SC/MATH 1506 3.00

York U

Course Overview

Lessons & Practice

I. Welcome

1. Review of Functions

4hr

1.1.1. Numbers4 min

1.2.1. Interval Notation 4 min

1.2.2. Set Notation3 min

1.2.3. Example4 min

1.2.4. Practice2 min

1.2.5. Practice52 sec

1.2.6. Cheatsheet

1.3.1. Domain2 min

1.3.2. Range2 min

1.3.3. Example2 min

1.3.4. Practice 40 sec

1.3.5. Practice 3 min

1.4.1. Operations with Functions3 min

1.4.2. Example2 min

1.4.3. Practice2 min

1.4.4. Practice1 min

1.5.1. Even and Odd Functions3 min

1.5.2. Example2 min

1.6.1. Transformation of Graphs2 min

1.6.2. Example1 min

1.6.3. Practice2 min

1.7.1. Basic of Polynomials4 min

1.7.2. Example2 min

1.7.3. Practice3 min

1.7.4. Polynomial Graphs & Characteristics4 min

1.7.5. Example2 min

1.7.6. Practice2 min

1.8.1. Factoring 5 min

1.8.2. Factoring a Difference & Sum of Cubes3 min

1.8.3. Example2 min

1.8.4. Practice46 sec

1.8.5. Practice2 min

1.8.6. Practice2 min

1.9.1. Dividing Polynomials - Long Division6 min

1.9.2. Example3 min

1.9.3. Dividing Polynomials - Synthetic Division8 min

1.9.4. Example2 min

1.9.5. Practice2 min

1.9.6. Practice3 min

1.10.1. Rational Functions4 min

1.10.2. Solving Rational Equations3 min

1.10.3. Example5 min

1.10.4. Example3 min

1.10.5. Practice6 min

1.10.6. Practice2 min

1.11.1. Radical Functions59 sec

1.11.2. Solving Radical Equations5 min

1.11.3. Example5 min

1.11.4. Practice8 min

1.12.1. Piecewise Functions4 min

1.12.2. Example5 min

1.12.3. Practice3 min

1.13.1. Absolute Value Function1 min

1.13.2. Example3 min

1.14.1. Inverse Functions3 min

1.14.2. Example3 min

1.14.3. Practice2 min

1.15.1. Exponential Functions3 min

1.15.2. Example1 min

1.15.3. Example2 min

1.16.1. Logarithmic Functions4 min

1.16.2. Example3 min

1.16.3. Example:3 min

1.16.4. Practice2 min

1.17.1. Inverse Trigonometric Functions4 min

1.17.2. Example3 min

1.17.3. Practice2 min

1.17.4. Practice2 min

1.18.1. Trigonometric Functions6 min

1.18.2. Example4 min

1.18.3. Trig Identities2 min

1.18.4. Practice3 min

1.18.5. Practice4 min

1.19.1. Solving Quadratic Equations5 min

1.20.1. Power Functions7 min

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

3hr

2.1.1. Intro to Systems of Linear Equations (Simultaneous Equations)3 min

2.2.1. Solving by Substitution12 min

2.2.2. Example5 min

2.2.3. Practice Level 12 min

2.2.4. Practice Level 25 min

2.2.5. Practice Level 37 min

2.3.1. Solving by Simple Elimination12 min

2.3.2. Example3 min

2.3.3. Practice Level 13 min

2.3.4. Practice Level 22 min

2.3.5. Practice Level 24 min

2.4.1. Solving by Multiplication before Elimination8 min

2.4.2. Example4 min

2.4.3. Example4 min

2.4.4. Practice Level 14 min

2.4.5. Practice Level 24 min

2.4.6. Practice5 min

2.5.1. No Solution or Many Solutions5 min

2.5.2. Example 1 7 min

2.5.3. Example 2 4 min

2.5.4. Practice4 min

2.6.1. Solving Linear Systems5 min

2.6.2. Homogeneous Systems2 min

2.6.3. Example3 min

2.6.4. Example5 min

2.6.5. Practice2 min

2.6.6. Practice5 min

2.7.1. Geometric Interpretation of Solutions to SLEs4 min

2.7.2. Example3 min

2.7.3. Practice3 min

2.8.1. Basics of Matrices3 min

2.8.2. Matrix Arithmetic3 min

2.8.3. Example1 min

2.8.4. Practice2 min

2.9.1. Augmented Matrix3 min

2.9.2. Example3 min

2.9.3. Example1 min

2.9.4. Practice2 min

2.9.5. Practice2 min

2.10.1. Reducing a Matrix5 min

2.10.2. Example3 min

2.10.3. Example7 min

2.10.4. Practice2 min

2.10.5. Practice3 min

2.10.6. Practice

2.11.1. Matrix Inverse4 min

2.11.2. Example3 min

2.11.3. Practice32 sec

2.11.4. Practice2 min

2.12.1. Solving Matrix Equations2 min

2.12.2. Example52 sec

2.12.3. Example4 min

2.12.4. Practice2 min

2.12.5. Practice54 sec

2.12.6. Practice2 min

2.13.1. Cramer's Rule3 min

2.13.2. Example2 min

2.13.3. Practice3 min

3. Limits, Continuity & Derivatives

1.7hr

3.1.1. Average and Instanteous Rate of Change6 min

3.1.2. Instantaneous Rate of Change & the Tangent Line2 min

3.1.3. Average & Instantaneous Rate of Change

3.1.4. Instantaneous rate of change

3.1.5. Practice Level 3

3.2.1. Limit Basics2 min

3.2.2. Example1 min

3.3.1. Limit Laws 2 min

3.3.2. Practice1 min

3.4.1. Infinite Limits2 min

3.4.2. Example1 min

3.4.3. Example3 min

3.5.1. Limits at Infinity3 min

3.5.2. Example60 sec

3.5.3. Example3 min

3.5.4. Example4 min

3.5.5. Practice 3 min

3.5.6. Practice3 min

3.6.1. Continuity2 min

3.6.2. Example2 min

3.6.3. Practice4 min

3.7.1. L’Hopital’s Rule2 min

3.7.2. Example2 min

3.7.3. Practice5 min

3.8.1. Computing Limits by Factoring1 min

3.8.2. Example1 min

3.8.3. Practice2 min

3.9.1. Computing Limits by Multiplying by the Conjugate3 min

3.9.2. Example3 min

3.9.3. Practice3 min

3.10.1. Computing Limits by Getting a Common Denominator1 min

3.10.2. Example2 min

3.10.3. Practice4 min

3.11.1. The Definition of a Derivative

3.11.2. Example: Definition of a Derivative5 min

3.11.3. When is Function Not Differentiable?

4. Differentiation Rules and Working with Derivatives

3hr

4.1.1. Differentiation Laws51 sec

4.2.1. The Power Rule1 min

4.2.2. Example2 min

4.2.3. Practice51 sec

4.3.1. Derivatives of Exponential Functions1 min

4.3.2. Example52 sec

4.3.3. Example3 min

4.3.4. Practice1 min

4.4.1. The Product Rule49 sec

4.4.2. Example2 min

4.4.3. Example2 min

4.4.4. Practice2 min

4.5.1. The Quotient Rule1 min

4.5.2. Example2 min

4.5.3. Practice4 min

4.6.1. The Chain Rule1 min

4.6.2. Example2 min

4.6.3. Practice3 min

4.7.1. Derivatives of Logarithmic Functions1 min

4.7.2. Example56 sec

4.7.3. Example2 min

4.7.4. Practice2 min

4.7.5. Practice: Log and Ln2 min

4.8.1. Derivatives of Trigonometric Functions1 min

4.8.2. Example39 sec

4.8.3. Example3 min

4.8.4. Example1 min

4.8.5. Practice3 min

4.8.6. Practice2 min

4.9.1. Derivatives of Inverse Functions52 sec

4.9.2. Example2 min

4.9.3. Practice3 min

4.10.1. Implicit Differentiation2 min

4.10.2. Example3 min

4.10.3. Example3 min

4.10.4. Practice3 min

4.11.1. Related Rates1 min

4.11.2. Related Rates7 min

4.11.3. Example: Related rates intro6 min

4.11.4. Example: Related Rates 25 min

4.11.5. Example: Related Rates 17 min

4.11.6. Practice: Related Rates5 min

4.11.7. Related Rates

4.11.8. Practice: Related Rates 5

4.12.1. Logarithmic Differentiation2 min

4.12.2. Example2 min

4.12.3. Practice3 min

4.13.1. Higher Order Derivatives2 min

4.13.2. Example3 min

4.13.3. Practice2 min

4.13.4. Practice2 min

4.14.1. Inverse Trig Derivatives1 min

4.14.2. Example1 min

4.14.3. Practice3 min

4.15.1. Tangent Lines1 min

4.15.2. Example3 min

4.15.3. Practice2 min

4.16.1. Linear Approximation4 min

4.16.2. Linearization (Linear Approximation)59 sec

4.16.3. Example: Linear approximation2 min

4.16.4. Linear Approximation5 min

4.16.5. Linear Approximation

4.16.6. Practice: Linear Approximation4 min

4.16.7. New Practice Question

4.16.8. Linear Approximation

4.16.9. New Practice Question

4.17.1. Taylor Polynomials 1 min

4.17.2. Example6 min

4.17.3. Example4 min

4.17.4. Practice

4.18.1. Taylor Polynomial Remainder2 min

4.18.2. Example3 min

4.18.3. Practice

5. Applications of Derivatives

4hr

5.1.1. Extreme Value Theorem1 min

5.2.1. Maximum and Minimum on Closed Intervals2 min

5.2.2. Example4 min

5.2.3. Practice3 min

5.2.4. Practice3 min

5.3.1. Intermediate Value Theorem

5.3.2. Example: Intermediate Value Theorem1 min

5.3.3. New Practice Question

5.3.4. New Practice Question

5.4.1. The Mean Value Theorem1 min

5.4.2. Example2 min

5.4.3. Practice2 min

5.5.1. Rolle's Theorem1 min

5.5.2. Example2 min

5.5.3. Practice1 min

5.6.1. Fermat's Theorem47 sec

5.7.1. Newton's Method1 min

5.7.3. Example4 min

5.7.4. Practice

5.7.5. Practice2 min

5.8.1. L’Hopital’s Rule2 min

5.8.2. Example2 min

5.8.3. Practice5 min

5.9.1. Curve Sketching2 min

5.9.2. Example7 min

5.9.3. Practice9 min

5.9.4. Practice

5.10.1. Solving General Indeterminate Forms2 min

5.10.2. Example2 min

5.10.3. Practice5 min

5.10.4. Practice2 min

5.11.1. Intervals of Increase and Decrease1 min

5.11.2. Example2 min

5.11.3. Practice3 min

5.12.1. Critical Points and Extrema2 min

5.12.2. Example

5.12.3. Practice3 min

5.13.1. 1st and 2nd Derivative Tests3 min

5.13.2. Example7 min

5.13.3. Example

5.13.4. Practice3 min

5.14.1. Concavity and Inflection Points56 sec

5.14.2. Example6 min

5.14.3. Practice6 min

5.15.1. Optimization1 min

5.15.2. Example4 min

5.15.3. Example4 min

5.15.4. Practice6 min

5.15.5. Practice4 min

5.16.1. Position, Velocity, and Acceleration1 min

5.16.2. Example3 min

5.16.3. Practice2 min

5.17.1. Periodic Functions3 min

5.17.2. Sinusoidal Functions7 min

5.17.3. Transformations of Sinusoidal Functions (Pt 1)5 min

5.17.4. Transformations of Sinusoidal Functions (Pt 2)4 min

5.17.5. Practice Level 28 min

5.17.6. Practice: Periodic Functions7 min

5.18.1. Related Rates

5.18.2. Related Rates5 min

5.18.3. Related Rates5 min

5.18.4. Linear Approximation4 min

5.18.5. Linear Approximation

5.18.6. Taylor Series from Definition7 min

5.18.7. Taylor Polynomials

5.18.8. Maclaurin Polynomial

5.18.9. Newton's Method2 min

5.18.10. Newton's Method

5.18.11. L'Hopital's Rule

5.18.12. L'Hopital's Rule

5.18.13. L'Hopital's Rule

5.18.14. Limits

5.18.15. L'Hopital's Rule

5.18.16. L'Hopital's Rule

5.18.17. Limits

5.18.18. Limits

5.18.19. Extreme Value Theorem

5.18.20. Rolle's Theorem1 min

5.18.21. Rolle's Theorem6 min

5.18.23. MVT2 min

5.18.24. MVT3 min

5.18.26. Intervals of Increase and Decrease

5.18.27. Intervals of Increase and Decrease3 min

5.18.28. Critical Points6 min

5.18.29. Critical Points1 min

5.18.30. Extrema5 min

5.18.31. Extrema6 min

5.18.32. Second Derivative Test10 min

5.18.33. Curve Sketching

5.18.34. Curve Sketching12 min

5.18.35. Curve Sketching

5.18.36. Optimization

5.18.37. Optimization

5.18.38. Optimization

6. Differential Equations and Applications in Science

1.9hr

6.1.1. Differential Equations8 min

6.1.2. Direction Fields/Slope Fields5 min

6.1.3. Practice Question: DE Solution Graphs3 min

6.1.4. Euler's Method (Approximating Solutions)4 min

6.1.5. Practice

6.2.1. Separable First Order Differential Equations3 min

6.2.2. Practice (separable DE)2 min

6.2.3. Practice (IVP)3 min

6.2.4. Practice (IVP)3 min

6.2.5. Practice (IVP*)5 min

6.2.6. Practice (separable DE)1 min

6.3.1. Linear First Order Differential Equations7 min

6.3.2. Practice (integrating factor)1 min

6.3.3. Practice (linear DE)3 min

6.3.4. Practice (IVP)3 min

6.3.5. Practice (IVP)4 min

6.4.1. Common DE Applications (Word Problems)

6.4.2. Practice (population)3 min

6.4.3. Practice (population)4 min

6.4.4. Practice (cooling & heating)3 min

6.4.5. Practice (mixing tank)6 min

6.4.6. Practice (mixing tank)8 min

6.5.1. Exponential Growth and Decay3 min

6.5.2. Example4 min

6.5.3. Example5 min

6.5.4. Practice5 min

6.6.1. Newton’s Law of Cooling1 min

6.6.2. Example5 min

6.6.3. Practice2 min

6.7.1. Velocity and Acceleration

6.7.2. Displacement, Velocity, & Acceleration9 min

6.7.3. Velocity and Acceleration

6.7.4. Exponential growth and decay

6.7.5. Exponential growth and decay

6.7.6. Exponential growth and decay

6.7.7. Exponential growth and decay

6.7.8. Newton's Law of heating and cooling

6.Q. DE Quiz4 Qns

Midterm Exam Overview

Course Notes

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