Advanced Engineering Mathematics in plain view

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Subject classification: this is a mathematics resource.

Chapter 1 Linear Algebra[edit | edit source]

Linear Algebra Note[edit | edit source]

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[edit | edit source]

Vector Calculus Note[edit | edit source]

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)

See also Vector & Tensor Analysis in plain view.

Chapter 3. Complex Analysis[edit | edit source]

Complex Analysis Note[edit | edit source]

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[edit | edit source]

- 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[edit | edit source]

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[edit | edit source]

Difference Equation Note[edit | edit source]

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[edit | edit source]

Laplace Transform Note[edit | edit source]

- Laplace Transform Note (H1.pdf)

Chapter 7. z-Transform[edit | edit source]

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

Z Transform Note[edit | edit source]

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[edit | edit source]

  • Strum-Louiville Problem
For flash animation, see

Fourier Analysis Note[edit | edit source]

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[edit | edit source]

  • 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

Chapter 10. Partial Difference Equations[edit | edit source]

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External Links[edit | edit source]