6th-Convocation-List-of-Graduating-Students.pdf
List-of-Toppers-Graduating-in-Academic-Year-2020-21.pdf
SYLLABUS
Semester – I
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School of Engineering & Technology
Course Outline |
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Course Title: Engineering Mathematics I Course Code- 23BTC-0MA11T |
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Semester: I |
Academic Year: 2023 |
Core/Elective: Core |
Credits: 4 |
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Course Designed by: Dr. Manimala E-mail: manimala@sushantuniversity.edu.in |
Course Instructor: Dr. Manimala E-mail: manimala@sushantuniversity.edu.in |
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Pre-requisites: Basic concept of Matrix, Calculus, Sequence & Series and Trigonometry |
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1. Course Outcomes:
1. Upon successful completion of the course, the students should be able to
CO1: Describe matrix algebra to solving engineering problems. Determine the eigenvalues and eigenvectors of a matrix
CO2: Distinguish between the concepts of sequence and series. Determine convergence and divergence of series.
CO3: Represent complex numbers algebraically and geometrically. Understand De Moivre’s theorem and find the roots of complex numbers. Application of complex numbers for solving engineering problems
CO4: Understand application of Leibniz’s theorem & Taylor’s theorem in real life problems.
CO5: Demonstrate Knowledge of maxima and minima of function of two variables, Understand Homogeneous Function. asymptotes and curve tracing.
2. CO and PO mapping
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3. Syllabus: Total Hrs.: 40
UNIT I- Matrices Total: 10 hours
Matrices and its types, Rank of a matrix. Elementary transformations, Echelon-form of a matrix, normal form of a matrix, Inverse of a matrix by elementary transformations (Gauss– Jordan method).
Linear dependence and linear independence of vectors. Solution of system of linear equations. Non-homogeneous linear equations and homogeneous linear equations.
Characteristic equation – Eigen values – Eigen vectors – properties of Eigen values. Cayley- Hamilton theorem (without proof). Inverse of a matrix by using Cayley-Hamilton theorem. Modal matrix.
UNIT II – Infinite Series Total: 8 hours
Definition of Sequence and series. Convergence of series – comparison test – D’Alemberts Ratio test. Cauchy’s Root Test – Integral Test – Raabe’s Test – Logarithmic Test –Gauss Test.
Alternating series – Absolute convergence – Leibnitz’s Rule (without Proof).
UNIT III - Complex Number Total: 8 hours
De Moivre’s theorem and roots of complex numbers. Expansion of sin nq, cos nq and tan nq in powers of sinq, cosq, tanq.Complex exponential function, Complex trigonometry functions.
hyperbolic functions, Inverse hyperbolic functions, Logarithm of complex numbers. Summation of trigonometric series.
UNIT IV- Differential Calculus-I Total: 6 hours
Successive differentiation, Leibnitz theorem and applications. Taylor’s and Maclaurin's series (without Proof). Functions of two or more variables, limit and continuity, partial derivatives.
Total differential and differentiability, derivatives of composite and implicit functions.
UNIT V- Differential Calculus-II Total: 8 hours
Higher order partial derivatives. Homogeneous functions and applications, Euler's Theorem, Jacobians,. Maxima-minima of function of two variables. Lagrange's method of undetermined multipliers. Differentiation under integral sign (Leibnitz rule). Curvature, asymptotes, curve tracing.
4. Text Book(s):
5. Reference Book(s):
R1: Erwin, “Advanced Engineering Mathematics”, 9th Edition, John Wiley & Sons, 2006.
R2: Peter.V.O.Neil, Advanced Engineering Mathematics. Canada: Thomson, 2007.
R3: R.K.Jain and S.R.K.Iyengar, Advanced Engineering Mathematics. 3ed, NarosaPublishers, 2009
R4: H. K Dass, “Advanced engineering mathematics”, 8th Edition, S. Chand, 2008
R5: Jain Iyengar, “Advanced Engineering Mathematics”, 3rd Edition, Narosa Publishers, 2007.
