# MAT101 / Mathematics

## Syllabus

{% file src="<https://4020386663-files.gitbook.io/~/files/v0/b/gitbook-x-prod.appspot.com/o/spaces%2F3ZYLT7QIVGVNDP2woYe4%2Fuploads%2FK3ubwUUMs443Np5VaE3H%2FMAT101-Syllabus-BTECH-IT.pdf?alt=media&token=4c78b2ff-a56e-4aab-962a-877a9037d829>" %}

View: [CONCEPT-Distribution-Module-wise](https://drive.google.com/file/d/1J1yM1OFYvGASlZ6JvT6KxPJpzMrlGT1C/view?usp=drive_link)

{% embed url="<https://drive.google.com/file/d/1J1yM1OFYvGASlZ6JvT6KxPJpzMrlGT1C/view?usp=drive_link>" %}

### References:

{% embed url="<https://dpvipracollege.ac.in/wp-content/uploads/2022/12/h.k.dass_.pdf>" %}
Advanced Engineering Mathematics by HK Das (S Chand Publications)
{% endembed %}

***

## Resources

<details>

<summary>M1: Differential Calculus</summary>

\[⤓] [L1-Successive\_Differentiation-1](https://drive.google.com/file/d/1gglydM1YyNlwvjBc_Lydv4kmtqdIJqIh/view?usp=sharing)

\[⤓][ L2-Successive\_Differentiation-1](https://drive.google.com/file/d/12AK3zf2gqmYXyA02k88esDE2fWUTd5AC/view?usp=drive_link)

\[⤓] [L3-Successive\_Differentiation-1](https://drive.google.com/file/d/13SbAc3b11tsMGzALQ8yeVR0N81aYmFug/view?usp=drive_link)

\[⤓] [L4-Leibnitz-Theorem](https://drive.google.com/file/d/1xHa5S9QzqfoeSesHk1E5k9mGshH_PRW1/view?usp=drive_link)

\[⤓] [L5-Leibnitz-Theorem](https://drive.google.com/file/d/1e-NH9Jg5nZ6WXR0Ujaw3UwFth3_KUs2A/view?usp=drive_link)

\[⤓] [L6-Rolles-Theorem](https://drive.google.com/file/d/15lSHJ8tgG4rE1Q_n_Yb6UWA0glv1Jy6-/view?usp=drive_link)

\[⤓] [L7-MeanValueTheorem](https://drive.google.com/file/d/16IhQYH9MtDi_vbrtGJ9JnSurPFYDditA/view?usp=drive_link)

\[⤓] [L8-MeanValueTheorem](https://drive.google.com/file/d/1wlByo7os9tasz6CEv-vus4-T3mwU8WuH/view?usp=drive_link)

\[⤓] [L9-Partial-Differentiaion](https://drive.google.com/file/d/1RZL7fN1AaxqAU8C5Huw7dLmlqIUA9RM5/view?usp=drive_link)

\[⤓][ L10-Maxima-Minima](https://drive.google.com/file/d/1vyEg0ZyHAxyyKQVyngNHRjSRq6ThLYe4/view?usp=drive_link)

\[ ▶︎ ] [L1-Partial Differentiation (Basic Concepts)](https://youtu.be/_T7rcF1mrIw?si=r_EgCLw2p-CKQtWq)

\[ ▶︎ ] [L2-Partial Differentiation (Basic Questions)](https://youtu.be/YtWqxK-3TQk?si=D3dWUyhtqMxWY-un)

\[ ▶︎ ] [L3-Partial Derivative of 1st Order - Part 1](https://youtu.be/FtKWs--F1pc?si=s8E5rKVxZ4kGI-DF)

\[ ▶︎ ] [L4-Partial Derivative of 1st Order - Part 2](https://youtu.be/YZXI_iBV4v4?si=AtfJhucx07wwbqEg)

\[ ▶︎ ] [L5-Partial Derivative of 1st Order - Part 3](https://youtu.be/_iZAhNZTPww?si=UQY_yhG9p-9aC3hd)

\[ ▶︎ ] [L1-Successive Differentiation (Algebraic Fn) ](https://youtu.be/SYjzQypOtiw?si=IkuYHz9npqtwNX-o)

\[ ▶︎ ] [L2-Successive Differentiation (nth Order Deriv. of Trigono Fn)](https://youtu.be/3o-QLMvD2dg?si=ncdADkwuhNOfU00N)

\[ ▶︎ ] [L3-Successive Differentiation (Leibnitz Theorem)](https://youtu.be/PHIGwMmi7iU?si=DQwLUq3Uau4pb-Wr)

\[ ▶︎ ] [L1-Differential Calculus (Rolle's Theorem)](https://youtu.be/bQ_B9cHBYfQ?si=y5VZIiaXIHtNBQGL)&#x20;

\[ ▶︎ ] [L2-Differential Calculus (LMVT) ](https://youtu.be/B_k3cWFoTp4?si=zZMih7mXu8Dh2TXf)

\[ ▶︎ ] [L3-Differential Calculus (Taylor's & Maclaurin's Theorem)](https://youtu.be/Em6cGzwOq-Y?si=9yswxjMP6PcKTK0F)&#x20;

\[ ▶︎ ] [L4-Differential Calculus (Standard Expansions)](https://youtu.be/uYN6AdndsgE?si=JHoiqFKMiZ_NK3PX)

\[ ▶︎ ] [Total Derivatives (Concept & Problems)](https://youtu.be/m1nAHb0wUXg?si=SEKxgQ0ugqJ3lzED)

\[ ▶︎ ] [L1-Maxima & Minima (Appl of Partial Derivative)](https://youtu.be/In3oZPIymm8?si=unne7rIElM60Aftt)

\[ ▶︎ ] [L2-Maxima & Minima (Appl of Partial Derivative)](https://youtu.be/T5HzdeSnlhM?si=Ksvmj4tVU094CDWy)

</details>

<details>

<summary>M2: Integral Calculus</summary>

\[⤓] [L11-Definite-Integral-Beta-Gamma-fn](https://drive.google.com/file/d/1rRN61dTKAH5XepHk37UYfJztrxJVHSLs/view?usp=drive_link)

\[⤓] [L12-RelationInBetaGamma-fn](https://drive.google.com/file/d/1VEW9iGyRoCTmczebJDT4Hn6x9L_vIDh4/view?usp=drive_link)

\[⤓][ L13-Area-of-CartesianCurve](https://drive.google.com/file/d/1QAIYDJbp7dTDuN2dzgCANd0-9OWdtP74/view?usp=drive_link)

\[⤓] [L14-VolOfRevolution](https://drive.google.com/file/d/18K6HOy25OMbr_bDjw-kAp0bAFNrcl_lS/view?usp=drive_link)

\[⤓] [L15-SurfaceOfRevolution](https://drive.google.com/file/d/1DJxz_4MdhM4GkkB2lOCbDXc0zSYV5BMT/view?usp=drive_link)

\[⤓] [L16-MultipleIntegrals](https://drive.google.com/file/d/1FKnZmcm7AE1VqxQiJBMpUu2IhYMbUW6B/view?usp=drive_link)

\[ ▶︎ ] [L1-Beta & Gamma Function (Property)](https://youtu.be/LLX0UjUGL5w?si=NKLYXahN8H_ON2nh)

\[ ▶︎ ][ L2-Beta & Gamma Function (Tricks to Solve Different Function)](https://youtu.be/G01UYZ_YZDA?si=SjFfjSwt0ht9DWDw)

\[ ▶︎ ] [L3-Beta & Gamma Function (Types of Beta function) - Part 1](https://youtu.be/BW1ZsjChbno?si=hJOKXuaTNyVpyqal)

\[ ▶︎ ][ L4-Beta & Gamma Function (Types of Beta function) - Part 2](https://youtu.be/ID5qjCARkL4?si=zmmMzo7atiqe-np7)

\[ ▶︎ ] [Double Integrals (Evaluation of Direct Double Integral)](https://youtu.be/swF628VHQDo?si=PRRGFkGFQ-PeDNI1)

\[ ▶︎ ] [Double Integrals (Cartesian to Polar)](https://youtu.be/3IgY__Hpv1k?si=RRwqCYlzf0JmJRT1)

\[ ▶︎ ] [Double Integrals (Limit is not given (Region))](https://youtu.be/GtgY7Jw8avY?si=SpoUYwwrTAPCUuYb)

\[ ▶︎ ] [Double Integrals (Area by Double Integration)](https://youtu.be/FVZhdEPldIk?si=iE1FXPHk3bxU_0Km)

</details>

<details>

<summary>M3: Vector Calculus</summary>

\[⤓] [L1-Vector-Calculus](https://drive.google.com/file/d/1kXNltRedx7V4HZXhJXV8qEgGpEFc2Hx0/view?usp=drive_link)

\[⤓] [L2-Vector-Calculus](https://drive.google.com/file/d/1KWIK__ZLBJsDrY5QrhICyDMRnIzAItHr/view?usp=drive_link)

\[⤓][ L3-Vector-Calculus](https://drive.google.com/file/d/124Yl1espEwkTbld1Mlc40Pgj4ZMYxkBi/view?usp=drive_link)

\[⤓][ L5-Vector-Calculus](https://drive.google.com/file/d/1mMVB96bhGhfI7ZFi4h4h_9AfXrZrhbRl/view?usp=drive_link)

\[⤓] [L6-Vector-Calculus](https://drive.google.com/file/d/1EebQr1g5elwVPwF9lTrOJfwqv2KdXluR/view?usp=drive_link)

\[⤓] [L7-Vector-Calculus](https://drive.google.com/file/d/1sYf9OiUxv7YyjDJL9EfAb81I0H1aG0Fp/view?usp=drive_link)

\[⤓] [L8-Vector-Calculus](https://drive.google.com/file/d/1SXQ7An-ed1r0qSCPh4OG19U3mPTtkaQ-/view?usp=drive_link)

\[ ▶︎ ] [L1-Vector-Diff. (Gradient & Directional Derivative)](https://youtu.be/NAJuuEKwOIQ?si=q1_oq39XXqGarKan)

\[ ▶︎ ][ L2-Vector-Diff. (Angle between the Normals)](https://youtu.be/GRkThi4L4sU?si=ASYmL09rph9M-THS)

\[ ▶︎ ] [L3-Vector-Diff. (Divergence & Curl)](https://youtu.be/iWW0LVd8bVQ?si=VRkMUpIpYp0uJczP)

\[ ▶︎ ] [L4-Vector-Diff. (One Shot)](https://youtu.be/t7VGyM7jOsU?si=0Uvg6cLrAyRLGQ9g)

\[ ▶︎ ] [L1-Vector-Integration. (Line Integral) - Part 1](https://youtu.be/IE5tAyIQviE?si=HTJHsVtqNZT_ohtq)

\[ ▶︎ ] [L2-Vector-Integration. (Line Integral) - Part 2](https://youtu.be/hPspDNnnAxQ?si=05y_hk2qqhz8_0CM)&#x20;

\[ ▶︎ ] [L3-Vector-Integration. (Green's Theorem)](https://youtu.be/jc0md5xkHYY?si=7MzoLtDZBOiN596v)

\[ ▶︎ ] [L4-Vector-Integration. (Stoke's Theorem)](https://youtu.be/ZYOGVj98UVE?si=3EvpTZp14R4_cjn3)

\[ ▶︎ ] [L5-Vector-Integration. (One Shot)](https://youtu.be/9NIOJICQ6vc?si=OGnsk3orcO1HR7tc)

</details>

<details>

<summary>M4: Matrices</summary>

\[⤓] [L1-Matrices](https://drive.google.com/file/d/1FHexM2UuH23y1ud5LcwYa6fUKHwQKIWb/view?usp=drive_link)

\[⤓][ L2-Matrices](https://drive.google.com/file/d/1zJ7WjpBI60wSZRW0fX84BnbAhHx-3fhE/view?usp=drive_link)

\[⤓] [L3-Matrices](https://drive.google.com/file/d/161NT3nHmzkqT5J1FheGAVA67Gm9Dd7CC/view?usp=drive_link)

\[⤓] [L4-Matrices](https://drive.google.com/file/d/1xCUNz1SMY7lboh6csJFUiVS8YdnvjMX6/view?usp=drive_link)

\[⤓] [L5-Matrices](https://drive.google.com/file/d/1knnwJPvkgRVqrkkqmsndAB3Yezz1D2eV/view?usp=drive_link)

\[⤓] [L6-Matrices](https://drive.google.com/file/d/1DEhShZVpeqA9L346P8Vwm3pUQcLhZPev/view?usp=drive_link)

\[⤓][ L7-Matrices](https://drive.google.com/file/d/1Fb65zSpd65ZdjGemIp1g11Nr8V8jgtWQ/view?usp=drive_link)

\[ ▶︎ ] [Shortcut Trick to find Inverse Matrix 2x2 & 3x3](https://youtu.be/vXMfuIWSYrg?si=rmaQBWXoGX7X3Bu5)

\[ ▶︎ ] [L1-Matrices (Types & Operations)](https://youtu.be/YNkv74VuXvk?si=0ayYfa9xOm3fOsRg)

\[ ▶︎ ] [L2-Properties of Matrices & Orthogonal Matrix](https://youtu.be/w9ZcD15DECM?si=8EGKdTHhtl41F6fL)

\[ ▶︎ ] [L3-Unitary Matrix](https://youtu.be/PeRzg4mfNEI?si=gLC_3uuvxRGlkhjG)

\[ ▶︎ ] [L4-Rank of Matrix (Normal Form)](https://youtu.be/E7iXLYx8_GI?si=P9Lt42K-bf4gg1Rh)

\[ ▶︎ ] [L5-Part-1 Reduction of Matrix to Normal Form ](https://youtu.be/GPAjA9mmhnw?si=UHm5NJlrSZXfva6M)

\[ ▶︎ ] [L6-Part-2 Reduction of Matrix to Normal Form](https://youtu.be/FUku0LVo87k?si=9pBxs2TTicfiUl4N)

\[ ▶︎ ] [L7-Part-1 Matrices - Linear Dependence & Independence](https://youtu.be/gqq_aPn4NcI?si=DPrIVGTe-QCSRHNY)

\[ ▶︎ ] [L8-Part-1 Matrices - Linear Dependence & Independence](https://youtu.be/cWsLTf-6YuA?si=EnRDOKdygJW_H8RR)

\[ ▶︎ ] [L9-Conditions of Consistency](https://youtu.be/Z3bylFBtD3A?si=mGmz7TkoQmMqqFpc)

\[ ▶︎ ] [L1-Eigen Values & Vectors (Values Not Repeated)](https://youtu.be/p4A0XDL6_XQ?si=f33UK89jBrNSorWl)

\[ ▶︎ ] [L2-Eigen Values & Vectors (Values Repeated)](https://youtu.be/b6Mab8ZIpSU?si=KwAM-e61EYSCcM4_)

\[ ▶︎ ] [L3-Eigen Values & Vectors (All Numerical Types)](https://youtu.be/1_ryGlULx98?si=wLWyOG11dlsP5ybW)

\[ ▶︎ ] [L4-Eigen Values & Vectors (Cayley-Hamilton Theorem) Part-1](https://youtu.be/Z0YZgTGCm5s?si=SvOv9DHIOwcqaXPK)

\[ ▶︎ ] [L5-Eigen Values & Vectors (Cayley-Hamilton Theorem) Part-2](https://youtu.be/kN_fttxDRKY?si=0AZMLh88igwlnPEZ)

\[ ▶︎ ] [L6-Eigen Values & Vectors (Diagnoalization of Matrix) Part-1](https://youtu.be/GARl7AJEq0o?si=HAhbwUdhtJc0GgAL)

\[ ▶︎ ] [L7-Eigen Values & Vectors (Diagnoalization of Matrix) Part-2](https://youtu.be/4NbJRM8WRsU?si=_iAp6x95CGdJaR-S)

\[ ▶︎ ] [L8-Eigen Values & Vectors (Functions of Square Matrix)](https://youtu.be/66Y2uQJQ_ew?si=onCOLqmfFkI39dFt)

\[ ▶︎ ] [Solution of Systems of Linear Eqs - Gauss Jordan Method](https://youtu.be/oPkTasoJngA?si=dzPTQi5NjspRNYsU)

\[ ▶︎ ] [Solution of Systems of Linear Eqs - Gauss Elimination Method](https://youtu.be/Gkit1hUTsX8?si=gZ5zEtmpHyEicnIk)

</details>

<details>

<summary>M5: Linear Algebra &#x26; Vector Space</summary>

\[⤓] [L1-Group-ring-fields](https://www-users.cse.umn.edu/~brubaker/docs/152/152groups.pdf)

\[⤓] [L2-VectorSpace](https://www.statlect.com/matrix-algebra/linear-spaces)

\[⤓] [L3-LinearDependenceVectors](https://www.superprof.co.uk/resources/academic/maths/analytical-geometry/vectors/linearly-dependent-vectors.html#chapter_linearly-dependent-vectors)

\[⤓] [L4-LinearTransformMaps](https://www.statlect.com/matrix-algebra/linear-map)

\[⤓] [L5-LinearMap-Range-Kernel](https://people.tamu.edu/~yvorobets/MATH304-2010A/Lect2-08web.pdf)

\[⤓] [L6-InverseLinearTransform](https://staff.csie.ncu.edu.tw/chia/Course/LinearAlgebra/sec2-3.pdf)

\[⤓] [L7-RankNullityTheorem](https://brilliant.org/wiki/rank-nullity-theorem/)

\[⤓] [L8-LinearMap-Composition](https://www.statlect.com/matrix-algebra/composition-of-linear-maps)

\[⤓] [L9-LinearMap-Matrix](https://www.statlect.com/matrix-algebra/matrix-of-a-linear-map)

\[ ▶︎ ] [Group (Definition+Ex)](https://youtu.be/0a7OEwnoW7c?si=nZY0VeQdqPpTBBA2)

\[ ▶︎ ] [Ring (Definition+Ex)](https://youtu.be/mEkHlJ27qwY?si=6f7WudyvJAXiq7QT)

\[ ▶︎ ] [Fields (Definition+Ex)](https://youtu.be/Y_wHlCJ0zt8?si=RGWAPNjAxLtmVtsI)

\[ ▶︎ ] [Vector Space (Definition+Ex](https://youtu.be/1XlT3Y2oyAU?si=c1DT_g8LB7BOYYU1))

\[ ▶︎ ] [Linear Transformation](https://youtu.be/1fLxcBJB_t8?si=eM_hxf-1LZ5CEbp1)

\[ ▶︎ ] [Theorems of Linear Dependence & Independence](https://youtu.be/wGiJkeuJDcM?si=-pyri59YENDGTapf)

\[ ▶︎ ] [Matrix Representation of Linear Transformation](https://youtu.be/NCsoLIlz_lU?si=mo98C1nZUvHi2s_f)

\[ ▶︎ ] [Inverse of Linear Transformation](https://youtu.be/bXeQILCHnVY?si=kgztOV7imdkrt0Sb)

\[ ▶︎ ] [Rank Nullity Theorem (Statement+Proof)](https://youtu.be/HnFFuXDi9p8?si=hhqPn6rEmguzI8Uu)

\[ ▶︎ ] [Rank Nullity Theorem (Numerical](https://youtu.be/3HoSPQmpzKc?si=e99OCXsX7wQsBzYe))

\[ ▶︎ ] [Linear Algebra in ONE SHOT](https://youtu.be/UaKBee1-Xbs?si=aIDFIxZKoZ1TKHvL)

</details>

***

## Notes

\[⤓] \[PDF] [Maths-Topics-One-PAGE](https://drive.google.com/file/d/13kBhXStMgQOqmmvVK4oyYzqxwuOwC8lb/view?usp=drive_link)

\[⤓] (PDF) [MAT101-Midsem-ShortNotes](https://drive.google.com/file/d/1hinI1cPMg_1XoCahUkQ3Jd00zof_TyjK/view?usp=drive_link)

## Questions Directory

{% file src="<https://4020386663-files.gitbook.io/~/files/v0/b/gitbook-x-prod.appspot.com/o/spaces%2F3ZYLT7QIVGVNDP2woYe4%2Fuploads%2FPVY9xu6YhTYXBBqVmr3n%2FQB_MAT101.pdf?alt=media&token=8a83e567-7ea2-4c19-82de-e50bbd275988>" %}
Official-QB-MAT101
{% endfile %}

### Assignment Questions

\[⤓] [MAT101-Assignment-Qs-Dec23-Btech](https://drive.google.com/file/d/1IvvCgqiQcSFSX8BLdl_ERgWymde2UY_M/view?usp=sharing)

{% embed url="<https://drive.google.com/file/d/1IvvCgqiQcSFSX8BLdl_ERgWymde2UY_M/view?usp=drive_link>" %}

### Previous Year Questions

\[⤓] [MidSem-PYQ-MAT101-Oct23-Btech](https://drive.google.com/file/d/1JzKonlRSMQaZG_4do6--cAI88sqvm-F2/view?usp=drive_link)

\[⤓] [EndSem-PYQ-MAT101-Jan24-Btech ](https://drive.google.com/file/d/1bH8mnyGaVurAvbDqDK6hRzB0l2BR1Oyd/view?usp=drive_link)

{% embed url="<https://drive.google.com/file/d/1bH8mnyGaVurAvbDqDK6hRzB0l2BR1Oyd/view>" %}

\[⤓] [EndSem-PYQ-MAT101-Jan23-Btech](https://drive.google.com/file/d/1JLjpuWPRkI1IjLDRui4b8UCk099J8rW-/view?usp=drive_link)&#x20;

{% embed url="<https://drive.google.com/file/d/1JLjpuWPRkI1IjLDRui4b8UCk099J8rW-/view>" %}

### Back Papers

\[⤓] [MAT101-PYQ-BackQPaper-BTECH-CSE-IT-Sem3Nov25](https://drive.google.com/file/d/17TONT7YVWWg1ZUzZK-k6hi5C8MOlUsYa/view?usp=drive_link)\*

> \*Credit: Harshvardhan Singh (BTECH IT \[2023-2027])

{% embed url="<https://drive.google.com/file/d/17TONT7YVWWg1ZUzZK-k6hi5C8MOlUsYa/view?usp=drive_link>" %}

### Expected Questions

\[⤓] [MAT101-Expected-Qs-Priority-1](https://drive.google.com/file/d/1rgqc1umieyWZLDXLQ3Tyo3M6rxToCLnd/view?usp=drive_link)

{% embed url="<https://drive.google.com/file/d/1rgqc1umieyWZLDXLQ3Tyo3M6rxToCLnd/view?usp=drive_link>" %}

\[⤓] [MAT101-Expected-Qs-Priority-2](https://drive.google.com/file/d/1jYoOzkHcSnv1EqmTDaJrGdKc_PQiEc7L/view?usp=drive_link)

{% embed url="<https://drive.google.com/file/d/1jYoOzkHcSnv1EqmTDaJrGdKc_PQiEc7L/view?usp=drive_link>" %}

## External Sources

**Ref: IISC Notes on Linear Algebra: Matrices, Vectors, Determinants & Linear Systems**

URL: <https://iqti.iisc.ac.in/wp-content/uploads/2021/06/LinearAlgebra_Kreyszig.pdf>

{% embed url="<https://iqti.iisc.ac.in/wp-content/uploads/2021/06/LinearAlgebra_Kreyszig.pdf>" %}
Linear Algebra: Matrices, Vectors, Determinants & Linear Systems
{% endembed %}

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