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It is a matter of great pride that the Institute of Aeronautical Engineering (IARE) is ranked one among the Top 200 best Engineering colleges as per NIRF (National Institutional Ranking Framework), Ministry of Education (MoE), Govt. of India since 2017.

Matrices and Calculus

This course is a foundation for all engineering branches. It includes concepts of Matrices, Eigen Values, Eigen Vectors, Functions of Single, Several Variables, Fourier Series and Multiple Integrals. This course is applicable for simulation, colour imaging processing and optimal solutions in all engineering problems

Ms. B Praveena
Assistant Professor

E-mail: b.praveena@iare.ac.in

ELRV VIDEO YouTube Links:

S.No Topic Name YouTube Links
1 Linear Partial Differential Equations of First Order https://www.youtube.com/watch?v=OUu7qeUPhZQ
2 Partial Differential Equations https://www.youtube.com/watch?v=CBV-hGsexTI
3 Partial Differential Equations by Eliminating Arbitrary Functions https://www.youtube.com/watch?v=sh_K-LCwYq8
4 Non linear Partial Differential Equations of First Order https://www.youtube.com/watch?v=PP6d6w-QJd0
5 Vector Calculus https://www.youtube.com/watch?v=hZ1fRzTXzgQ
6 Vector Calculus Solenoidal Vector https://www.youtube.com/watch?v=zIKlk-dLEzg
7 Vector Calculus Line Integral https://www.youtube.com/watch?v=W8f1c6sMFWY
8 Introduction to Laplace Transform https://www.youtube.com/watch?v=qPtSbvdvAYg
9 Evaluation of Double Integrals in Cartesian Coordinates https://www.youtube.com/watch?v=fePzYKKASHo
10 Evaluation of Triple Integrals in Cartesian Coordinates https://www.youtube.com/watch?v=-tFsRISoeWI
11 Properties of Fourier Transforms https://www.youtube.com/watch?v=o26iUXFJydc
12 Laplace Transform Linear and Shifting Properties https://www.youtube.com/watch?v=CSjaL8M6DHk
13 Laplace Transform Derivatives and Integration https://www.youtube.com/watch?v=Kh0zK8C8YGA
14 Application of Laplace Transforms https://www.youtube.com/watch?v=pW2-VnYz5L4
15 Inverse Laplace Transform of First, Second Shifting Theorems and Change of Scale P https://www.youtube.com/watch?v=Og0g1sIEmws
16 Inverse Laplace Transform of Derivatives, Integrals, Multiplied & Divided by S https://www.youtube.com/watch?v=RUKq8F5aCsY
17 Use of Partial Fractions to Find Laplace Transform https://www.youtube.com/watch?v=4OFecaZ8y-8
18 Gauss Divergence Theorem and Problems https://www.youtube.com/watch?v=FF-DQWLD3Hg
19 Green’s Theorem in a Plane https://www.youtube.com/watch?v=TOduftrOr74
20 Stokes Theorem https://www.youtube.com/watch?v=yfF3Ecu84ms
21 Convolution Theorem https://www.youtube.com/watch?v=gquc2dDaDHs
22 Laplace Transform Periodic Functions and Inverse Laplace Transform Basic Concepts https://www.youtube.com/watch?v=X-Ri_vca-XQ
23 Surface Integrals https://www.youtube.com/watch?v=BaswZzJOcKg
24 Charpits Method https://www.youtube.com/watch?v=d9RCUovgvr0
25 Problem Solving on Charpit’s Method https://www.youtube.com/watch?v=NFIWesjA-sY
26 Problems on Green’s Theorem in a Plane https://www.youtube.com/watch?v=5a5hXALiIGk
27 Problems on Gauss Divergence Theorem https://www.youtube.com/watch?v=JLc-Sj4SKfI
28 Problems on Stoke’s Theorem https://www.youtube.com/watch?v=mMY5d7zrT48
29 Problems on Convolution Theorem https://www.youtube.com/watch?v=3fdHkBVqR0o
30 Double Integral https://www.youtube.com/watch?v=mVyblscv75w
31 Double Integral in Polar Coordinates https://www.youtube.com/watch?v=cG4l5WgkuqQ
32 Volume Integral https://www.youtube.com/watch?v=ZbTBzd0hnEU
33 Problems on Double Integral in Polar Coordinates https://www.youtube.com/watch?v=IQhr4IcCj0Y
34 Change the Order of Integration https://www.youtube.com/watch?v=x1i-GWmlsjY
35 Area of Double Integral https://www.youtube.com/watch?v=A06xtszFW7Q
36 Problems on Change the Order of Integration https://www.youtube.com/watch?v=gtlcJgnVDTg
37 Problems on Area of a Double Integral https://www.youtube.com/watch?v=Zt0F3Yx9-jg
38 Area of Double Integral in Polar Coordinates https://www.youtube.com/watch?v=vy6d5RGtB7c
39 Laplace Transform - Definitions and Terminology https://www.youtube.com/watch?v=dMJcdH66VMI
40 Rank of a Matrix https://www.youtube.com/watch?v=RVPrU80KfBM
41 Echelon Form of a Matrix https://www.youtube.com/watch?v=IjmDlzaxdIw
42 Normal Form of a Matrix https://www.youtube.com/watch?v=rcIZuVwajkU
43 Matrices Definitions With Examples https://www.youtube.com/watch?v=oGQoUawcnrI
44 Jacobian Problems https://www.youtube.com/watch?v=y7en3KMfcBA
45 Fourier Series Problems https://www.youtube.com/watch?v=VmCTQXectk4
46 Fourier Series https://www.youtube.com/watch?v=le-YpTWJkDs
47 Half Range Fourier Series Problems https://www.youtube.com/watch?v=r7KecsL6L0w
48 Fourier Series of fx Defined in C1 C + 2l https://www.youtube.com/watch?v=5sY98iv4hfs
49 Fourier Series Problems in (0,l) https://www.youtube.com/watch?v=pecBX1tEmAg
50 Cayley Hamilton Theorem Problems https://www.youtube.com/watch?v=H2IQRy8nulI
51 Eigen Values and Eigen Vectors Problems for Distinct Roots https://www.youtube.com/watch?v=gkYeFsbfyRA
52 Linearly Independent and Independent Vectors https://www.youtube.com/watch?v=8mwFXMHxMUw
53 Eigen Values and Eigen Vector Problems for 22matrix https://www.youtube.com/watch?v=WD9F1LT-tWw
54 Eigen Value Problems https://www.youtube.com/watch?v=rj0ya37yw9o
55 Rolle’s Theorem Problems https://www.youtube.com/watch?v=vFX6z19n7nU
56 Lagrange’s Theorem Problems https://www.youtube.com/watch?v=fC4hZLAxGgo
57 Lagrange's Theorem Problems https://www.youtube.com/watch?v=nc2_bGbwW9w
58 Cauchy's Theorem Problem https://www.youtube.com/watch?v=KynvdGmqIws
59 Definitions of Matrices https://www.youtube.com/watch?v=7xnZKQXmw9o
60 Definitions on Eigen values and Eigen vector https://www.youtube.com/watch?v=kWxoBhAdX3k
61 Definitions on Functions of Single and Several Variables https://www.youtube.com/watch?v=MyYAmODguvc
62 Definitions on Fourier Series https://www.youtube.com/watch?v=gAEVBnnmhM4
63 Question Bank Discussion on Module I https://www.youtube.com/watch?v=P5JA5w1Vkio
64 Question Bank on Fourier Series https://www.youtube.com/watch?v=RFvAj_DS_Zc
65 Question Bank Discussion on Functions of Single and Several Variables https://www.youtube.com/watch?v=k2rJSgQCwv8
66 Outcome Based Education https://www.youtube.com/watch?v=SzFnjmWiCc0
67 Diagonalization of a matrix https://www.youtube.com/watch?v=QqeCVRIXHcg
68 Problem on Diagonalization of a matrix for Distinct Eigen Values https://www.youtube.com/watch?v=5sYPD_51FAM
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