Differential Equations and Linear Algebra
Teacher
Mrs. Saubhagyalaxmi Singh
Category
Core Courses
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Course Name : Differential Equations and Linear Algebra
Code(Credit) :CUTM1001 (2-0-1)
Course Objectives
• Introduce students to how to solve linear Differential Equations with different methods.
• To solve the system of linear equations appearing in the problems of electrical engineering, mechanical engineering etc.
• To use Eigen values and Eigen vectors in Control theory, vibration analysis, electric circuits, advanced dynamics problems.
• Introduce students how to solve first order and second order differential equations
Course Outcomes
Upon successful completion of this course, students will be able to:
| COs | Course Outcomes | Mapping with COs with POs
(High-H, Low-L, Medium-M) |
| CO1 | Understanding and knowledge is the importance of linear functions in mathematics. | PO1(H) |
| CO2 | Learn fundamental and analytical concepts of ODE theories where and how such equations arise in applications to scientific and engineering problems. | PO1(H) |
| CO3 | Solving systems of linear equations using Gauss- elimination to reduce to echelon form. | PO1(H), PO2(H) |
| CO4 | Have deep understanding to handle various types of problems using different types of methods. | PO1(H), PO2(H), PO5(H) |
Course Syllabus
Module-I:
First order linear differential equations and its applications
Project-1: Some applications of differential equations in RL-RC electrical circuit problems
Module-II:
Second order linear homogeneous differential equations (Real roots, Real equal roots, Complex conjugate roots) and its applications.
Project-2: RLC Circuit, Pendulum
Module-III:
Second order linear non-homogeneous differential equations, Finding particular integral consisting of exponential, trigonometric (Sine, cosine) using inverse operator method
Project-3: Simple mass-spring system, Damped vibration system
Module-IV:
Basic concepts of a matrices, solution of linear system of equations by Gauss elimination method, linearly independent and dependent of a vectors, rank of a matrix.
Project 4: Report on finding the traffic flow in the net of one-way streets
Module-V:
Determinants and Cramer’s Rule, Fundamental theorem of linear system of equations.
Module-VI:
Eigenvalues and Eigen vectors of a matrix.
Project 5: (i)Find the limit states of the Markov process model.
(ii)Find the growth rate in the Leslie model
Module-VII:
Symmetric, Skew-Symmetric , Orthogonal Matrices and Properties
Project 6: To make a report to show that the product of two orthogonal matrices is orthogonal, and so is the inverse of an orthogonal matrix. What does this mean in terms of rotations?
Text Books:
1. Advanced engineering mathematics by Erwin Kreyszig, 8th edition
Chapter-6 (6.1-6.6), Chapter-7 (7.1,7.3)
2. Higher Engineering by B.V. Ramana
Chapter-8(8.1,8.2,8.9,8.10,8.21), Chapter-9 (9.2,9.3,9.5)
Reference Books:
1. J. Sinha Roy and S. Padhy, A Course of Ordinary and Partial Differential Equations, Kalyani Publishers, New Delhi.
2. G.B. Thomas, M.D. Weir, J.R. Hass, Thomas’ Calculus, Pearson Publication.
3. R.G. Bartle, D.R. Sherbert, Introduction to Real Analysis, Wiley Publication
Session 3
Applications of First order linear differential equations( Kirchhoff's law)
Kirchhoff's law
Session 6
Second order linear homogeneous differential equations
Second order linear homogeneous differential equations
Session 7
Solution of Second order linear homogeneous differential equations
Second order linear homogeneous differential equations
Session 8
Applications of Second-Order Differential Equations
Pdf -Applications of Second-Order Differential Equations
Session 11
Second order linear non-homogeneous differential equations
Second order linear non-homogeneous differential equations
Session 12
Finding particular integral consisting of exponential
Finding particular integral consisting of exponential
Session 13
Finding particular integral consisting of trigonometric (Sine, cosine) using inverse operator method
https://www.youtube.com/watch?v=r6mkGRLpm_w
Session 14 & 15
Project-3 (2 hrs)
Simple mass-spring system
https://www.youtube.com/watch?v=FJBPNJR2QJU
Session 16
Session 17
Linear system of equations by Gauss elimination method
Pdf-Linear algebra
https://www.youtube.com/watch?v=2j5Ic2V7wq4
Session 18
Linearly independent and dependent of a matrices, Rank of a matrix
Pdf-http://courseware.cutm.ac.in/wp-content/uploads/2020/06/Linear-Algebra-3.pdf
https://www.youtube.com/watch?v=uQhTuRlWMxw
https://www.youtube.com/watch?v=k7RM-ot2NWY
Session 19 & 20
Project-4 (Flip Class) (2 hrs)
Report on finding the traffic flow in the net of one-way streets
Session 21
Determinants of a matrix, Cramer’s Rule
Pdf-Determinant
Pdf-Linear algebra
https://www.youtube.com/watch?v=Ip3X9LOh2dk
Session 22
Conditions of Existence and Uniqueness of Solutions
https://www.slideshare.net/Pokar/system-of-linear-equations-45700370
https://www.youtube.com/watch?v=8JhhMhN_45Q
Session 24
Properties of Eigenvalues and Eigen Vectors
Pdf-Eigen values and eigen functions
https://www.youtube.com/watch?v=8F0gdO643Tc
Session 25
Some application problems of Eigenvalues and Eigen Vectors
Pdf-Eigen values and eigen functions
https://www.youtube.com/watch?v=R13Cwgmpuxc
Session 26 & 27
Project-5 (Flip Class) (2hrs)
(i)Find the limit states of the Markov process model.
(ii)Find the growth rate in the Leslie model
Session 28
Symmetric, Skew-Symmetric and Orthogonal Matrices
Pdf-Symmetric matrix
https://www.youtube.com/watch?v=v5abfTlztTc
Session 29
Properties of Symmetric, Skew-Symmetric and Orthogonal Matrices
https://www.youtube.com/watch?v=v5abfTlztTc
Session 30
Problems of Symmetric, Skew-Symmetric and Orthogonal Matrices
https://www.youtube.com/watch?v=v5abfTlztTc
Session 31 & 32
Project-6 (Flip class) (2 hrs)
To make a report to show that the product of two orthogonal matrices is orthogonal, and so is the inverse of an orthogonal matrix. What does this mean in terms of rotations?
Case Studies
Case Studies
Our Main Teachers
Mrs. Saubhagyalaxmi Singh
Assistant Professor in School of Applied Sciences, Department of Mathematics
VIEW PROFILEMrs. Saubhagyalaxmi Singh works as an Assistant Professor, Department of Mathematics, Centurion University of Technology and Management. She has over 6 years of teaching experience with exposure to Utkal University, Bhubaneswar, Department of Mathematics. She has published 6 papers communicated to different International Journals. She has guided 7 M.Sc. projects in her area. She has […]