Maths.Engineering Platform Walkthrough

Maths.Engineering Platform Walkthrough

1. Matrix Introduction

1.1 Introduction

1.2 Types of matrix

1.3 Types of matrix

1.4 Types of matrix

1.5 Application of matrices

1.6 Matrix Introduction

1.7 Matrix Addition

1.8 Matrix Multiplication

1.9 Determinant of Matrix

1.10 Inverse of a Matrix

2. Characteristic Equation

2.1 Introduction

2.2 Solved problem 1

2.3 Solved problem 2

2.4 Solved problem 3

2.5 Solved problem 4

2.6 Exercises

3. Eigen Values and Eigen Vectors of a Matrix

3.1 Introduction

3.2 Eigen vectors

3.3 Solved problem 1

3.4 Solved problem 2

3.5 Solved problem 3

3.6 Solved problem 4

3.7 Solved problem 5

3.8 Solved problem 6

3.9 Solved problem 7

3.10 Solved problem 8

3.11 Solved problem 9

3.12 Solved problem 10

3.13 Solved problem 11

3.14 Exercises

4. Properties of Eigen Values and Eigen Vectors

4.1 Introduction

4.2 Properties of Eigen values

4.3 Properties of Eigen vectors

4.4 Solved problem 1

4.5 Solved problem 2

4.6 Solved problem 3

4.7 Solved problem 4

4.8 Solved problem 5

4.9 Solved problem 6

4.10 Solved problem 7

4.11 Solved problem 8

4.12 Solved problem 9

4.13 Solved problem 10

4.14 Solved problem 11

4.15 Solved problem 12

4.16 Solved problem 13

4.17 Solved problem 14

4.18 Exercises

5. Cayley - Hamilton Theorem

5.1 Introduction

5.2 Solved problem 1

5.3 Solved problem 2

5.4 Solved problem 3

5.5 Solved problem 4

5.6 Solved problem 5

5.7 Solved problem 6

5.8 Solved problem 7

5.9 Solved problem 8

5.10 Solved problem 9

5.11 Solved problem 10

5.12 Exercises

6. Diagonalisation of Matrix (Similarity Transformation)

6.1 Introduction

6.2 Modal and spectral matrices

6.3 Solved problem 1

6.4 Solved Problem 2

6.5 Solved problem 3

6.6 Solved problem 4

6.7 Solved problem 5

6.8 Exercises

7. Diagonalisation of Matrix (Orthogonal Transformation)

7.1 Introduction

7.2 Solved problem 1

7.3 Solved problem 2

7.4 Solved problem 3

7.5 Exercises

8. Reduction of Quadratic Form to Canonical Form

8.1 Introduction

8.2 Fundamental theorem on Quadratic forms

8.3 Index and Signature of the real Quadratic forms

8.4 Nature of the Quadratic forms

8.5 Solved problem 1

8.6 Solved problem 2

8.7 Solved problem 3

8.8 Solved problem 4

8.9 Solved problem 5

8.10 Solved problem 6

8.11 Exercises

9. Stretching of an Elastic Membrance

9.1 Introduction

9.2 Solved problem 1

9.3 Solved problem 2

9.4 Solved problem 3

9.5 Exercises

10. Free vibration of a two mass system

10.1 Introduction