AMATH 1201

UWO

Course Overview

Lessons & Practice

I. Welcome

1. Modeling

29min

1.I. Chapter Intro6 min

1.1.1. Dimensional Analysis4 min

1.1.2. Dimensionally Homogeneity3 min

1.1.3. Example: Dimensional Analysis7 min

1.2.1. Recursive Sequences9 min

1.2.2. Solving Recursive Equations

1.2.3. Fibonacci Example

2. Differential Equations

55min

2.1.1. Differential Equations8 min

2.2.1. Definition of a Linear Differential Equation2 min

2.2.2. Linear (First Order) Differential Equations7 min

2.2.3. Example: Autonomous Differential Equation1 min

2.2.4. Practice 1

2.2.5. Practice 2

2.2.6. Practice 3

2.3.1. Slope Fields5 min

2.3.2. Practice - slope fields

2.3.3. Equilibria2 min

2.3.4. Stability of equilibrium points4 min

2.3.5. Example: Phase Plots, Stability and Equilibria

2.4.1. Logistic Growth4 min

2.4.2. Example: Logistic Growth Model 5 min

2.4.3. Practice - Exponential growth and decay

2.5.1. Mixing Tank 2 min

2.5.2. Practice 18 min

2.5.3. Practice 23 min

2.5.4. Practice 34 min

3. Probability

21min

3.1.1. Introduction to Probability4 min

3.1.2. Properties of Probability7 min

3.1.3. Probability Table1 min

3.1.4. Conditional Probability7 min

3.1.5. Practice 1

3.1.6. Practice 2

3.1.7. Practice 3

3.1.8. Type I & Type II Error2 min

3.1.9. Practice 4

4. Random Variables

25min

4.1.1. Random Variable & Probability Distribution Function6 min

4.1.2. Discrete Random Variable & Cumulative Distribution Function3 min

4.1.3. Continuous Variable & Probability Distribution Function10 min

4.2.1. Mean, Variance, Standard Deviation6 min

5. Vectors, Functions of Vectors, Eigenvalues, Eigenvectors

1.4hr

5.1.1. Matrix Basics7 min

5.1.2. Matrix Properties5 min

5.1.3. Matrix Addition (and Subtraction)3 min

5.1.4. Dot Product4 min

5.1.5. Cross Product4 min

5.1.6. Matrix Multiplication14 min

5.1.7. Diagonal Matrix3 min

5.1.8. Determinant3 min

5.1.9. Determinant Properties15 min

5.2.1. Linear Independence6 min

5.2.2. Example2 min

5.2.3. Example1 min

5.2.4. Practice3 min

5.3.1. Defining Eigenvalues and Eigenvectors7 min

5.3.2. Eigenvalues and Eigenvectors of Square Matrices7 min

5.3.3. Complex Eigenvalues

6. Application to age-structured populations

41min

6.1.1. Diagonalization6 min

6.1.2. Example7 min

6.1.3. Practice 12 min

6.1.4. Practice 22 min

6.1.5. Perron-Frobenius

6.2.1. Linear Dynamical Systems and Recurrence Relations9 min

6.2.2. Example7 min

6.2.3. Practice8 min

7. Systems of Differential Equations

21min

7.1.1. Matrix-Vector Form of a Linear System8 min

7.1.2. Systems of Linear Differential Equations3 min

7.1.3. Systems of Differential Equations

7.1.4. Practice

7.2.1. Homogeneous Systems5 min

7.2.2. Example: Homogeneous Systems2 min

7.2.3. Practice: Homogeneous System2 min

8. Differential Equations

1.2hr

8.1.1. Differential Equations8 min

8.1.2. Direction Fields/Slope Fields5 min

8.1.3. Practice Question: DE Solution Graphs3 min

8.2.1. Separable First Order Differential Equations3 min

8.2.2. Practice (separable DE)2 min

8.2.3. Practice (IVP)3 min

8.2.4. Practice (IVP)3 min

8.2.5. Practice (IVP*)5 min

8.2.6. Practice (separable DE)1 min

8.3.1. Linear First Order Differential Equations7 min

8.3.2. Practice (integrating factor)1 min

8.3.3. Practice (linear DE)3 min

8.3.4. Practice (IVP)3 min

8.3.5. Practice (IVP)4 min

8.4.1. Exponential Growth and Decay3 min

8.4.2. Example4 min

8.4.3. Example5 min

8.4.4. Practice5 min

8.4.5. Practice (population)3 min

8.4.6. Practice (population)4 min

8.5.1. Second-Order Reducible DE

8.5.2. Practice: Dependent Variable Missing

8.5.3. Practice: Independent Variable Missing

8.Q. DE Quiz4 Qns

Mock Exams

ME.1. Midterm Test - Exam-like Practice Problem Set17 Qns

ME.2. Final Exam - Mock Assessment46 Qns

ME.2 Final Exam - Mock Assessment

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Final Exam - Mock Assessment

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