MathematicsI
SYLLABUS
Semester – I
School of Engineering & Technology Course Outline


Course Title: Engineering Mathematics I Course Code 23BTC0MA11T 

Semester: I 
Academic Year: 2023 
Core/Elective: Core 
Credits: 4 
Course Designed by: Dr. Manimala Email: manimala@sushantuniversity.edu.in 
Course Instructor: Dr. Manimala Email: manimala@sushantuniversity.edu.in 

Prerequisites: Basic concept of Matrix, Calculus, Sequence & Series and Trigonometry 
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

PO1 
PO2 
PO3 
PO4 
PO5 
PO6 
PO7 
PO8 
PO9 
PO10 
PO11 
PO12 
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PSO2 
PSO3 
CO1 
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CO2 
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CO3 


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CO4 



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CO5 

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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, Echelonform 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. Nonhomogeneous 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 CayleyHamilton 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 CalculusI 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 CalculusII Total: 8 hours
Higher order partial derivatives. Homogeneous functions and applications, Euler's Theorem, Jacobians,. Maximaminima 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):
 N.P.Bali and Manish Goyal, “A Text book of Engineering Mathematics”, Laxmi Publications (P) Limited, 2010
 Dr. B. S. Grewal, “A text book of Higher Engineering Mathematics”. 40 ed. Khanna Publishers, 2009
 B.V.Ramana, “A text book of Mathematics”,Tata MC Graw Hill, 2009
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.