MATH 100A

UBC

Course Overview

Grade Boosters

Lessons & Practice

I. Welcome

2. Limits and Continuity

1.9hr

2.1.1. Limit Basics2 min

2.1.2. Example1 min

2.2.1. Limit Laws 2 min

2.2.2. Practice1 min

2.3.1. One-Sided Limits2 min

2.3.2. Example: One-Sided Limit2 min

2.3.3. Practice: One-Sided Limits3 min

2.4.1. Infinite Limits2 min

2.4.2. Example1 min

2.4.3. Example3 min

2.5.1. Limits at Infinity3 min

2.5.2. Example60 sec

2.5.3. Example3 min

2.5.4. Example4 min

2.5.5. Practice 3 min

2.5.6. Practice3 min

2.6.1. Indeterminate Forms50 sec

2.7.1. Computing Limits by Factoring1 min

2.7.2. Example1 min

2.7.3. Practice2 min

2.8.1. Computing Limits by Multiplying by the Conjugate3 min

2.8.2. Example3 min

2.8.3. Practice3 min

2.9.1. Computing Limits by Getting a Common Denominator1 min

2.9.2. Example2 min

2.9.3. Practice4 min

2.10.1. The Fundamental Trig Limit2 min

2.10.2. Example3 min

2.11.1. The Squeeze Theorem2 min

2.11.2. Example2 min

2.11.3. Practice2 min

2.12.1. Continuity2 min

2.12.2. Example2 min

2.12.3. Practice4 min

2.13.1. The Intermediate Value Theorem2 min

2.13.2. Example2 min

2.13.3. Practice2 min

2.14.1. The Epsilon Delta Definition of a Limit

2.14.2. Example3 min

2.14.3. Practice

3. Derivatives and Simple Differential Equations

1.4hr

3.1.1. Derivatives as a Rate of Change2 min

3.1.2. Average Rate of Change46 sec

3.1.3. Example2 min

3.1.4. Practice1 min

3.2.1. The Limit Definition of a Derivative2 min

3.2.2. Example3 min

3.2.3. Practice5 min

3.2.4. When is Function Not Differentiable?

3.3.1. Tangent Lines1 min

3.3.2. Example3 min

3.3.3. Practice2 min

3.4.1. Linearization (Linear Approximation)59 sec

3.4.2. Example3 min

3.4.3. Practice3 min

3.4.4. Practice3 min

3.5.1. Derivatives of Exponential Functions1 min

3.5.2. Example52 sec

3.5.3. Example3 min

3.5.4. Practice1 min

3.6.1. Normal Lines1 min

3.6.2. Example3 min

3.6.3. Practice1 min

3.7.1. Derivatives of Inverse Functions52 sec

3.7.2. Example2 min

3.7.3. Practice3 min

3.8.1. Differential Equations8 min

3.8.2. Direction Fields/Slope Fields5 min

3.8.3. Practice Question: DE Solution Graphs3 min

3.9.1. Separable First Order Differential Equations3 min

3.9.2. Practice (separable DE)2 min

3.9.3. Practice (IVP)3 min

3.9.4. Practice (IVP)3 min

3.9.5. Practice (IVP*)5 min

3.9.6. Practice (separable DE)1 min

4. Differentiation Rules

2hr

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. The Product Rule49 sec

4.3.2. Example2 min

4.3.3. Example2 min

4.3.4. Practice2 min

4.4.1. The Quotient Rule1 min

4.4.2. Example2 min

4.4.3. Practice4 min

4.5.1. Derivatives of Trigonometric Functions1 min

4.5.2. Example39 sec

4.5.3. Example3 min

4.5.4. Example1 min

4.5.5. Practice3 min

4.5.6. Practice2 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. Logarithmic Differentiation2 min

4.8.2. Example2 min

4.8.3. Practice3 min

4.9.1. Implicit Differentiation2 min

4.9.2. Example3 min

4.9.3. Example3 min

4.9.4. Practice3 min

4.10.1. Inverse Trig Derivatives1 min

4.10.2. Example1 min

4.10.3. Practice3 min

4.11.1. Higher Order Derivatives2 min

4.11.2. Example3 min

4.11.3. Practice2 min

4.11.4. Practice2 min

5. Applications of Differentiation

4hr

5.1.1. Related Rates1 min

5.1.2. Example5 min

5.1.3. Example4 min

5.1.4. Practice2 min

5.1.5. Practice4 min

5.1.6. Practice4 min

5.2.1. Differentials2 min

5.2.2. Example3 min

5.2.3. Practice2 min

5.3.1. Intervals of Increase and Decrease1 min

5.3.2. Example2 min

5.3.3. Practice3 min

5.4.1. Critical Points and Extrema2 min

5.4.3. Practice3 min

5.5.1. 1st and 2nd Derivative Tests3 min

5.5.2. Example7 min

5.5.4. Practice3 min

5.6.1. Maximum and Minimum on Closed Intervals2 min

5.6.2. Example4 min

5.6.3. Practice3 min

5.6.4. Practice3 min

5.7.1. Concavity and Inflection Points56 sec

5.7.2. Example6 min

5.7.3. Practice6 min

5.8.1. Curve Sketching2 min

5.8.2. Example7 min

5.8.3. Practice9 min

5.8.4. Practice

5.9.1. Linearization (Linear Approximation)59 sec

5.9.2. Example3 min

5.9.3. Practice3 min

5.9.4. Practice3 min

5.10.1. Taylor Polynomials 1 min

5.10.2. Example6 min

5.10.3. Example4 min

5.10.4. Practice

5.11.1. Taylor Polynomial Remainder2 min

5.11.2. Example3 min

5.11.3. Practice

5.12.1. Optimization1 min

5.12.2. Example4 min

5.12.3. Example4 min

5.12.4. Practice6 min

5.12.5. Practice4 min

5.13.1. Related Rates

5.13.2. Related Rates5 min

5.13.3. Related Rates5 min

5.13.4. Linear Approximation4 min

5.13.5. Linear Approximation

5.13.6. Newton's Method2 min

5.13.7. Newton's Method

5.13.8. L'Hopital's Rule

5.13.9. L'Hopital's Rule

5.13.10. L'Hopital's Rule

5.13.11. Limits

5.13.12. L'Hopital's Rule

5.13.13. L'Hopital's Rule

5.13.14. Limits

5.13.15. Limits

5.13.16. Extreme Value Theorem

5.13.17. Rolle's Theorem1 min

5.13.18. Rolle's Theorem6 min

5.13.20. MVT2 min

5.13.21. MVT3 min

5.13.23. Intervals of Increase and Decrease

5.13.24. Intervals of Increase and Decrease3 min

5.13.25. Critical Points6 min

5.13.26. Critical Points1 min

5.13.27. Extrema5 min

5.13.28. Extrema6 min

5.13.29. Second Derivative Test10 min

5.13.30. Curve Sketching

5.13.31. Curve Sketching12 min

5.13.32. Curve Sketching

5.13.33. Optimization

5.13.34. Optimization

5.13.35. Optimization

6. Applications of Differentiation for Science

41min

6.1.1. Position, Velocity, and Acceleration1 min

6.1.2. Example3 min

6.1.3. Practice2 min

6.2.1. Exponential Growth and Decay3 min

6.2.2. Example4 min

6.2.3. Example5 min

6.2.4. Practice5 min

6.3.1. Newton’s Law of Cooling1 min

6.3.2. Example5 min

6.3.3. Practice2 min

6.4.1. Velocity and Acceleration

6.4.2. Displacement, Velocity, & Acceleration9 min

6.4.3. Velocity and Acceleration

6.4.4. Exponential growth and decay

6.4.5. Exponential growth and decay

6.4.6. Exponential growth and decay

6.4.7. Exponential growth and decay

6.4.8. Newton's Law of heating and cooling

7. Differential Equations

41min

7.1.1. Linear First Order Differential Equations7 min

7.1.2. Practice (integrating factor)1 min

7.1.3. Practice (linear DE)3 min

7.1.4. Practice (IVP)3 min

7.1.5. Practice (IVP)4 min

7.2.1. Exponential Growth and Decay3 min

7.2.2. Example4 min

7.2.3. Example5 min

7.2.4. Practice5 min

7.2.5. Practice (population)3 min

7.2.6. Practice (population)4 min

7.3.1. Second-Order Reducible DE

7.3.2. Practice: Dependent Variable Missing

7.3.3. Practice: Independent Variable Missing

7.Q. Exam-Like Practice Questions4 Qns

8. Computation Week

12min

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

8.1.2. Practice

8.2.1. Newton's Method1 min

8.2.3. Example4 min

8.2.4. Practice

8.2.5. Practice2 min

9. Multivariable Functions

1.1hr

9.1.1. Functions of Several Variables5 min

9.1.2. Practice3 min

9.2.1. Partial derivatives6 min

9.2.2. Practice: First Partial derivatives2 min

9.2.3. Practice: Second Partial Derivatives3 min

9.3.1. Chain Rule7 min

9.3.2. Practice: Chain Rule2 min

9.3.3. Practice: Chain Rule2 min

9.3.4. Practice: Chain Rule*3 min

9.3.5. Implicit Differentiation2 min

9.4.1. Gradient and directional derivative7 min

9.4.2. Practice: Gradient and directional derivative

9.5.1. Tangent plane3 min

9.5.2. Practice: Tangent Plane

9.5.3. Linear (Tangent Plane) Approximation3 min

9.5.4. Practice: Linear approximation

9.6.1. Differentials4 min

9.6.2. Practice: Differentials

9.6.3. Practice: Differentials

9.7.1. Local Max & Min4 min

9.7.2. Absolute Max & Min5 min

9.7.3. Lagrange Multipliers3 min

9.7.4. Practice: Lagrange Multipliers

9.7.5. Practice: Lagrange Multipliers

9.8.1. Multivariable Functions Quiz12 Qns

10. Differential Equations

1.2hr

10.1.1. Differential Equations8 min

10.1.2. Direction Fields/Slope Fields5 min

10.1.3. Practice Question: DE Solution Graphs3 min

10.2.1. Separable First Order Differential Equations3 min

10.2.2. Practice (separable DE)2 min

10.2.3. Practice (IVP)3 min

10.2.4. Practice (IVP)3 min

10.2.5. Practice (IVP*)5 min

10.2.6. Practice (separable DE)1 min

10.3.1. Linear First Order Differential Equations7 min

10.3.2. Practice (integrating factor)1 min

10.3.3. Practice (linear DE)3 min

10.3.4. Practice (IVP)3 min

10.3.5. Practice (IVP)4 min

10.4.1. Exponential Growth and Decay3 min

10.4.2. Example4 min

10.4.3. Example5 min

10.4.4. Practice5 min

10.4.5. Practice (population)3 min

10.4.6. Practice (population)4 min

10.5.1. Second-Order Reducible DE

10.5.2. Practice: Dependent Variable Missing

10.5.3. Practice: Independent Variable Missing

10.Q. Exam-Like Practice Questions4 Qns

Mock Exams

ME.1. Test 1 - Mock Assessment15 Qns

ME.2. Test 2 - Mock Assessment15 Qns

ME.3. Final Exam - Mock Assessment25 Qns

Test 2 Overview

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Test 2 Mock

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