Mathematics 1

1. Differential calculus

1.1. Taylor's theorem

1.2. Maxima and minima

1.3. Lagranges multiplier

2. Matrices, determinants, linear systems of equations

2.1. Concepts of algebric matrices

2.1.1. Types of matrices

2.1.2. Vector space

2.1.3. Sub space

2.1.4. Basis and dimensions

2.2. Gauss elimination

2.3. Gauss jordan

2.4. Linear dependence and independence

2.5. Linear transformation

2.6. Inverse transformation

2.7. Applications of matrices

2.8. Cramers rule

3. Ordinary DE

3.1. Variable seperable

3.2. Definitions

3.3. Solutions of DE

3.4. Homogeneous

3.5. Equations reducible to homogeneous

3.6. Exact DE

3.7. Orthogonal trajectory

3.7.1. Applications

3.7.2. Differential equations

3.8. Equations reducible to exact form

3.8.1. Linear differential equations

3.8.2. Reduce form

4. Linear DE of 2nd and high order

4.1. Second order linear homogeneous equations with constant coefficients

4.2. Differential operators

4.2.1. Homogeneous equations

4.2.2. Definitions and formulas

4.3. Euler-cauchy equations

4.4. Linear dependence and independence

4.5. High order linear homogeneous equations

4.5.1. Applications

4.5.2. Equations

5. Eigen values problems

5.1. Eigen values

5.2. Eigen vectors

5.3. Basis

5.4. Complex matrices

5.5. Quadratic form

5.6. Skew hermitian forms

5.7. Similar matrices

5.7.1. Diagonalization of matrices

5.7.2. Transformation of forms to principal axis

5.7.2.1. Conic section

5.8. Caley hamilton theorem