MATH 127

UWaterloo

Course Overview

Lessons & Practice

I. Welcome

1. Pre-Calculus Review/Functions

1.7hr

1.1.1. Piecewise Functions4 min

1.1.2. Example5 min

1.1.3. Practice3 min

1.2.1. Absolute Value Function1 min

1.2.2. Example3 min

1.3.1. Basic of Polynomials4 min

1.3.2. Example2 min

1.3.3. Practice3 min

1.3.4. Polynomial Graphs & Characteristics4 min

1.3.5. Example2 min

1.3.6. Practice2 min

1.4.1. Factoring 5 min

1.4.2. Factoring a Difference & Sum of Cubes3 min

1.4.3. Example2 min

1.4.4. Practice46 sec

1.4.5. Practice2 min

1.4.6. Practice2 min

1.5.1. Inverse Functions3 min

1.5.2. Example3 min

1.5.3. Practice2 min

1.6.1. Exponential Functions3 min

1.6.2. Example1 min

1.6.3. Example2 min

1.7.1. Logarithmic Functions4 min

1.7.2. Example3 min

1.7.3. Example:3 min

1.7.4. Practice2 min

1.8.1. Trigonometric Functions6 min

1.8.2. Example4 min

1.8.3. Trig Identities2 min

1.8.4. Practice3 min

1.8.5. Practice4 min

1.9.1. Inverse Trigonometric Functions4 min

1.9.2. Example3 min

1.9.3. Practice2 min

1.9.4. Practice2 min

1.10.1. Graphs of Sinusoidal Functions

1.11.1. Transformations of Sinusoidal Functions (Pt 1)

1.11.2. Example

1.11.3. Transformations of Sinusoidal Functions (Pt 2)

1.11.4. Example

1.11.5. Practice Level One

1.11.6. Practice Level Two

1.11.7. Practice Level Three

1.12.1. Graphs of Reciprocal Trigonometric Functions

1.12.2. Example

1.12.3. Example

1.12.4. Practice Level One

1.12.5. Practice Level Two

1.12.6. Practice Level Three

1.13.1. Equivalent Sinusoidal Functions (Radians)

1.13.2. Example

1.13.3. Practice Level 1

1.13.4. Practice Level 2

1.13.5. Practice Level 3

1.14.1. Applications of Trigonometric Functions

1.14.2. Example

1.14.3. Practice Level 1

1.14.4. Practice Level 2

1.14.5. Practice Level 3

2. Limits & Continuity

1.8hr

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. The Squeeze Theorem2 min

2.6.2. Example2 min

2.6.3. Practice2 min

2.7.1. Indeterminate Forms50 sec

2.8.1. Computing Limits by Factoring1 min

2.8.2. Example1 min

2.8.3. Practice2 min

2.9.1. Computing Limits by Multiplying by the Conjugate3 min

2.9.2. Example3 min

2.9.3. Practice3 min

2.10.1. Computing Limits by Getting a Common Denominator1 min

2.10.2. Example2 min

2.10.3. Practice4 min

2.11.1. The Fundamental Trig Limit2 min

2.11.2. Example3 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

3. Derivatives & Differentiation Rules

6hr

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. Differentiation Laws51 sec

3.4.1. The Power Rule1 min

3.4.2. Example2 min

3.4.3. Practice51 sec

3.5.1. Tangent Lines1 min

3.5.2. Example3 min

3.5.3. Practice2 min

3.6.1. Normal Lines1 min

3.6.2. Example3 min

3.6.3. Practice

3.6.4. Practice1 min

3.7.1. Higher Order Derivatives2 min

3.8.1. The Product Rule49 sec

3.8.2. Example2 min

3.8.3. Example2 min

3.8.4. Practice2 min

3.9.1. The Quotient Rule1 min

3.9.2. Example2 min

3.9.3. Practice4 min

3.10.1. The Chain Rule1 min

3.10.2. Example2 min

3.10.3. Practice3 min

3.11.1. Derivatives of Trigonometric Functions1 min

3.11.2. Example39 sec

3.11.3. Example3 min

3.11.4. Example1 min

3.11.5. Practice3 min

3.11.6. Practice2 min

3.12.1. Derivatives of Exponential Functions1 min

3.12.2. Example52 sec

3.12.3. Example3 min

3.12.4. Practice1 min

3.13.1. Derivatives of Logarithmic Functions1 min

3.13.2. Example56 sec

3.13.3. Example2 min

3.13.4. Practice2 min

3.13.5. Practice: Log and Ln2 min

3.14.1. Implicit Differentiation2 min

3.14.2. Example3 min

3.14.3. Example3 min

3.14.4. Practice3 min

3.15.1. Derivatives of Inverse Functions52 sec

3.15.2. Example2 min

3.15.3. Practice3 min

3.16.1. Inverse Trig Derivatives1 min

3.16.2. Example1 min

3.16.3. Practice3 min

3.17.1. Logarithmic Differentiation2 min

3.17.2. Example2 min

3.17.3. Practice3 min

3.18.1. Differentials2 min

3.18.2. Example3 min

3.18.3. Practice2 min

3.19.1. Linearization (Linear Approximation)59 sec

3.19.2. Example3 min

3.19.3. Practice3 min

3.19.4. Practice3 min

3.20.1. Newton's Method1 min

3.20.2. Example

3.20.3. Example4 min

3.20.4. Practice

3.20.5. Practice: Newton's Method2 min

3.21.1. L’Hopital’s Rule2 min

3.21.2. Example2 min

3.21.3. Practice5 min

3.22.1. Solving General Indeterminate Forms2 min

3.22.2. Example2 min

3.22.3. Practice5 min

3.22.4. Practice2 min

3.23.1. Intervals of Increase and Decrease1 min

3.23.2. Example2 min

3.23.3. Practice3 min

3.24.1. Extreme Value Theorem1 min

3.25.1. Critical Points and Extrema2 min

3.25.2. Example

3.25.3. Practice3 min

3.26.1. 1st and 2nd Derivative Tests3 min

3.26.2. Example7 min

3.26.3. Example

3.26.4. Practice3 min

3.27.1. Maximum and Minimum on Closed Intervals2 min

3.27.2. Example4 min

3.27.3. Practice3 min

3.27.4. Practice3 min

3.28.1. Concavity and Inflection Points56 sec

3.28.2. Example6 min

3.28.3. Practice6 min

3.29.1. Curve Sketching2 min

3.29.2. Example7 min

3.29.3. Practice9 min

3.29.4. Practice

3.30.1. Optimization1 min

3.30.2. Example4 min

3.30.3. Example4 min

3.30.4. Practice6 min

3.30.5. Practice4 min

3.31.1. Related Rates1 min

3.31.2. Example5 min

3.31.3. Example4 min

3.31.4. Practice2 min

3.31.5. Practice4 min

3.31.6. Practice4 min

3.32.1. Derivative by Definition

3.32.2. Basic Derivatives

3.32.3. Basic Derivatives1 min

3.32.4. Derivative by Definition

3.32.5. Chain Rule

3.32.6. Chain Rule

3.32.7. Quotient Rule10 min

3.32.8. Quotient Rule2 min

3.32.9. Power of a Function Rule2 min

3.32.10. Implicit Differentiation

3.32.11. Implicit Differentiation

3.32.12. Second Derivative6 min

3.32.13. Logarithmic Differentiation4 min

3.32.14. Logarithmic Differentiation

3.32.15. Inverse Trigonometric Derivatives

3.32.16. Tangent Lines

3.32.17. Tangent Lines

3.32.18. Horizontal Tangent Lines2 min

3.32.19. Product Rule6 min

3.32.20. Product Rule4 min

3.32.21. Product Rule4 min

3.32.22. Related Rates

3.32.23. Related Rates5 min

3.32.24. Related Rates5 min

3.32.25. Normal Line5 min

3.32.26. Linear Approximation4 min

3.32.27. Linear Approximation

3.32.28. Newton's Method2 min

3.32.29. Newton's Method

3.32.30. L'Hopital's Rule

3.32.31. L'Hopital's Rule

3.32.32. Limits

3.32.33. L'Hopital's Rule

3.32.34. L'Hopital's Rule

3.32.35. L'Hopital's Rule

3.32.36. Limits

3.32.37. Extreme Value Theorem

3.32.38. Rolle's Theorem1 min

3.32.39. Rolle's Theorem6 min

3.32.45. Intervals of Increase and Decrease3 min

3.32.46. Intervals of Increase and Decrease

3.32.47. Critical Points6 min

3.32.48. Critical Points1 min

3.32.49. Extrema6 min

3.32.50. Second Derivative Test10 min

3.32.51. Extrema5 min

3.32.52. Curve Sketching

3.32.53. Curve Sketching12 min

3.32.54. Curve Sketching

3.32.55. Optimization

3.32.56. Optimization

3.32.57. Optimization

4. Integral Calculus

2.8hr

4.1.1. Antiderivatives (Indefinite Integral)3 min

4.2.1. Antiderivatives (Indefinite Integral) of Trig Functions4 min

4.2.2. Example1 min

4.2.3. Practice1 min

4.2.4. Practice1 min

4.3.1. Antiderivatives (Indefinite Integrals) of Inverse Trig Functions2 min

4.3.2. Example1 min

4.3.3. Practice1 min

4.4.1. Antiderivatives (Indefinite Integral) of Exponential Functions1 min

4.4.2. Example42 sec

4.4.3. Practice1 min

4.4.4. Practice2 min

4.5.1. Antiderivatives (Indefinite Integral) of

\frac{1}{x}

2 min

4.5.2. Example2 min

4.5.3. Practice1 min

4.6.1. Finite Sums & Summation Notation3 min

4.6.2. Example5 min

4.6.3. Practice4 min

4.6.4. Practice4 min

4.7.1. Approximating Areas & Riemann Sums 3 min

4.7.2. Example4 min

4.7.3. Practice3 min

4.8.1. The Definite Integrals & Area Under a Curve2 min

4.8.2. Example7 min

4.8.3. Practice2 min

4.8.4. Practice12 min

4.9.1. Properties of the Definite Integral2 min

4.9.2. Practice2 min

4.9.3. Practice2 min

4.10.1. Computing Definite Integrals Geometrically44 sec

4.10.2. Example1 min

4.10.3. Practice1 min

4.11.1. Fundamental Theorem of Calculus - Part I2 min

4.11.2. Example1 min

4.11.3. Example48 sec

4.11.4. Practice1 min

4.11.5. Practice2 min

4.12.1. Fundamental Theorem of Calculus - Part 21 min

4.12.2. Example2 min

4.12.3. Example

4.12.4. Practice 4 min

4.12.5. Practice3 min

4.12.6. Practice1 min

4.13.1. Integration by Substitution2 min

4.13.2. Example4 min

4.13.3. Example3 min

4.13.4. Example (w/ Back-Substitution)4 min

4.13.5. Practice

4.13.6. Practice

4.13.7. Practice

4.13.8. Practice (w/ Back-Substitution)

4.14.1. Area between curves1 min

4.14.2. Example5 min

4.14.3. Example5 min

4.14.4. Practice

Mock Exam

ME.1. Final Exam - Mock Assessment20 Qns

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ME.1 Final Exam - Mock Assessment

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