1. Sequences and Series

2.1hr

1.1.1. Power Series4 min

1.1.2. Practice Question: Power Series Representation2 min

1.1.3. Practice Question: Power Series Representation2 min

1.2.1. Taylor Polynomials 1 min

1.2.2. Example6 min

1.2.3. Example4 min

1.2.4. Practice

1.3.1. Taylor Polynomial Remainder2 min

1.3.2. Example3 min

1.3.3. Practice

1.4.1. Tangent Planes & Linear Approximation5 min

1.5.1. Gradient Vectors, Tangent Planes, Normal Lines2 min

1.6.2. Related Rates5 min

1.6.3. Related Rates5 min

1.6.4. Linear Approximation4 min

1.6.5. Linear Approximation

1.6.6. Taylor Series from Definition7 min

1.6.7. Taylor Polynomials

1.6.8. Maclaurin Polynomial

1.6.9. Newton's Method2 min

1.6.10. Newton's Method

1.6.11. L'Hopital's Rule

1.6.12. L'Hopital's Rule

1.6.13. L'Hopital's Rule

1.6.14. Limits

1.6.15. L'Hopital's Rule

1.6.16. L'Hopital's Rule

1.6.17. Limits

1.6.18. Limits

1.6.19. Extreme Value Theorem

1.6.20. Rolle's Theorem1 min

1.6.21. Rolle's Theorem6 min

1.6.26. Intervals of Increase and Decrease

1.6.27. Intervals of Increase and Decrease3 min

1.6.28. Critical Points6 min

1.6.29. Critical Points1 min

1.6.30. Extrema5 min

1.6.31. Extrema6 min

1.6.32. Second Derivative Test10 min

1.6.33. Curve Sketching

1.6.34. Curve Sketching12 min

1.6.35. Curve Sketching

1.6.36. Optimization

1.6.37. Optimization

1.6.38. Optimization

2. Vectors

1.5hr

2.1.1. Vectors in 2D and 3D Systems2 min

2.1.2. Example

2.1.3. Example2 min

2.1.4. Practice52 sec

2.1.5. Practice1 min

2.2.1. Properties of Vectors, Length of Vectors, and Unit Vectors5 min

2.2.2. Example1 min

2.2.3. Vector Arithmetic, Properties of Vectors, Length1 min

2.2.4. Practice3 min

2.2.5. Practice1 min

2.3.1. Dot Product4 min

2.3.2. Example2 min

2.3.3. Example2 min

2.3.4. Practice4 min

2.4.1. Cross Product2 min

2.4.2. Example2 min

2.4.3. Practice1 min

2.4.4. Practice4 min

2.5.1. Equations of Lines5 min

2.5.2. Example3 min

2.5.3. Example2 min

2.5.4. Practice2 min

2.6.1. Equations of Planes5 min

2.7.1. Quadratic Surfaces and Level Curves

2.Q. Checkpoint Quiz8 Qns

3. Partial Differentiation

31min

3.1.1. Partial Derivatives3 min

3.1.2. Higher Order Partial Derivatives & Differentials2 min

3.2.1. Chain Rule2 min

3.2.2. Chain Rule & Implicit Differentiation3 min

3.3.1. Directional Derivative & Gradient Vector2 min

3.Q. Checkpoint Quiz10 Qns

4. Applications

1.3hr

4.1.1. Introduction to Applications of Partial Derivatives1 min

4.2.1. Maximums, Minimums, and Critical Points5 min

4.3.1. Absolute Max and Min2 min

4.3.2. Example3 min

4.3.3. Example6 min

4.3.4. Practice6 min

4.4.1. Lagrange Multipliers3 min

4.5.1. Parametric Curves6 min

4.5.2. Example: Parametric Curve4 min

4.5.3. Practice Question: Parametric Curve2 min

4.5.4. Practice Question: Parametric Curves Graphs3 min

4.5.5. New Practice Question

4.6.1. Arc Length41 sec

4.6.2. Example: Arc Length6 min

4.6.3. Practice: Arc Length Function4 min

4.6.4. Practice Question: Arc Length Function4 min

4.Q. Checkpoint Quiz9 Qns

5. Multiple Integrals and Polar Coordinates

2.2hr

5.1.1. Introduction to Multiple Integrals1 min

5.2.1. Double Integrals over Rectangular Regions4 min

5.2.2. Example: Double Integrals over Rectangular Regions (1)2 min

5.2.3. Example: Double Integrals over Rectangular Regions (2)5 min

5.2.4. Example: Iterated Integrals (1)4 min

5.3.1. Double Integrals over General Regions1 min

5.3.2. Example: Double Integrals over General Regions (1)5 min

5.3.3. Example: Double Integrals over General Regions (2)2 min

5.3.4. Practice: Double Integrals over General Regions (1)3 min

5.3.5. Practice: Double Integrals over General Regions (2)5 min

5.4.1. Polar Coordinates7 min

5.4.2. New Practice Question

5.5.1. Double Integrals in Polar Coordinates2 min

5.5.2. Example: Double Integrals in Polar Coordinates (1)3 min

5.5.3. Example: Double Integrals in Polar Coordinates (2)3 min

5.5.4. Practice: Double Integrals in Polar Coordinates (1)3 min

5.5.5. Practice: Double Integrals in Polar Coordinates (2)2 min

5.6.1. Application of the Double Integral 4 min

5.6.2. Example: Mass (1)2 min

5.6.3. Example: Center of Mass (2)5 min

5.6.4. Example: Surface Area (3)

5.6.5. Practice: Center of Mass (1)5 min

5.6.6. Practice: Center of Mass (2)4 min

5.6.7. Practice: Surface Area (3)

5.7.1. Triple Integrals over Rectangular Regions1 min

5.7.2. Triple Integrals over Regions of General Shape2 min

5.7.3. Example: Triple Integrals over Regions of General Shape (1)2 min

5.7.4. Example: Triple Integrals over Regions of General Shape (2)3 min

5.7.5. Practice: Triple Integrals over Regions of General Shape (1)3 min

5.7.6. Practice: Triple Integrals over Regions of General Shape (2)2 min

5.7.7. Practice: Changing the Order of Integration - Triple Integrals (3)12 min

5.7.8. Practice Question: Changing the Order of Integration - Triple Integrals (4)7 min

5.8.1. Spherical Coordinates

5.9.1. Triple Integrals in Cylindrical Coordinates2 min

5.9.2. Triple Integrals in Spherical Coordinates1 min

5.9.3. Example: Triple Integrals in Cylindrical Coordinates (1)2 min

5.9.4. Example: Triple Integrals in Spherical Coordinates (2)4 min

5.9.5. Practice: Triple Integrals in Cylindrical Coordinates (1)3 min

5.9.6. Practice: Triple Integrals in Spherical Coordinates (2)4 min

5.9.7. Practice: Triple Integrals in Cylindrical Coordinates & Spherical Coordinates (3)7 min

5.Q. Checkpoint Quiz2 Qns

6. Curves

8min

6.1.1. Frenet Frame5 min

6.1.2. What Do We Mean by r(t)?1 min

6.1.3. A Parameterization for

y = y(x)

2 min

6.1.4.

s

,

\hat{T}

,

\hat{N}

,

\hat{B}

,

\kappa

and

\tau

of a helix.

MATH 222

Course Overview

1. Sequences and Series

2. Vectors

3. Partial Differentiation

4. Applications

5. Multiple Integrals and Polar Coordinates

6. Curves

Midterm Overview

Course Notes