1. Vectors and the Geometry of Space

49min

1.1.1. Equations of Lines5 min

1.1.2. Example3 min

1.1.3. Example2 min

1.1.4. Practice2 min

1.2.1. Equations of Planes5 min

1.3.1. Quadratic Surfaces and Level Curves

1.Q. Checkpoint Quiz8 Qns

2. Vector Functions

26min

2.1.1. Vector-Valued Functions5 min

2.1.2. Example2 min

2.1.3. Practice: Derivative of a vector-valued function1 min

2.2.1. Arc Length6 min

2.2.2. Curvature5 min

2.2.3. Example2 min

2.2.4. Example2 min

2.2.5. Practice3 min

3. Partial Derivatives

1.2hr

3.1.1. Functions of Several Variables5 min

3.1.2. Practice3 min

3.2.1. Partial derivatives6 min

3.2.2. Practice: First Partial derivatives2 min

3.2.3. Practice: Second Partial Derivatives3 min

3.3.1. Tangent plane3 min

3.3.2. Practice: Tangent Plane

3.3.3. Linear (Tangent Plane) Approximation3 min

3.3.4. Practice: Linear approximation

3.4.1. Chain Rule7 min

3.4.2. Practice: Chain Rule2 min

3.4.3. Practice: Chain Rule2 min

3.4.4. Practice: Chain Rule*3 min

3.4.5. Implicit Differentiation2 min

3.5.1. Gradient and directional derivative7 min

3.5.2. Practice: Gradient and directional derivative

3.6.1. Local Max & Min4 min

3.6.2. Absolute Max & Min5 min

3.6.3. Lagrange Multipliers3 min

3.6.4. Practice: Lagrange Multipliers

3.6.5. Practice: Lagrange Multipliers

3.7.1. Lagrange Multipliers3 min

3.8.1. Multivariable Functions Quiz12 Qns

4. Multiple Integrals

2.6hr

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 Coordinates2 min

4.7.2. Triple Integrals in Spherical Coordinates1 min

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

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

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

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

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

4.8.1. Change of Variables6 min

4.8.2. Example: Change of variables 18 min

4.8.3. Example: Change of variables 25 min

4.8.4. Practice: Change of variables 18 min

4.8.5. Practice: Change of variables 24 min

4.Q. Checkpoint Quiz2 Qns

5. Infinite Sequences and Series

4hr

5.1.1. The Divergence Test5 min

5.1.2. The Divergence Test51 sec

5.1.3. The Divergence Test49 sec

5.1.4. The Divergence Test31 sec

5.1.5. The Divergence Test1 min

5.1.6. The Divergence Test40 sec

5.1.7. The Divergence Test37 sec

5.1.8. The Divergence Test1 min

5.1.9. The Divergence Test31 sec

5.2.1. The Integral Test14 min

5.2.2. The Integral Test7 min

5.2.3. The Integral Test4 min

5.2.4. The Integral Test7 min

5.2.5. The Integral Test3 min

5.2.6. The Integral Test5 min

5.2.7. The Integral Test3 min

5.2.8. The Integral Test2 min

5.2.9. The Integral Test5 min

5.2.10. P-Series

\sum_{n}^{\infty}\limits \frac{1}{n^p}

4 min

5.3.1. The Limit Comparison Test15 min

5.3.2. The Limit Comparison Test3 min

5.3.3. The Limit Comparison Test5 min

5.3.4. The Limit Comparison Test6 min

5.3.5. The Limit Comparison Test2 min

5.3.6. The Limit Comparison Test9 min

5.3.7. The Limit Comparison Test34 sec

5.3.8. The Limit Comparison Test6 min

5.3.9. The Limit Comparison Test30 sec

5.3.10. The Limit Comparison Test43 sec

5.4.1. The Root and Ratio Test4 min

5.4.2. The Root and Ratio Test4 min

5.4.3. The Root and Ratio Test4 min

5.4.4. The Root and Ratio Test4 min

5.4.5. The Root and Ratio Test6 min

5.4.6. The Root and Ratio Test5 min

5.4.7. The Root and Ratio Test4 min

5.4.8. The Root and Ratio Test1 min

5.4.9. The Root and Ratio Test2 min

5.4.10. The Root and Ratio Test3 min

5.5.1. The Alternating Series Test: Step 16 min

5.5.2. The Alternating Series Test: Step 24 min

5.5.3. The Conditional Convergence Test for Alternating Series4 min

5.5.4. The Conditional Convergence Test for Alternating Series50 sec

5.5.5. The Conditional Convergence Test for Alternating Series45 sec

5.5.6. The Conditional Convergence Test for Alternating Series1 min

5.5.7. The Conditional Convergence Test for Alternating Series1 min

5.5.8. The Conditional Convergence Test for Alternating Series2 min

5.5.9. The Conditional Convergence Test for Alternating Series2 min

5.5.10. The Conditional Convergence Test for Alternating Series2 min

5.5.11. The Conditional Convergence Test for Alternating Series2 min

5.6.1. Definitions of Power Series9 min

5.6.2. Practice (radius of convergence)2 min

5.6.3. Practice (radius & interval of convergence)7 min

5.6.4. Practice: Radius & Interval of Convergence4 min

5.7.1. Representing Functions as Power Series2 min

5.7.2. Practice2 min

5.7.3. Practice2 min

5.7.4. Practice (w/ partial fractions)7 min

5.7.5. Differentiation and Integration of Power Series3 min

5.7.6. Practice (differentiating power series)4 min

5.7.7. Practice (integrating power series)4 min

5.7.8. Practice (integrating power series*)8 min

5.8.1. Taylor and Maclaurin Series6 min

5.8.2. Practice (Taylor series)7 min

5.8.3. Common Maclaurin Series (Memorize!)*5 min

5.8.4. Practice (Maclaurin series)2 min

5.8.5. Practice (Maclaurin series)3 min

5.8.6. Practice (Maclaurin series of an integral)2 min

5.8.7. Practice (evaluating a series*)3 min

5.Q. Sequences and Series Quiz13 Qns

MATH 262

Course Overview

1. Vectors and the Geometry of Space

2. Vector Functions

3. Partial Derivatives

4. Multiple Integrals

5. Infinite Sequences and Series

Final Exam Overview

Course Notes