1. Vectors

1.2hr

1.1.1. Basics of Vectors5 min

1.1.2. Example1 min

1.1.3. Example1 min

1.1.4. Practice2 min

1.2.1. Vector Operations8 min

1.2.7. Practice (Tricky)5 min

1.3.1. Vector Properties4 min

1.3.2. Example3 min

1.3.3. Example3 min

1.3.4. Practice: Vector Properties2 min

1.4.1. Vector Norm5 min

1.5.1. Unit Vectors5 min

1.5.2. Example2 min

1.5.3. Practice2 min

2. Products of Vectors

1.2hr

2.1.1. Basics of Dot Product2 min

2.1.2. Example2 min

2.1.3. Practice1 min

2.2.1. Dot Product Properties3 min

2.3.1. Angle Between Vectors3 min

2.3.2. Example2 min

2.3.3. Example2 min

2.3.4. Practice: Dot Product & Angle2 min

2.3.5. Practice2 min

2.3.6. Practice

2.4.1. Projection and Perpendicular3 min

2.4.6. Practice: Projections

2.5.1. Cross Product4 min

2.5.2. Example3 min

2.5.3. Practice2 min

2.6.1. Cross Product Properties4 min

2.7.1. Cross Product and Area2 min

2.7.2. Example3 min

2.7.3. Practice4 min

2.8.1. Volume of a Parallelepiped1 min

2.8.2. Example2 min

2.8.3. Practice1 min

3. Equations of Lines and Planes

1.4hr

3.1.1. Lines in

\reals^n

3.2.1. Equations of Planes in

\reals^3

3.2.6. Practice (Tricky)4 min

3.3.1. Hyperplanes3 min

3.3.2. Example1 min

3.3.3. Practice3 min

3.4.1. Distances5 min

3.5.1. Intersection of Two Lines3 min

3.6.1. Intersection of Lines and Planes2 min

4. Systems of Linear Equations (SLEs) (Linear Systems)

1.8hr

4.1.1. Basics of Systems of Linear Equations8 min

4.1.2. Example3 min

4.1.3. Practice2 min

4.1.4. Practice3 min

4.2.1. Augmented Matrix3 min

4.3.1. Echelon Forms5 min

4.4.1. Reducing a Matrix5 min

4.5.1. Rank of a Matrix5 min

4.5.2. Example3 min

4.5.3. Practice38 sec

4.5.4. Practice1 min

4.6.1. Solving Linear Systems5 min

4.6.2. Homogeneous Systems2 min

4.7.1. Geometric Interpretation of Solutions to SLEs4 min

4.7.2. Example3 min

4.7.3. Practice3 min

4.8.1. Polynomial Interpolation5 min

4.8.2. Example4 min

4.8.3. Practice4 min

5. Matrices

1.5hr

5.1.1. Basics of Matrices3 min

5.1.2. Matrix Arithmetic3 min

5.1.3. Example1 min

5.1.4. Practice2 min

5.2.1. Matrix Multiplication6 min

5.3.1. Matrix Transpose3 min

5.3.2. Symmetric Matrices3 min

5.3.3. Example3 min

5.3.4. Practice60 sec

5.3.5. Practice2 min

5.4.1. Matrix Inverse4 min

5.4.2. Example3 min

5.4.3. Practice32 sec

5.4.4. Practice2 min

5.5.1. Matrix Inverse Algorithm3 min

5.5.2. Example2 min

5.5.3. Example2 min

5.5.4. Practice2 min

5.6.1. Elementary Matrices7 min

5.7.1. Invertible Matrix Theorem2 min

5.7.2. Example1 min

5.7.3. Practice1 min

5.8.1. Solving Matrix Equations2 min

5.8.2. Example52 sec

5.8.3. Example4 min

5.8.4. Practice2 min

5.8.5. Practice54 sec

5.8.6. Practice2 min

6. Determinants

58min

7. Vector Spaces and Subspaces

1.3hr

8. Orthogonality

12min

8.1.1. Orthonormal Set3 min

8.1.2. Example2 min

8.1.3. Gram-Schmidt Process3 min

8.1.4. Example4 min

8.1.5. Practice

8.2.1. Orthogonal Matrices

8.2.2. Orthogonal Complement

8.2.3. Orthogonal Projection

9. Complex Numbers

1.3hr

9.1.1. Basics of Complex Numbers4 min

9.1.2. Operations With Complex Numbers9 min

9.1.3. Example5 min

9.1.4. Practice3 min

9.2.1. Polar Form7 min

9.2.2. Geometric Interpretation of Multiplication4 min

9.2.3. Example8 min

9.2.4. Practice1 min

9.2.5. Practice4 min

9.3.1. Powers and Root6 min

9.4.1. Quadratic Formula3 min

9.4.2. Example3 min

9.4.3. Example7 min

9.4.4. Practice3 min

10. Linear Transformations

49min

10.1.1. Linear Transformations6 min

10.1.2. Example2 min

10.1.3. Example3 min

10.1.4. Practice2 min

10.1.5. Practice8 min

10.2.1. Composition and Inverse3 min

10.2.2. Example4 min

10.2.3. Practice3 min

10.3.1. Special Linear Transformations in

\reals^2

5 min

10.3.2. Example3 min

10.3.3. Practice3 min

10.3.4. Practice4 min

11. Eigenvalues and Eigenvectors (Spectral Theory)

1.7hr

12. Differential Equations

20min

12.1.1. Definition of a Linear Differential Equation2 min

12.1.2. Simplest Differential Equation:

y'=ay

5 min

12.1.3. Initial Value Problems2 min

12.1.4. Practice

12.1.5. Practice

12.1.6. Example2 min

12.2.1. Systems of Linear Differential Equations3 min

12.2.2. Solving a System of Linear DEs2 min

12.2.3. Example4 min

12.2.4. Practice

12.2.5. Practice

12.3.1. Higher Order Linear DEs

12.3.2. Example

12.3.3. Practice

12.3.4. Practice

13. Least Squares Approximation

10min

13.1.1. Least Squares Approximation6 min

13.1.2. Example4 min

13.1.3. Example: Least Squares for Polynomials

13.1.4. Practice

14. Cryptography (COMING SOON)

Mock Exams

MATH-1270

Course Overview

1. Vectors

2. Products of Vectors

3. Equations of Lines and Planes

4. Systems of Linear Equations (SLEs) (Linear Systems)

5. Matrices

6. Determinants

7. Vector Spaces and Subspaces

8. Orthogonality

9. Complex Numbers

10. Linear Transformations

11. Eigenvalues and Eigenvectors (Spectral Theory)

12. Differential Equations

13. Least Squares Approximation

14. Cryptography (COMING SOON)

Mock Exams

Midterm Overview

Course Notes