MATH 200

UBC

Course Overview

Lessons & Practice

1. Vectors & Geometry of Space

1.5hr

1.1.1. Vectors in 2D and 3D Systems2 min

1.1.3. Example2 min

1.1.4. Practice52 sec

1.1.5. Practice1 min

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

1.2.2. Example1 min

1.2.3. Vector Arithmetic, Properties of Vectors, Length1 min

1.2.4. Practice3 min

1.2.5. Practice1 min

1.3.1. Dot Product4 min

1.3.2. Example2 min

1.3.3. Example2 min

1.3.4. Practice4 min

1.4.1. Cross Product2 min

1.4.2. Example2 min

1.4.3. Practice1 min

1.4.4. Practice4 min

1.5.1. Equations of Lines5 min

1.5.2. Example3 min

1.5.3. Example2 min

1.5.4. Practice2 min

1.6.1. Equations of Planes5 min

1.6.2. Example3 min

1.6.3. Example9 min

1.6.4. Practice7 min

1.6.5. Practice4 min

1.7.1. Quadratic Surfaces and Level Curves

1.7.2. Example3 min

1.7.3. Example2 min

1.7.4. Practice2 min

1.7.5. Practice4 min

1.Q. Checkpoint Quiz8 Qns

2. Vector Functions

17min

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

2.1.2. Example2 min

2.1.3. Example1 min

2.1.4. Practice1 min

2.2.1. Tangent, Normal, Binormal Vectors 2 min

2.2.2. Example2 min

2.2.3. Example2 min

2.2.4. Practice3 min

3. Partial Derivatives

31min

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.Q. Checkpoint Quiz10 Qns

4. Applications of Partial Derivatives

1.2hr

4.1.1. Introduction to Applications of Partial Derivatives1 min

4.2.1. Tangent Planes & Linear Approximation5 min

4.2.2. Example2 min

4.2.3. Example3 min

4.2.4. Practice2 min

4.2.5. Practice2 min

4.3.1. Gradient Vectors, Tangent Planes, Normal Lines2 min

4.3.3. Example3 min

4.3.4. Practice

4.4.1. Maximums, Minimums, and Critical Points5 min

4.4.2. Example5 min

4.4.3. Example5 min

4.4.4. Practice4 min

4.4.5. Practice3 min

4.5.1. Absolute Max and Min2 min

4.5.2. Example3 min

4.5.3. Example6 min

4.5.4. Practice6 min

4.6.1. Lagrange Multipliers3 min

4.6.2. Example3 min

4.6.4. Practice3 min

4.6.5. Practice4 min

4.Q. Checkpoint Quiz9 Qns

5. Multiple Integrals

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. Double Integrals in Polar Coordinates2 min

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

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

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

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

5.5.1. Application of the Double Integral 4 min

5.5.2. Example: Mass (1)2 min

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

5.5.4. Example: Surface Area (3)

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

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

5.5.7. Practice: Surface Area (3)

5.6.1. Triple Integrals over Rectangular Regions1 min

5.6.2. Triple Integrals over Regions of General Shape2 min

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

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

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

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

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

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

5.7.1. Triple Integrals in Cylindrical Coordinates2 min

5.7.2. Triple Integrals in Spherical Coordinates1 min

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

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

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

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

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

5.Q. Checkpoint Quiz2 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

Test 2 Overview

Course Notes

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