Dear Students, you all are requested to kindly go through the books as given in your course syllabus. These notes have been prepared from the same books (taking in to account the syllabus of the course) but there may be some useful information (available in those book) that may be missing in these lecture notes. In any case if you are reading these notes then for any comments, suggestions or error you can contact me at:
Ankush Pathania, Room - 207, G Block, First Floor, Department of Mathematics, apathania@thapar.edu
Kindly note that these lecture notes were prepared first in 2019 and then revised/modified every year till 2021. But after 2021 due to engagement in other institutional work I am not able to revise/modify these lecture notes. However, they will serve the purpose for which they were prepared. But still you are requested to kindly check the latest syllabus and guidelines of Mathematics - II (now Differential Equations and Linear Algebra, UMA023) on the LMS.
Note: The course has been renamed as Differential Equations and Linear Algebra (UMA023) from this session (2024-25). Some minor changes have been there in the Syllabus of UMA023. For more recent information and updates of this course UMA023 kindly check LMS on regular basis.
Official old google site of Mathematics - II (UMA004)
Overview of the Course (Kindly check the LMS for the latest evaluation scheme)
Questions for Practice (For practice students can try the questions from the books as mentioned in this document)
Previous year Papers with solution and marking scheme.
Lectures and Video content of other faculty
Official Video Lectures of Mathematics - II (UMA004) (Differential equations by Dr Parimita, Laplace Transform, Fourier Series and Linear Algebra by Dr Kavita)
Old video recordings of my online lecture class, COE19-22, (Session 2020-21, Even)
Old Video recordings of my online lecture class, ELE4-5+ECM2 (Session 2020-21, Even)
Unit 1 (Ordinary Differential Equations)
For videos: 1. You can watch Official Video Lectures of Mathematics - II (UMA004)
2. Also, you can watch (for portion Lecture notes 10 onwards) the online class recordings of COE19-22 or ELE1-5+ECM2 (2020-21, Even)
1. Lecture Notes 1 & 2_New (General Overview, Variable Separable method, Equations Reducible to Separable Form)
2. Lecture Notes 3 & 4_New (Homogeneous DE, Non-Homogeneous DE, Exact DE)
3. Lecture Notes 5 & 6_New (Integrating Factor to make DE exact, Finding Integrating factor by Inspection, Leibnitz DE, Bernoulli DE)
Note: 1. All the topics that are in Bold are excluded in the syllabus of UMA023.
2. Syllabus covered up to Lecture Notes 6 is now under "Review of First order DE" in the course UMA023
4. Lecture Notes 7_New (Second Order Linear Differential equations, Some Theorems and Results)
5. Lecture Notes 8 & 9_New (Use of Known Solution to Find Other, HDE with Constant Coefficients, Cauchy Euler HDE, Legendre HDE)
6. Lecture Notes 10 & 11_New (Method of Undetermined Coefficients (MOUC))
7. Lecture Notes 12_New (Method of Variation of Parameters (MOVP), Cauchy Euler NHDE, Legendre NHDE)
8. Lecture Notes 13_New (Proof of Lemma 1 and Lemma 2) (OPTIONAL)
9. Lecture Notes 14_New (Application of DE: Electric circuits (LRC Circuits). New topic added: Vibrations in the Mechanical system (problems of mass attached to spring). Lecture notes to be added
10. Lecture Notes 15_New (Operator Method a new topic added in the course UMA023. Lecture Notes to be added)
Unit 2 (Laplace Transformation and Laplace Transform)
For videos: 1. You can watch the online class recordings of COE19-22 or ELE1-5+ECM2 (2020-21, Even)
2. For the other unofficial Video lectures of this unit (up to Lecture Notes 20) you can check the YouTube Playlist. In this playlist the last few articles have also been added from the online class recordings.
10. Lecture Notes 15_New (Laplace Transform (LT) Overview, Piecewise Continuous Function and Exponential Order)
11. Lecture Notes 16 & 17_New (Formulas of LT, first three properties of LT, First shifting property (P1), Differentiation of LT (P2), Integration of LT (P3))
12. Lecture Notes 18 & 19_New (Formulas of Inverse LT, Inverse LT of First three properties of LT)
13. Lecture Notes 20_New (Property 4 (P4) LT of derivative and Property 5 (P5) LT of integral, Application of LT to Differential Equations, Inverse LT of P5)
14. Lecture Notes 21 & 22_New (Qs of Convolution Theorem and Second Shifting Property)
15. Lecture Notes 23 & 24_New (Proof of Convolution theorem and Second shifting theorem, Dirac - Delta function and some other examples) (OPTIONAL)
Unit 3 (Fourier Series)
For videos: 1. You can watch the online class recordings of COE19-22 or ELE1-5+ECM2 (2020-21, Even)
2. For other unofficial Video lectures of this unit you can check the YouTube Playlist
16. Lecture Notes 25 & 26_New (Fourier Series, Fourier Series of Odd/Even Function)
17. Lecture Notes 27 & 28_New (Convergence of Fourier Series, Half Range Fourier Sine and Cosine Series)
18. Lecture Notes 29 & 30_New (Derivation of the Heat Equation)
19. Lecture Notes 30 & 31_New (Derivation of the Wave Equation)
Unit 4 (Linear Algebra)
For videos: 1. You can watch the online class recordings of COE19-22 or ELE1-5+ECM2 (2020-21, Even)
2. For other unofficial Video lectures you can check the YouTube Playlist
20. Lecture Notes 32 to 34_New (Row Reduced Echelon Form, Rank and System of Linear Equations)
21. Lecture Notes 34 to 36_New (Vector space and Subspace)
22. Lecture Notes 36 to 39_New (Span of the Set, LI & LD set of vectors, Basis and Dimensions)
23. Lecture Notes 39 to 40_New (Linear Transformation, Eigenvalues and Eigenvectors)