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math2.html
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<title>Mathematics II</title>
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<h1>Mathematics II</h1>
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<h2>Syllabus</h2>
<h5>Module 1: (16 Lecture hours)</h5>
<p>System of Linear equations, Gauss elimination, Solution by LU decomposition, Determinant, Rank of a matrix, Linear independence, Consistency of linear system, General form of solution.<br>
Vector spaces, Subspaces, Basis and dimension, Linear transformation, Rank-nullity theorem, Inner-product, Orthogonal set, Gram-Schmidt orthogonalisation, Matrix representation of linear transformation, Basis changing rule.<br>
Types of matrices and their properties, Eigenvalue, Eigenvector, Eigenvalue problems, Cayley-Hamiltonian theorem and its applications, Similarity of matrices, Diagonalisation, Quadratic form, Reduction to canonical form.</p>
<h5>Module 2: (13 Lecture hours)</h5>
<p>Ordinary Differential Equations (ODE): Formation of ODE, Existence and uniqueness solution of first order ODE using examples, Methods of solutions of first order ODE, Applications of first order ODE.<br>
Linear ODE: Homogenous equations, Fundamental system of solutions, Wronskian, Solution of second order non-homogeneous ODE with constant coefficients: Method of variation of parameters, Method of undetermined coefficients, Euler-Cauchy equations, Applications to engineering problems, System of linear ODEs with constant coefficients.</p>
<h5>Module 3: (10 Lecture hours)</h5>
<p>Gamma function, Beta function: Properties and evaluation of integrals.<br>
Laplace transform, Necessary condition for existence, General properties, Inverse Laplace transform, Transforms of derivatives and integrals, Differentiation and Integration of transform, Unit-step function, Shifting theorems, Transforms of periodic functions, Convolution, Solution of differential equations and integral equations using Laplace transform.</p>
<h3>References:</h3>
<ol>
<li>H. Anton, I. Bivensand S. Davis, Calculus, 10th edition, New York: John Wiley & Sons, 2015.</li>
<li>G. B. Thomas, M.D. Weirand J. Hass, Thomas’ Calculus, 12th edition, New Delhi, India: Pearson Education, 2015.</li>
<li>E. Kreyszig, Advanced Engineering Mathematics, 10th edition, New York: John Wiley & Sons, 2015. [click here for solution manual]</li>
<li>Apostol, Calculus Vol 1, 1st ed. New Delhi: Wiley, 2014.</li>
</ol>
</div>
<hr>
<div>
<h3 style="text-align: center;">Subject Content</h3>
<h4>PPTs/NOTES</h4>
<p style="color: #7579e7"><em>"Need to cram last minute? The attatched PDF contains notes for all the 3 modules. You’re welcome, we saved your butts :)"</em></p>
<div>
<details>
<summary style="margin: 10px 0 10px 0;">NOTES (Module 1, 2 & 3)</summary>
<ul>
<li>Linear Equations anad Matrices<a href="#" download><button type="button" class="btn btn-indigo btn-md" >(Download PDF)</button></a></li>
<li>Matrix Operations<a href="#" download><button type="button" class="btn btn-indigo btn-md" >(Download PDF)</button></a></li>
<li>Differential Equations<a href="#" download><button type="button" class="btn btn-indigo btn-md" >(Download PDF)</button></a></li>
<li>DE and Curves<a href="#" download><button type="button" class="btn btn-indigo btn-md" >(Download PDF)</button></a></li>
<li>Laplace Transforms<a href="#" download><button type="button" class="btn btn-indigo btn-md" >(Download PDF)</button></a></li>
</ul>
</details>
</div>
<h4 style="margin-top: 20px;">Video Lectures</h4>
<div>
<details>
<summary style="margin: 10px 0 10px 0;">Module 1</summary>
<ul>
<li><a href="https://www.youtube.com/watch?v=4QFsiXfgbzM&list=PLbRMhDVUMngeVrxtbBz-n8HvP8KAWBpI5" target="_blank">Engineering Mathematics II</a>
<p>NOTE: <strong>Start from Lecture- 37</strong>. Few videos in this playlist are not necessary and this lecture series is not in the same order as that of our syllabus; cross check with syllabus</p>
<div class="iframe-container">
<iframe width="560" height="315" src="https://www.youtube.com/embed/videoseries?list=PLbRMhDVUMngeVrxtbBz-n8HvP8KAWBpI5" frameborder="0" allow="autoplay;encrypted-media" allowfullscreen></iframe>
</div></li>
<li><a href="https://www.youtube.com/playlist?list=PLU6SqdYcYsfK-Gk_te5_dgSoWyUlUMOUh" target="_blank">Gauss elimination, Solution by LU decomposition</a>
<p>NOTE: Few videos in this playlist are not necessary and this lecture series is not in the same order as that of our syllabus; cross check with syllabus</p>
<div class="iframe-container">
<iframe width="560" height="315" src="https://www.youtube.com/embed/videoseries?list=PLU6SqdYcYsfK-Gk_te5_dgSoWyUlUMOUh" frameborder="0" allow="autoplay;encrypted-media" allowfullscreen></iframe>
</div></li>
<li><a href="https://www.youtube.com/watch?v=ccaHV-ukK2o" target="_blank">Rank Of Matrix</a>
<div class="iframe-container">
<iframe width="560" height="315" src="https://www.youtube.com/embed/ccaHV-ukK2o" frameborder="0" allow="accelerometer; autoplay; clipboard-write; encrypted-media; gyroscope; picture-in-picture" allowfullscreen></iframe>
</div></li>
<li><a href="https://www.youtube.com/playlist?list=PLU6SqdYcYsfJOGZdxUpDk3w9o-w94-RoG" target="_blank">Vector Space</a>
<p>NOTE: Few videos in this playlist are not necessary and this lecture series is not in the same order as that of our syllabus; cross check with syllabus</p>
<div class="iframe-container">
<iframe width="560" height="315" src="https://www.youtube.com/embed/videoseries?list=PLU6SqdYcYsfJOGZdxUpDk3w9o-w94-RoG" frameborder="0" allow="autoplay;encrypted-media" allowfullscreen></iframe>
</div></li>
</ul>
</details>
<details>
<summary style="margin: 10px 0 10px 0;">Module 2 & 3</summary>
<ul>
<li><a href="https://www.youtube.com/watch?v=OET0qwat15o&list=PLdM-WZokR4tbGKbeK8fDIdEN0NEcvAQlC" target="_blank">Ordinary Differential Equation</a>
<p>NOTE: Few videos in this playlist are not necessary and this lecture series is not in the same order as that of our syllabus; cross check with syllabus</p>
</li>
<li><a href="https://www.youtube.com/watch?v=4QFsiXfgbzM&list=PLbRMhDVUMngeVrxtbBz-n8HvP8KAWBpI5" target="_blank">ODE</a>
<p>NOTE: <strong>Start from Lecture- 51</strong>. Few videos in this playlist are not necessary and this lecture series is not in the same order as that of our syllabus; cross check with syllabus</p>
<div class="iframe-container">
<iframe width="560" height="315" src="https://www.youtube.com/embed/videoseries?list=PLbRMhDVUMngeVrxtbBz-n8HvP8KAWBpI5" frameborder="0" allow="autoplay;encrypted-media" allowfullscreen></iframe>
</div>
</li>
<li><a href="https://www.youtube.com/playlist?list=PLU6SqdYcYsfKBwI-gt4_3stvN0esrPCAq" target="_blank">Gamma & Beta Function</a>
<p>NOTE: Few videos in this playlist are not necessary and this lecture series is not in the same order as that of our syllabus; cross check with syllabus</p>
<div class="iframe-container">
<iframe width="560" height="315" src="https://www.youtube.com/embed/videoseries?list=PLU6SqdYcYsfKBwI-gt4_3stvN0esrPCAq" frameborder="0" allow="autoplay;encrypted-media" allowfullscreen></iframe>
</div>
</li>
<li><a href="https://www.youtube.com/playlist?list=PLU6SqdYcYsfILCRFpIM3fQdVIzOo71snJ" target="_blank">Laplace Transform</a>
<p>NOTE: Few videos in this playlist are not necessary and this lecture series is not in the same order as that of our syllabus; cross check with syllabus</p>
<div class="iframe-container">
<iframe width="560" height="315" src="https://www.youtube.com/embed/videoseries?list=PLU6SqdYcYsfILCRFpIM3fQdVIzOo71snJ" frameborder="0" allow="autoplay;encrypted-media" allowfullscreen></iframe>
</div>
</li>
</ul>
</details>
</div>
<h4 style="margin-top: 20px;">Question Paper</h4>
<div>
<details>
<summary style="margin: 10px 0 10px 0;">Previous Year Paper</summary>
<ul>
<li>END SEM/T1/T2 (.zip file)<a href="#" download><button type="button" class="btn btn-indigo btn-md" >(Download ZIP)</button></a></li></li>
</ul>
</details>
</div>
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