Advanced Engineering Mathematics in plain view

Subject classification: this is a mathematics resource.

Chapter 1 Linear Algebra

• Vectors (1.A.pdf, 1.B.pdf)

• Row Reduction (A.pdf, B.pdf)

• Elementary Matrix (A.pdf, B.pdf)

• Determinants (A.pdf, B.pdf)

• Eigen Spaces (A.pdf, B.pdf)

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

• Motions (1.A.pdf, 1.B.pdf)

• Derivatives (2.A.pdf, 2.B.pdf)

• Divergence and Curl (3.A.pdf, 3.B.pdf)

• Line Integral (4.A.pdf, 4.B.pdf)

• Double Integral (5.A.pdf, 5.B.pdf)

• Surface Integral (6.A.pdf, 6.B.pdf)

• Triple Integral (7.A.pdf, 7.B.pdf)

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)

See also Vector & Tensor Analysis in plain view.

Chapter 3. Complex Analysis

• Complex Functions (1.A.pdf, 1.B.pdf)

• Complex Integrals (2.A.pdf, 2.B.pdf)

• Complex Series (3.A.pdf, 3.B.pdf)

• Residue Integrals (4.A.pdf, 4.B.pdf)

• Complex Exponential and Logarithm (5.A.pdf, 5.B.pdf)

• Complex Trigonometric and Hyperbolic (7.A.pdf, 7.B.pdf)

• Conformal Mapping (6.A.pdf, 6.B.pdf)

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.

• Using Scientific Calculators - Casio, Sharp, TI, HP

Chapter 4. Ordinary Differential Equations

• Background (0.B.pdf), (0.T.pdf)

- Differential (1A.pdf)

- Integral (2A.pdf)

- Partial Derivative (3A.pdf)

- Complex Variable (4A.pdf)

• First-Order Differential Equation (1.A.pdf, 1.B.pdf), (1.T.pdf)

- Separable Equations (1A.pdf)

- Linear Equations (2A.pdf)

- Exact Equations (3A.pdf)

- Substitution Method (4A.pdf)

• Second-Order Differential Equation (2.A.pdf, 2.B.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)

• Initial Value Problems (4A.pdf, 4B.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

• Definitions (1.A.pdf, 1.B.pdf)

• Inverse Transform (2.A.pdf)

• Properties (3.A.pdf)

• Example Pairs (4.A.pdf, 4.B.pdf)

• LTI Systems (5.A.pdf)

• Bi-lateral Transform (6.A.pdf, 6.B.pdf)

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

• Fourier Series (2.A.pdf, 2.B.pdf)

• Strum-Louiville Problem

• Fourier Transform (3.A.pdf, 3.B.pdf)

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

• Complex Numbers (1.A.pdf, 1.B.pdf)

Chapter 10. Partial Difference Equations

go to [ Electrical_&_Computer_Engineering_Studies ]

External Links

• M Corral's Vector Calculus Book

• Paul's Online Math Notes

• Links to Visual Complex Analysis

• Complex Analysis Project by John H. Mathews