# Advanced Engineering Mathematics in plain view

 Subject classification: this is a mathematics resource.

## Chapter 1 Linear Algebra

#### Linear Algebra Note

1. Vector Note (H1.pdf)
2. Inverse Matrix Note (H1.pdf)
3. Cramer's Rule (H1.pdf)
4. Gauss-Jordan Elimination Note (H1.pdf)
5. Row Reduction Note (H1.pdf)
6. Linear Systems Note (H1.pdf)
7. Eigenvalues Note (H1.pdf)

## Chapter 2 Vector Calculus

#### Vector Calculus Note

1. Vector Function Note (H1.pdf)
2. Partial Derivative Note (H1.pdf)
3. Curl & Divergence Note (H1.pdf)
4. Multiple Integrals Note (H1.pdf)
5. Line Integrals Note (H1.pdf)
6. Surface Integrals Note (H1.pdf)
7. Green's Theorem Note (H1.pdf)

## Chapter 3. Complex Analysis

#### Complex Analysis Note

1. Complex Number Note (H1.pdf)
2. Complex Function Note (H1.pdf)
3. Complex Integration Note (H1.pdf)
4. Complex Series Note (H1.pdf)
5. Residue Integration Note (H1.pdf)
6. Inversion Integration Note (H1.pdf)
7. Complex Curl, Div Note (H1.pdf)
8. Conformal Mapping Note (H1.pdf)
9. Complex Exp and Log Function Note (H1.pdf)
10. Complex Trig and TrigH Function Note (H1.pdf)
11. Complex Inverse Trig and TrigH Functions Note (H1.pdf)

See also Complex Analysis in plain view.

## Chapter 4. Ordinary Differential Equations

- Differential (1A.pdf)
- Integral (2A.pdf)
- Partial Derivative (3A.pdf)
- Complex Variable (4A.pdf)
- Separable Equations (1A.pdf)
- Linear Equations (2A.pdf)
- Exact Equations (3A.pdf)
- Substitution Method (4A.pdf)
- Linear Equations (1A.pdf)
- Reduction of Orders (2A.pdf)
- Undetermined Coefficients (3A.pdf)
- Variation of Parameters (4A.pdf)
- Cauchy-Euler Equations (5A.pdf)
- Green's Function (6A.pdf)
• Higher-Order Differential Equation (3.A.pdf)
• Boundary Value Problems (1A.pdf))
• Series Solutions
• Numerical Solutions
• Systems of Linear Differential Equations
• Systems of Non-linear Differential Equations

#### ODE Note

1. First ODE Note (H1.pdf)
2. Second ODE Note (H1.pdf)
3. Linear Differential Equation System Note
Background on Matrix Algebra (H1.pdf)
Systems of LDE (H1.pdf)
4. Series Solution Note

## Chapter 5. Ordinary Difference Equations

#### Difference Equation Note

DiffEQ-1: First Order Difference Equations Note (H1.pdf)
DiffEQ-2: Second Order Difference Equations Note (H2.pdf)
DiffEQ-3: Higher Order Difference Equations Note (H3.pdf)
DiffEQ-4: Non-linear Difference Equations Note (H4.pdf)

## Chapter 6. Laplace Transform

#### Laplace Transform Note

- Laplace Transform Note (H1.pdf)

## Chapter 7. z-Transform

• Definitions
• Inverse Transform
• Properties
• Example Pairs
• Bi-lateral Transform

#### Z Transform Note

z-Trans-1: Definitions (H1.pdf)
z-Trans-2: Inverse Transform (H2.pdf)
z-Trans-3: Principles (H3.pdf)
z-Trans-4: Properties (H4.pdf)
z-Trans-5: Example Pairs (H5.pdf)
z-Trans-6: Comparison-1 : Geometric Series (H6.pdf)
z-Trans-7: Comparison-2 : Residue Integral (H7.pdf)
z-Trans-8: Bi-lateral Transform

## Chapter 8. Fourier Analysis

• Strum-Louiville Problem
For flash animation, see fourier-series.com

#### Fourier Analysis Note

1. Fourier Series Note
Fourier Series (H1.pdf)
Cosine & Sine Series (H1.pdf)
Complex Fourier Series (H1.pdf)
Fourier Integral (H1.pdf)
2. Strum-Louiville Problem Note
Bessel Equation (H1.pdf)
Legendre Equation (H1.pdf)
Background (H1.pdf)
Eigenfunctions (H1.pdf)

## Chapter 9. Partial Differential Equations

• Boundary Value Problem (BVP) in Rectangular Coordinates
1. Overview (H1.pdf)
2. Heat Equation (H1.pdf)
3. Wave Equation (H1.pdf)
4. Laplace Equation (H1.pdf)
5. Separable PDE (H1.pdf)
4. Nonhomogeneous PDE (H1.pdf)
• Boundary Value Problem (BVP) in Other Coordinates
• Integral Transform Method
• Numerical Solutions