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Introduction to Complex Numbers

5

What is a Complex Number?
Modulus-Amplitude form
Problems on Modulus-Amplitude form
De Moivre’s Theorem
nth Root of a Complex Number

Sequence and Series of Functions

3

Introduction
Pointwise Convergence
Sequence of Functions

Matrices

2

Basic Matrices
Algebraic Operations on Matrices

Linear Tansformations

2

Matrix Representation of Linear Transformations
Theorems on Matrix Representation of Linear Transformations

Inner Product Spaces

6

Introuction to Inner Product Space
Properties of Inner Products
Norm of Vector in Inner Product Space
Conjugate Transpose of a Matrix
Orthogonal and Orthonormal Sets
Theorems on Inner Product Space: Part-1
- Theorem-1

Previous Year Question Papers

21

Vidyasagar University- Quesitions Papers

Integral Calculus

2

Area Bounded by Curves
- 1-Find The Whole Area of The Curve
- 2-Find The Whole Area of The Curve

Hyperbolic Functions

1

Formulas: Hyperbolic Functions

Differential Calculus

2

Asymptotes
- Excercise on Asymptote
- 1-Obtain The Asymptotes of The Curve

Group Theory

24

Conjugacy Classes
Finite Abelian Groups
- Exploring Finite Abelian Groups: Problem Set Part-II
- Exploring Finite Abelian Groups: Problem Set Part-I
Automorphism
Sylow's Theorem
- Sylow p-subgroup Fundamentals in Group Theory

Probability and Statistic

8

Probability Distributions
Two Dimensional Distributions

LPP

5

Characteristic of an Optimal Solution
Simplex Method
- Fundamental Theorem of LPP: Exploring LPP Optimality

Partial Differential Equations

5

Cauchy Problem and Wave Equations
- D’Alembert Wave Equation: Cauchy Problem & Solution
Construction of PDE
- List of Solved Problems on Construction of PDE
- Solved Problems on PDE Construction: Expert Solutions
First Order PDE
- List of Solved Problems on First Order PDE
Second Order PDE
- List of Solved Problems on Second Order PDE

Laplace Transformations

1

Piecewise Continuous: Definition and Examples

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Cauchy Problem and Wave Equations

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D’Alembert Wave Equation: Cauchy Problem & Solution

Last Updated: February 25, 2025

Discover the step-by-step D’Alembert solution for the one-dimensional wave equation. Our guide solves the Cauchy problem with clear steps.

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