MATH 209

U of A

Course Overview

Lessons & Practice

I. Review of Derivatives

1. Review of Derivatives

21min

1.I. Chapter Intro

1.1.1. Interpretation of Derivatives8 min

1.2.1. Derivative Rules7 min

1.3.1. Tangent and Normal Lines4 min

1.4.1. Implicit Differentiation1 min

2. Review of Integration

24min

2.I. Chapter Intro

2.1.1. Antiderivatives & Indefinite Integrals6 min

2.2.1. Review: Sigma Notation6 min

2.3.1. Definite Integrals3 min

2.4.1. Fundamental Theorem of Calculus 13 min

2.5.1. U-Substitution (Integration by Substitution)6 min

3. Week 1-4: Partial Derivatives

1.7hr

3.1.1. Partial Derivatives3 min

3.1.2. Higher Order Partial Derivatives & Differentials2 min

3.1.3. Example1 min

3.1.4. Example1 min

3.1.5. Practice1 min

3.1.6. Practice2 min

3.2.1. Chain Rule2 min

3.2.2. Chain Rule & Implicit Differentiation3 min

3.2.3. Example2 min

3.2.4. Example1 min

3.2.5. Practice2 min

3.2.6. Practice

3.3.1. Directional Derivative & Gradient Vector2 min

3.3.2. Example2 min

3.3.3. Example2 min

3.3.4. Practice2 min

3.3.5. Practice2 min

3.4.1. Introduction to Applications of Partial Derivatives1 min

3.5.1. Tangent Planes & Linear Approximation5 min

3.5.2. Example2 min

3.5.3. Example3 min

3.5.4. Practice2 min

3.5.5. Practice2 min

3.6.1. Gradient Vectors, Tangent Planes, Normal Lines2 min

3.6.3. Example3 min

3.6.4. Practice

3.7.1. Maximums, Minimums, and Critical Points5 min

3.7.2. Example5 min

3.7.3. Example5 min

3.7.4. Practice4 min

3.7.5. Practice3 min

3.8.1. Absolute Max and Min2 min

3.8.2. Example3 min

3.8.3. Example6 min

3.8.4. Practice6 min

3.9.1. Lagrange Multipliers3 min

3.9.2. Example3 min

3.9.4. Practice3 min

3.9.5. Practice4 min

3.Q. Checkpoint Quiz10 Qns

4. Week 5-9: Multiple Integrals

2hr

4.1.1. Introduction to Multiple Integrals1 min

4.2.1. Double Integrals over Rectangular Regions4 min

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

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

4.2.4. Example: Iterated Integrals (1)4 min

4.3.1. Double Integrals over General Regions1 min

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

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

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

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

4.4.1. Double Integrals in Polar Coordinates2 min

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

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

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

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

4.5.1. Application of the Double Integral 4 min

4.5.2. Example: Mass (1)2 min

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

4.5.4. Example: Surface Area (3)

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

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

4.5.7. Practice: Surface Area (3)

4.6.1. Triple Integrals over Rectangular Regions1 min

4.6.2. Triple Integrals over Regions of General Shape2 min

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

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

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

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

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

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

4.7.1. Triple Integrals in Cylindrical Coordinate2 min

4.7.2. Example: Triple Integrals in Cylindrical Coordinate2 min

4.7.3. Practice: Triple Integrals in Cylindrical Coordinate3 min

4.8.1. Triple Integrals in Spherical Coordinate1 min

4.8.2. Example: Triple Integrals in Spherical Coordinate4 min

4.8.3. Practice: Triple Integrals in Spherical Coordinate4 min

4.8.4. Practice: Triple Integrals in Cylindrical & Spherical Coordinates7 min

4.Q. Checkpoint Quiz2 Qns

5. Week 10- 14: Vectors Calculus

48min

5.1.1. Vectors in 2D and 3D Systems2 min

5.1.3. Example2 min

5.1.4. Practice52 sec

5.1.5. Practice1 min

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

5.2.2. Example1 min

5.2.3. Vector Arithmetic, Properties of Vectors, Length1 min

5.2.4. Practice3 min

5.2.5. Practice1 min

5.3.1. Quadratic Surfaces and Level Curves

5.3.2. Example3 min

5.3.3. Example2 min

5.3.4. Practice2 min

5.3.5. Practice4 min

5.4.1. Functions of 2 & 3 Variables and Contour Curves5 min

5.4.2. Example2 min

5.4.3. Example1 min

5.4.4. Practice1 min

5.5.1. Tangent, Normal, Binormal Vectors 2 min

5.5.2. Example2 min

5.5.3. Example2 min

5.5.4. Practice3 min

5.Q. Checkpoint Quiz8 Qns

6. Appendix: Review Table for lines and planes

6.1.1. Vector, dot product, cross product, projection

6.2.1. Cross product

6.3.1. Line and plane equations, linear independent

6.4.1. Vectors and Geometry of Space

6.4.2. Partial Derivatives

6.4.3. Double Integrals

6.4.4. Triple Integrals

6.5.1. Trigonometric Functions

I Review of Derivatives

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