jacobians
CO 4 Remember the concept of Beta and Gamma function; analyze area and volume and K1 & K4
Dirichlet’s theorem in multiple integral
Apply the concept of Vector Calculus to analyze and evaluate directionalderivative, K3, K4& K5
CO 5 line, surface and volume integrals.
K1 – Remember, K2 – Understand, K3 – Apply, K4 – Analyze, K5 – Evaluate, K6 – Create
Text Books:
1. B. V. Ramana, Higher Engineering Mathematics, McGraw-Hill Publishing Company Ltd.,2008.
2. B. S. Grewal, Higher Engineering Mathematics, Khanna Publisher, 2005.
3. R K. Jain & S R K. Iyenger, Advance Engineering Mathematics, Narosa Publishing House2002.
Reference Books:
1. E. Kreyszig, Advance Engineering Mathematics, John Wiley & Sons, 2005.
2. Peter V. O’Neil, Advance Engineering Mathematics, Thomson (Cengage) Learning, 2007.
3. Maurice D. Weir, Joel Hass, Frank R. Giordano, Thomas, Calculus, Eleventh Edition,Pearson.
4. D. Poole, Linear Algebra: A Modern Introduction, 2nd Edition, Brooks/Cole, 2005.
5. Veerarajan T., Engineering Mathematics for first year, McGraw-Hill, New Delhi, 2008.
6. Ray Wylie C and Louis C Barret, Advanced Engineering Mathematics, McGraw-Hill;Sixth
Edition.
7. P. Sivaramakrishna Das and C. Vijayakumari, Engineering Mathematics, 1st Edition,Pearson
Education.
8. Advanced Engineering Mathematics. Chandrika Prasad, Reena Garg, 2018.
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