MATH 137

UWaterloo

Course Overview

Lessons & Practice

I. Welcome

1. Sequences and Convergence

20min

1.1.1. Sequences4 min

1.1.2. Example1 min

1.1.3. Practice3 min

1.2.1. Sequence Convergence7 min

1.2.2. Example5 min

1.2.3. Practice

2. Limits and Continuity

1.9hr

2.1.1. Limit Basics2 min

2.1.2. Example1 min

2.2.1. Indeterminate Forms50 sec

2.3.1. Limit Laws 2 min

2.3.2. Practice1 min

2.4.1. Computing Limits by Factoring1 min

2.4.2. Example1 min

2.4.3. Practice2 min

2.5.1. Computing Limits by Multiplying by the Conjugate3 min

2.5.2. Example3 min

2.5.3. Practice3 min

2.6.1. Computing Limits by Getting a Common Denominator1 min

2.6.2. Example2 min

2.6.3. Practice4 min

2.7.1. The Epsilon Delta Definition of a Limit

2.7.2. Example3 min

2.7.3. Practice

2.8.1. One-Sided Limits2 min

2.8.2. Example: One-Sided Limit2 min

2.8.3. Practice: One-Sided Limits3 min

2.9.1. The Squeeze Theorem2 min

2.9.2. Example2 min

2.9.3. Practice2 min

2.10.1. The Fundamental Trig Limit2 min

2.10.2. Example3 min

2.11.1. Limits at Infinity3 min

2.11.2. Example60 sec

2.11.3. Example3 min

2.11.4. Example4 min

2.11.5. Practice 3 min

2.11.6. Practice3 min

2.12.1. Infinite Limits2 min

2.12.2. Example1 min

2.12.3. Example3 min

2.13.1. Continuity2 min

2.13.2. Example2 min

2.13.3. Practice4 min

2.14.1. The Intermediate Value Theorem2 min

2.14.2. Example2 min

2.14.3. Practice2 min

2.15.1. Extreme Value Theorem1 min

3. Derivatives & Differentiation Rules

2.9hr

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

3.3.1. Tangent Lines1 min

3.3.2. Example3 min

3.3.3. Practice2 min

3.4.1. The Power Rule1 min

3.4.2. Example2 min

3.4.3. Practice51 sec

3.5.1. Derivatives of Trigonometric Functions1 min

3.5.2. Example39 sec

3.5.3. Example3 min

3.5.4. Example1 min

3.5.5. Practice3 min

3.5.6. Practice2 min

3.6.1. Derivatives of Exponential Functions1 min

3.6.2. Example52 sec

3.6.3. Example3 min

3.6.4. Practice1 min

3.7.1. Differentiation Laws51 sec

3.8.1. Higher Order Derivatives2 min

3.8.2. Example3 min

3.8.3. Practice2 min

3.8.4. Practice

3.8.5. Practice2 min

3.9.1. The Product Rule49 sec

3.9.2. Example2 min

3.9.3. Example2 min

3.9.4. Practice2 min

3.10.1. The Quotient Rule1 min

3.10.2. Example2 min

3.10.3. Practice4 min

3.11.1. The Chain Rule1 min

3.11.2. Example2 min

3.11.3. Practice3 min

3.12.1. Linearization (Linear Approximation)59 sec

3.12.2. Example3 min

3.12.3. Practice3 min

3.12.4. Practice3 min

3.13.1. Newton's Method1 min

3.13.2. Example

3.13.3. Example4 min

3.13.4. Practice

3.13.5. Practice: Newton's Method2 min

3.14.1. Derivatives of Inverse Functions52 sec

3.14.2. Example2 min

3.14.3. Practice3 min

3.15.1. Derivatives of Logarithmic Functions1 min

3.15.2. Example56 sec

3.15.3. Example2 min

3.15.4. Practice2 min

3.15.5. Practice: Log and Ln2 min

3.16.1. Inverse Trig Derivatives1 min

3.16.2. Example1 min

3.16.3. Practice3 min

3.17.1. Implicit Differentiation2 min

3.17.2. Example3 min

3.17.3. Example3 min

3.17.4. Practice3 min

3.18.1. Logarithmic Differentiation2 min

3.18.2. Example2 min

3.18.3. Practice3 min

4. The Mean Value Theorem, Taylor Polynomials, and Further Applications of Differentiation

4hr

4.1.1. Fermat's Theorem47 sec

4.2.1. Critical Points and Extrema2 min

4.2.3. Practice3 min

4.3.1. Maximum and Minimum on Closed Intervals2 min

4.3.2. Example4 min

4.3.3. Practice3 min

4.3.4. Practice3 min

4.4.1. Rolle's Theorem1 min

4.4.2. Example2 min

4.4.3. Practice1 min

4.5.1. The Mean Value Theorem1 min

4.5.2. Example2 min

4.5.3. Practice2 min

4.6.1. Intervals of Increase and Decrease1 min

4.6.2. Example2 min

4.6.3. Practice3 min

4.7.1. L’Hopital’s Rule2 min

4.7.2. Example2 min

4.7.3. Practice5 min

4.8.1. Solving General Indeterminate Forms2 min

4.8.2. Example2 min

4.8.3. Practice5 min

4.8.4. Practice2 min

4.9.1. 1st and 2nd Derivative Tests3 min

4.9.2. Example7 min

4.9.4. Practice3 min

4.10.1. Concavity and Inflection Points56 sec

4.10.2. Example6 min

4.10.3. Practice6 min

4.11.1. Curve Sketching2 min

4.11.2. Example7 min

4.11.3. Practice9 min

4.11.4. Practice

4.12.1. Taylor Polynomials 1 min

4.12.2. Example6 min

4.12.3. Example4 min

4.12.4. Practice

4.13.1. Taylor Polynomial Remainder2 min

4.13.2. Example3 min

4.13.3. Practice

4.14.1. Optimization1 min

4.14.2. Example4 min

4.14.3. Example4 min

4.14.4. Practice6 min

4.14.5. Practice4 min

4.15.1. Related Rates

4.15.2. Related Rates5 min

4.15.3. Related Rates5 min

4.15.4. Linear Approximation4 min

4.15.5. Linear Approximation

4.15.6. Taylor Series from Definition7 min

4.15.7. Taylor Polynomials

4.15.8. Maclaurin Polynomial

4.15.9. Newton's Method2 min

4.15.10. Newton's Method

4.15.11. L'Hopital's Rule

4.15.12. L'Hopital's Rule

4.15.13. L'Hopital's Rule

4.15.14. Limits

4.15.15. L'Hopital's Rule

4.15.16. L'Hopital's Rule

4.15.17. Limits

4.15.18. Limits

4.15.19. Extreme Value Theorem

4.15.20. Rolle's Theorem1 min

4.15.21. Rolle's Theorem6 min

4.15.23. MVT2 min

4.15.24. MVT3 min

4.15.26. Intervals of Increase and Decrease

4.15.27. Intervals of Increase and Decrease3 min

4.15.28. Critical Points6 min

4.15.29. Critical Points1 min

4.15.30. Extrema5 min

4.15.31. Extrema6 min

4.15.32. Second Derivative Test10 min

4.15.33. Curve Sketching

4.15.34. Curve Sketching12 min

4.15.35. Curve Sketching

4.15.36. Optimization

4.15.37. Optimization

4.15.38. Optimization

Midterm Exam Overview

Course Notes

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