1. Week #1 : Vectors

1.8hr

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

1.8.1. 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

2. Week #2: Cross products, Lines and Planes

2hr

2.1.1. Cross Product4 min

2.1.2. Example3 min

2.1.3. Practice2 min

2.2.1. Cross Product Properties4 min

2.3.1. Cross Product and Area2 min

2.3.2. Example3 min

2.3.3. Practice4 min

2.4.1. Volume of a Parallelepiped1 min

2.4.2. Example2 min

2.4.3. Practice1 min

2.5.1. Lines in

\reals^n

2.6.1. Equations of Planes in

\reals^3

2.6.6. Practice (Tricky)4 min

2.7.1. Hyperplanes3 min

2.7.2. Example1 min

2.7.3. Practice3 min

2.8.1. Distances5 min

2.9.1. Intersection of Two Lines3 min

2.10.1. Intersection of Lines and Planes2 min

2.10.2. Example2 min

2.10.3. Example3 min

2.10.4. Practice1 min

2.10.5. Practice1 min

3. Week #3: Linear Systems, Dependence, Solving Linear Systems, and Echelon Form

1.1hr

4. Week #4: Rank and Solving Linear Systems

30min

4.1.1. Rank of a Matrix5 min

4.1.2. Example3 min

4.1.3. Practice38 sec

4.1.4. Practice1 min

4.2.1. Reducing a Matrix5 min

5. Week #5: Resistor Networks

17min

5.1.1. Resistor Networks9 min

5.1.2. Resistor Networks Concept Clarifier 9 min

6. Week #6: Matrix Multiplication and Linear Transformations

47min

6.1.1. Basics of Matrices3 min

6.1.2. Matrix Arithmetic3 min

6.1.3. Example1 min

6.1.4. Practice2 min

6.2.1. Matrix Multiplication6 min

6.3.1. Linear Transformations6 min

7. Week #7: Rotations, Projections, Reflections in 2 D, and Composition of Linear Transformations

27min

7.1.1. Special Linear Transformations in

\reals^2

7.2.1. Composition and Inverse3 min

7.2.2. Example4 min

7.2.3. Practice3 min

8. Week #8: Random Walks, Transpose, Matrix Inverse, and Determinants

2.3hr

8.1.1. Introduction to Random Walks14 min

8.1.2. Random walks Practice Question3 min

8.2.1. Matrix Transpose3 min

8.2.2. Symmetric Matrices3 min

8.2.3. Example3 min

8.2.4. Practice60 sec

8.2.5. Practice2 min

8.3.1. Matrix Inverse Algorithm3 min

8.3.2. Example2 min

8.3.3. Example2 min

8.3.4. Practice2 min

8.4.1. Matrix Inverse4 min

8.4.2. Example3 min

8.4.3. Practice32 sec

8.4.4. Practice2 min

8.5.1. Elementary Matrices7 min

8.6.1. Invertible Matrix Theorem2 min

8.6.2. Example1 min

8.6.3. Practice1 min

8.7.1. Solving Matrix Equations2 min

8.7.2. Example52 sec

8.7.3. Example4 min

8.7.4. Practice2 min

8.7.5. Practice54 sec

8.7.6. Practice2 min

8.8.1. Basics of Determinants5 min

8.8.2. Example2 min

8.8.3. Practice2 min

8.8.4. Practice3 min

8.9.1. Determinant & EROs3 min

8.9.2. Example2 min

8.9.3. Practice2 min

8.10.1. Minors and Cofactors4 min

8.10.2. Determinants of Large Matrices4 min

8.10.3. Example3 min

8.10.4. Practice2 min

8.10.5. Practice4 min

8.11.1. Shortcut for

3 \times 3

Determinants2 min

8.11.2. Example1 min

8.11.3. Practice2 min

8.12.1. Determinants and Inverse3 min

8.12.2. Example3 min

8.12.3. Practice2 min

8.13.1. Cramer's Rule3 min

8.13.2. Example2 min

8.13.3. Practice3 min

9. Week 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. Week #10: Eigenvalues and Eigenvectors

1hr

10.1.1. Eigenvalues and Eigenvectors6 min

10.1.2. Example7 min

10.1.3. Practice8 min

10.1.4. Practice4 min

10.2.1. Complex Eigenvalues

10.2.2. Example

10.2.3. Example

10.2.4. Practice

10.3.1. Properties of Eigenvectors and Eigenvalues3 min

10.3.2. Example3 min

10.3.3. Example6 min

10.3.4. Practice2 min

10.4.1. Diagonalization6 min

10.4.2. Example7 min

10.4.3. Practice2 min

10.4.4. Practice6 min

11. Week #11: Random Walks (Markov chains)

42min

11.1.1. Markov Chains (Random Walks)7 min

11.1.2. Example6 min

11.1.3. Practice5 min

11.2.1. Linear Dynamical Systems and Recurrence Relations9 min

11.2.2. Example7 min

11.2.3. Practice8 min

12. Week #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

Mock Exams

ME.1. Midterm Exam #1 - Mock Assessment23 Qns

ME.2. Midterm Exam #2 - Mock Assessment34 Qns

ME.3. Final Exam - Mock Assessment46 Qns

MATH 152

Course Overview

1. Week #1 : Vectors

2. Week #2: Cross products, Lines and Planes

3. Week #3: Linear Systems, Dependence, Solving Linear Systems, and Echelon Form

4. Week #4: Rank and Solving Linear Systems

5. Week #5: Resistor Networks

6. Week #6: Matrix Multiplication and Linear Transformations

7. Week #7: Rotations, Projections, Reflections in 2 D, and Composition of Linear Transformations

8. Week #8: Random Walks, Transpose, Matrix Inverse, and Determinants

9. Week 9: Complex Numbers

10. Week #10: Eigenvalues and Eigenvectors

11. Week #11: Random Walks (Markov chains)

12. Week #12: Differential Equations

Mock Exams

ME.1 Midterm Exam #1 - Mock Assessment

Included in Wizeprep Plus

Midterm Exam #1 - Mock Assessment

Timer