MAT101 / Mathematics

Syllabus

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MAT101-Syllabus-BTECH-IT.pdf

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References:

https://dpvipracollege.ac.in/wp-content/uploads/2022/12/h.k.dass_.pdfdpvipracollege.ac.in

Advanced Engineering Mathematics by HK Das (S Chand Publications)

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Resources

M1: Differential Calculus

[⤓] L1-Successive_Differentiation-1

[⤓] L2-Successive_Differentiation-1

[⤓] L3-Successive_Differentiation-1

[⤓] L4-Leibnitz-Theorem

[⤓] L5-Leibnitz-Theorem

[⤓] L6-Rolles-Theorem

[⤓] L7-MeanValueTheorem

[⤓] L8-MeanValueTheorem

[⤓] L9-Partial-Differentiaion

[⤓] L10-Maxima-Minima

[ ▶︎ ] L1-Partial Differentiation (Basic Concepts)

[ ▶︎ ] L2-Partial Differentiation (Basic Questions)

[ ▶︎ ] L3-Partial Derivative of 1st Order - Part 1

[ ▶︎ ] L4-Partial Derivative of 1st Order - Part 2

[ ▶︎ ] L5-Partial Derivative of 1st Order - Part 3

[ ▶︎ ] L1-Successive Differentiation (Algebraic Fn)

[ ▶︎ ] L2-Successive Differentiation (nth Order Deriv. of Trigono Fn)

[ ▶︎ ] L3-Successive Differentiation (Leibnitz Theorem)

[ ▶︎ ] L1-Differential Calculus (Rolle's Theorem)

[ ▶︎ ] L2-Differential Calculus (LMVT)

[ ▶︎ ] L3-Differential Calculus (Taylor's & Maclaurin's Theorem)

[ ▶︎ ] L4-Differential Calculus (Standard Expansions)

[ ▶︎ ] Total Derivatives (Concept & Problems)

[ ▶︎ ] L1-Maxima & Minima (Appl of Partial Derivative)

[ ▶︎ ] L2-Maxima & Minima (Appl of Partial Derivative)

M2: Integral Calculus

[⤓] L11-Definite-Integral-Beta-Gamma-fn

[⤓] L12-RelationInBetaGamma-fn

[⤓] L13-Area-of-CartesianCurve

[⤓] L14-VolOfRevolution

[⤓] L15-SurfaceOfRevolution

[⤓] L16-MultipleIntegrals

[ ▶︎ ] L1-Beta & Gamma Function (Property)

[ ▶︎ ] L2-Beta & Gamma Function (Tricks to Solve Different Function)

[ ▶︎ ] L3-Beta & Gamma Function (Types of Beta function) - Part 1

[ ▶︎ ] L4-Beta & Gamma Function (Types of Beta function) - Part 2

[ ▶︎ ] Double Integrals (Evaluation of Direct Double Integral)

[ ▶︎ ] Double Integrals (Cartesian to Polar)

[ ▶︎ ] Double Integrals (Limit is not given (Region))

[ ▶︎ ] Double Integrals (Area by Double Integration)

M3: Vector Calculus

[⤓] L1-Vector-Calculus

[⤓] L2-Vector-Calculus

[⤓] L3-Vector-Calculus

[⤓] L5-Vector-Calculus

[⤓] L6-Vector-Calculus

[⤓] L7-Vector-Calculus

[⤓] L8-Vector-Calculus

[ ▶︎ ] L1-Vector-Diff. (Gradient & Directional Derivative)

[ ▶︎ ] L2-Vector-Diff. (Angle between the Normals)

[ ▶︎ ] L3-Vector-Diff. (Divergence & Curl)

[ ▶︎ ] L4-Vector-Diff. (One Shot)

[ ▶︎ ] L1-Vector-Integration. (Line Integral) - Part 1

[ ▶︎ ] L2-Vector-Integration. (Line Integral) - Part 2

[ ▶︎ ] L3-Vector-Integration. (Green's Theorem)

[ ▶︎ ] L4-Vector-Integration. (Stoke's Theorem)

[ ▶︎ ] L5-Vector-Integration. (One Shot)

M4: Matrices

[⤓] L1-Matrices

[⤓] L2-Matrices

[⤓] L3-Matrices

[⤓] L4-Matrices

[⤓] L5-Matrices

[⤓] L6-Matrices

[⤓] L7-Matrices

[ ▶︎ ] Shortcut Trick to find Inverse Matrix 2x2 & 3x3

[ ▶︎ ] L1-Matrices (Types & Operations)

[ ▶︎ ] L2-Properties of Matrices & Orthogonal Matrix

[ ▶︎ ] L3-Unitary Matrix

[ ▶︎ ] L4-Rank of Matrix (Normal Form)

[ ▶︎ ] L5-Part-1 Reduction of Matrix to Normal Form

[ ▶︎ ] L6-Part-2 Reduction of Matrix to Normal Form

[ ▶︎ ] L7-Part-1 Matrices - Linear Dependence & Independence

[ ▶︎ ] L8-Part-1 Matrices - Linear Dependence & Independence

[ ▶︎ ] L9-Conditions of Consistency

[ ▶︎ ] L1-Eigen Values & Vectors (Values Not Repeated)

[ ▶︎ ] L2-Eigen Values & Vectors (Values Repeated)

[ ▶︎ ] L3-Eigen Values & Vectors (All Numerical Types)

[ ▶︎ ] L4-Eigen Values & Vectors (Cayley-Hamilton Theorem) Part-1

[ ▶︎ ] L5-Eigen Values & Vectors (Cayley-Hamilton Theorem) Part-2

[ ▶︎ ] L6-Eigen Values & Vectors (Diagnoalization of Matrix) Part-1

[ ▶︎ ] L7-Eigen Values & Vectors (Diagnoalization of Matrix) Part-2

[ ▶︎ ] L8-Eigen Values & Vectors (Functions of Square Matrix)

[ ▶︎ ] Solution of Systems of Linear Eqs - Gauss Jordan Method

[ ▶︎ ] Solution of Systems of Linear Eqs - Gauss Elimination Method

M5: Linear Algebra & Vector Space

[⤓] L1-Group-ring-fields

[⤓] L2-VectorSpace

[⤓] L3-LinearDependenceVectors

[⤓] L4-LinearTransformMaps

[⤓] L5-LinearMap-Range-Kernel

[⤓] L6-InverseLinearTransform

[⤓] L7-RankNullityTheorem

[⤓] L8-LinearMap-Composition

[⤓] L9-LinearMap-Matrix

[ ▶︎ ] Group (Definition+Ex)

[ ▶︎ ] Ring (Definition+Ex)

[ ▶︎ ] Fields (Definition+Ex)

[ ▶︎ ] Vector Space (Definition+Ex)

[ ▶︎ ] Linear Transformation

[ ▶︎ ] Theorems of Linear Dependence & Independence

[ ▶︎ ] Matrix Representation of Linear Transformation

[ ▶︎ ] Inverse of Linear Transformation

[ ▶︎ ] Rank Nullity Theorem (Statement+Proof)

[ ▶︎ ] Rank Nullity Theorem (Numerical)

[ ▶︎ ] Linear Algebra in ONE SHOT

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Notes

[⤓] [PDF] Maths-Topics-One-PAGE

[⤓] (PDF) MAT101-Midsem-ShortNotes

Questions Directory

623KB

QB_MAT101.pdf

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Official-QB-MAT101

Assignment Questions

[⤓] MAT101-Assignment-Qs-Dec23-Btech

Previous Year Questions

[⤓] MidSem-PYQ-MAT101-Oct23-Btech

[⤓] EndSem-PYQ-MAT101-Jan24-Btech

[⤓] EndSem-PYQ-MAT101-Jan23-Btech

Back Papers

[⤓] MAT101-PYQ-BackQPaper-BTECH-CSE-IT-Sem3Nov25*

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

Expected Questions

[⤓] MAT101-Expected-Qs-Priority-1

[⤓] MAT101-Expected-Qs-Priority-2

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

Linear Algebra: Matrices, Vectors, Determinants & Linear Systems

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