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math1.html
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<!doctype html>
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<title>Mathematics I</title>
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<div class="syllabus">
<h1>Mathematics I</h1>
<!--<img src="images/math1-page-img.jpg" alt="LAB" class="math-img">-->
<h2>Syllabus</h2>
<h5>Module 1: (13 Lecture hours)</h5>
<p>Real valued function of real variable: Limit, Continuity, Differentiability, Local maxima and local minima, Curve sketching, Mean value theorems, Higher order derivatives, Taylor's theorem, Integration, Area under the curve, Improper integrals.<br>
Function of several variables: Limit, Continuity, Partial derivatives, Partial differentiation of composite functions, Differentiation under the integral sign, Local maxima and local minima, Saddle point, Taylor’s theorem, Hessian, Method of Lagrange multipliers.</p>
<h5>Module 2: (13 Lecture hours)</h5>
<p>Numerical sequences, Cauchy sequence, Convergence, Numerical series, Convergence, Tests for convergence, Absolute convergence, Sequence and series of functions, point-wise and uniform convergence, Power series, Radius of convergence, Taylor series.<br>
Double integral, Triple integral, Change of variables, Jacobian, Polar coordinates, Applications of multipleintegrals.</p>
<h5>Module 3: (13 Lecture hours)</h5>
<p>Parameterised curves in space, Arc length, Tangent and normal vectors, Curvature and torsion, Line integral, Gradient, Directional derivatives, Tangent plane and normal vector, Vector field, Divergence, Curl, Related identities, Scalar potential, Parameterised surface, Surface integral, Applications of surface integral, Integral theorems: Green's Theorem, Stokes' theorem, Gauss’ divergence theorem, Applications of vector integrals..</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>Limits and Continuity<a href="#" download><button type="button" class="btn btn-indigo btn-md" >(Download PDF)</button></a></p></li>
<li>Second Derivarive<a href="#" download><button type="button" class="btn btn-indigo btn-md" >(Download PDF)</button></a></p></li>
</ul>
</details>
</div>
<h4 style="margin-top: 20px;">Video Lectures</h4>
<p><a href="https://www.youtube.com/c/khanacademy/playlists?view=50&sort=dd&shelf_id=6">Khan Academy</a><span>; Here you can find all the contents required for Mathematics I, but its randomly distributed; cross check with your syllabus</span></p>
<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 I</a>
<p>NOTE: Few videos in this playlist are not necessary (After Lecture- 37 its Math II) 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/watch?v=ZXNrEI5lIWs&list=PLU6SqdYcYsfKqEg7zbrek8fh8TbxayiGr" target="_blank">Function of several variables</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=PLU6SqdYcYsfKqEg7zbrek8fh8TbxayiGr" frameborder="0" allow="autoplay;encrypted-media" allowfullscreen></iframe>
</div></li>
<li><a href="https://www.youtube.com/watch?v=NpR91wexqHA" target="_blank">Maxima And Minima of Two Variables Function</a>
<div class="iframe-container">
<iframe width="560" height="315" src="https://www.youtube.com/embed/NpR91wexqHA" frameborder="0" allow="accelerometer; autoplay; clipboard-write; encrypted-media; gyroscope; picture-in-picture" allowfullscreen></iframe>
</div></li>
</ul>
</details>
<details>
<summary style="margin: 10px 0 10px 0;">Module 2</summary>
<ul>
<li><a href="https://www.youtube.com/watch?v=vfg1mmsSMMM&list=PLU6SqdYcYsfJqbZvQECrwnlQrp4fg6isX" target="_blank">Numerical sequences</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=PLU6SqdYcYsfJqbZvQECrwnlQrp4fg6isX" frameborder="0" allow="autoplay;encrypted-media" allowfullscreen></iframe>
</div></li>
<li><a href="https://www.youtube.com/watch?v=0pv0QtOi5l8&list=PLSQl0a2vh4HB3NJGQ_EYP1qFEVdN9Ro68" target="_blank">Double and triple integrals</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=PLSQl0a2vh4HB3NJGQ_EYP1qFEVdN9Ro68" frameborder="0" allow="autoplay;encrypted-media" allowfullscreen></iframe>
</div></li>
<li><a href="https://www.youtube.com/watch?v=YXmeH1yevkk&list=PLU6SqdYcYsfLLtR4v24_ZIg6uQA9HtNSw">Jacobian</a></li>
</ul>
</details>
<details>
<summary style="margin: 10px 0 10px 0;">Module 3</summary>
<ul>
<li><a href="https://www.youtube.com/watch?v=n4JJ3fNKHUc&list=PLU6SqdYcYsfL7EIZrqNVMyQ5xMbCu18Mf" target="_blank">Arc Length</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=PLU6SqdYcYsfL7EIZrqNVMyQ5xMbCu18Mf" frameborder="0" allow="autoplay;encrypted-media" allowfullscreen></iframe>
</div></li>
<li><a href="https://www.youtube.com/playlist?list=PLU6SqdYcYsfJz9FAzbgocIjlkw4NXAar-" target="_blank">Vector Calculus</a>
<p>This playlist on vector calculus consists of following topics,<br>
i)Concept of vector point function and vector differentiation.<br>
ii)Gradient of a scalar field and directional derivative.<br>
iii)Divergence and curl of a vector field.<br>
iv)Line integral of vector field.<br>
v)Application of line integrals.<br>
vi)Greens theorem.<br>
vii)Stokes theorem.<br>
viii)Gauss divergence theorem.</p>
<div class="iframe-container">
<iframe width="560" height="315" src="https://www.youtube.com/embed/videoseries?list=PLU6SqdYcYsfJz9FAzbgocIjlkw4NXAar-" frameborder="0" allow="autoplay;encrypted-media" allowfullscreen></iframe>
</div></li>
</ul>
</details>
</div>
<h4 style="margin-top: 20px;">Question paper/Tutorial</h4>
<div>
<details>
<summary style="margin: 10px 0 10px 0;">Previous Year Questions</summary>
<ul>
<li>END SEM (.zip file)<a href="#"><button type="button" class="btn btn-indigo btn-md" >(Download ZIP)</button></a></li>
</ul>
</details>
<details>
<summary style="margin: 10px 0 10px 0;">Tutorials</summary>
<ul>
<li>Tutorial 1 (<a href="#">Solution here!!</a>)<a href="#"><button type="button" class="btn btn-indigo btn-md" >(Download PDF)</button></a></li>
<li>Tutorial 2<a href="#"><button type="button" class="btn btn-indigo btn-md" >(Download PDF)</button></a></li>
<li>Tutorial 3 (<a href="#">Solution here!!</a>)<a href="#"><button type="button" class="btn btn-indigo btn-md" >(Download PDF)</button></a></li>
<li>Tutorial 4<a href="#"><button type="button" class="btn btn-indigo btn-md" >(Download PDF)</button></a></li>
<li>Tutorial 5<a href="#"><button type="button" class="btn btn-indigo btn-md" >(Download PDF)</button></a></li>
<li>Tutorial 6<a href="#"><button type="button" class="btn btn-indigo btn-md" >(Download PDF)</button></a></li>
<li>Tutorial 7<a href="#"><button type="button" class="btn btn-indigo btn-md" >(Download PDF)</button></a></li>
<li>Tutorial 9<a href="#"><button type="button" class="btn btn-indigo btn-md" >(Download PDF)</button></a></li>
<li>Tutorial 10<a href="#"><button type="button" class="btn btn-indigo btn-md" >(Download PDF)</button></a></li>
<li>Tutorial 11<a href="#"><button type="button" class="btn btn-indigo btn-md" >(Download PDF)</button></a></li>
<li>Tutorial 12<a href="#"><button type="button" class="btn btn-indigo btn-md" >(Download PDF)</button></a></li>
</ul>
</details>
</div>
</div>
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