MATH 1600A/B

UWO

Course Overview

Grade Boosters

Lessons & Practice

I. Welcome

54 sec

1. Vectors

4hr

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

1.6.1. Basics of Dot Product2 min

1.6.2. Example2 min

1.6.3. Practice1 min

1.7.1. Dot Product Properties3 min

1.7.6. Cauchy-Schwarz & The Triangle Inequality

1.8.1. Angle Between Vectors3 min

1.8.2. Example2 min

1.8.3. Example2 min

1.8.4. Practice: Dot Product & Angle2 min

1.8.5. Practice2 min

1.8.6. Practice

1.9.1. Projection and Perpendicular3 min

1.9.6. Practice: Projections

1.10.1. Lines in

\reals^n

8 min

1.10.2. Example3 min

1.10.3. Example3 min

1.10.4. Practice2 min

1.10.5. Practice

1.10.6. Practice

1.11.1. Equations of Planes in

\reals^3

5 min

1.11.2. Example2 min

1.11.3. Example4 min

1.11.4. Practice2 min

1.11.5. Practice

1.11.6. Practice (Tricky)4 min

1.12.1. Distances5 min

1.12.2. Example3 min

1.12.3. Example3 min

1.12.4. Practice4 min

1.12.5. Practice3 min

1.13.1. Intersection of Two Lines3 min

1.13.2. Example2 min

1.13.3. Example3 min

1.13.4. Example2 min

1.13.5. Practice2 min

1.13.6. Practice7 min

1.14.1. Intersection of Lines and Planes2 min

1.14.2. Example2 min

1.14.3. Example3 min

1.14.4. Practice1 min

1.14.5. Practice1 min

1.15.1. Cross Product4 min

1.15.2. Example3 min

1.15.3. Practice2 min

1.16.1. Cross Product Properties4 min

1.16.2. Example2 min

1.16.3. Example2 min

1.16.4. Practice2 min

1.16.5. Practice2 min

1.17.1. Cross Product and Area2 min

1.17.2. Example3 min

1.17.3. Practice4 min

2. Systems of Linear Equations

2hr

2.1.1. Basics of Systems of Linear Equations8 min

2.1.2. Example3 min

2.1.3. Practice2 min

2.1.4. Practice3 min

2.2.1. Augmented Matrix3 min

2.3.1. Echelon Forms5 min

2.4.1. Reducing a Matrix5 min

2.5.1. Rank of a Matrix5 min

2.5.2. Example3 min

2.5.3. Practice38 sec

2.5.4. Practice1 min

2.6.1. Solving Linear Systems5 min

2.6.2. Homogeneous Systems2 min

2.7.1. Geometric Interpretation of Solutions to SLEs4 min

2.9.1. Linear Independence6 min

2.9.2. Example2 min

2.9.3. Example1 min

2.9.4. Practice3 min

3. Matrices

3hr

3.1.1. Basics of Matrices3 min

3.1.2. Matrix Arithmetic3 min

3.1.3. Example1 min

3.1.4. Practice2 min

3.2.1. Matrix Multiplication6 min

3.3.1. Matrix Transpose3 min

3.3.2. Symmetric Matrices3 min

3.3.3. Example3 min

3.3.4. Practice60 sec

3.3.5. Practice2 min

3.4.1. Matrix Inverse4 min

3.4.2. Example3 min

3.4.3. Practice32 sec

3.4.4. Practice2 min

3.5.1. Matrix Inverse Algorithm3 min

3.5.2. Example2 min

3.5.3. Example2 min

3.5.4. Practice2 min

3.6.1. Elementary Matrices7 min

3.7.1. Invertible Matrix Theorem2 min

3.7.2. Example1 min

3.7.3. Practice1 min

3.8.1. Solving Matrix Equations2 min

3.8.2. Example52 sec

3.8.3. Example4 min

3.8.4. Practice2 min

3.8.5. Practice54 sec

3.8.6. Practice2 min

3.9.1. Vector Spaces8 min

3.10.1. Subspaces4 min

3.10.2. Example3 min

3.10.3. Practice4 min

3.11.1. Basis and Dimension3 min

3.11.2. Example4 min

3.11.3. Basis and Dimension3 min

3.11.4. Practice4 min

3.12.1. Column Space and Null Space (Range and Kernel)3 min

3.12.2. Example

3.12.3. Practice3 min

3.13.1. Linear Transformations6 min

3.13.2. Example2 min

3.13.3. Example3 min

3.13.4. Practice2 min

3.13.5. Practice8 min

3.14.1. Composition and Inverse3 min

3.14.2. Example4 min

3.14.3. Practice3 min

3.15.1. Special Linear Transformations in

\reals^2

5 min

3.15.2. Example3 min

3.15.3. Practice3 min

3.15.4. Practice4 min

4. Eigenvalues and Eigenvectors

2hr

4.1.1. Eigenvalues and Eigenvectors6 min

4.1.2. Example7 min

4.1.3. Practice8 min

4.1.4. Practice4 min

4.2.1. Properties of Eigenvectors and Eigenvalues3 min

4.2.2. Example3 min

4.2.3. Example6 min

4.2.4. Practice2 min

4.3.1. Diagonalization6 min

4.3.2. Example7 min

4.3.3. Practice2 min

4.3.4. Practice6 min

4.4.1. Basics of Determinants5 min

4.4.2. Example2 min

4.4.3. Practice2 min

4.4.4. Practice3 min

4.5.1. Determinant & EROs3 min

4.5.2. Example2 min

4.5.3. Practice2 min

4.6.1. Minors and Cofactors4 min

4.6.2. Determinants of Large Matrices4 min

3 \times 3

Determinants2 min

4.7.2. Example1 min

4.7.3. Practice2 min

4.8.1. Determinants and Inverse3 min

4.8.2. Example3 min

4.8.3. Practice2 min

4.9.1. Cramer's Rule3 min

4.9.2. Example2 min

4.9.3. Practice3 min

5. Orthogonality

12min

5.1.1. Orthonormal Set3 min

5.1.2. Example2 min

5.1.3. Gram-Schmidt Process3 min

5.1.4. Example4 min

5.1.5. Practice

5.2.1. Orthogonal Matrices

5.2.2. Orthogonal Complement

5.2.3. Orthogonal Projection

6. Appendix C: Complex Numbers

46min

6.1.1. Basics of Complex Numbers4 min

6.1.2. Operations With Complex Numbers9 min

6.1.3. Example5 min

6.1.4. Practice3 min

6.2.1. Polar Form7 min

6.2.2. Geometric Interpretation of Multiplication4 min

6.2.3. Example8 min

6.2.4. Practice1 min

6.2.5. Practice4 min

Mock Exams

ME.1. Midterm Exam - Mock Assessment11 Qns

ME.2. Final Exam - Mock Assessment21 Qns

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