MATH 20C

UCSD

Course Overview

Lessons & Practice

I. Welcome

2. Vector Functions

24min

2.1.1. Vector-Valued Functions5 min

2.1.2. Arc Length6 min

2.1.3. Curvature5 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. Differentiation in Several Variable

1.9hr

3.1.1. Theory5 min

3.1.2. Example: Function w/ 2 Variables (1)2 min

3.1.3. Example: Function w/ 2 Variables (2)1 min

3.1.4. Practice: Contour Curves (1)1 min

3.2.1. Introduction to Partial Derivatives2 min

3.3.1. Partial Derivatives3 min

3.3.2. Higher Order Partial Derivatives & Differentials2 min

3.3.3. Example1 min

3.3.4. Example1 min

3.3.5. Practice1 min

3.3.6. Practice2 min

3.4.1. Tangent Planes & Linear Approximation5 min

3.4.2. Example2 min

3.4.3. Example3 min

3.4.4. Practice2 min

3.4.5. Practice2 min

3.5.1. Gradient Vectors, Tangent Planes, Normal Lines2 min

3.5.3. Example3 min

3.5.4. Practice

3.6.1. Directional Derivative & Gradient Vector2 min

3.6.2. Example2 min

3.6.3. Example2 min

3.6.4. Practice2 min

3.6.5. Practice2 min

3.7.1. Chain Rule2 min

3.7.2. Chain Rule & Implicit Differentiation3 min

3.7.3. Example2 min

3.7.4. Example1 min

3.7.5. Practice2 min

3.7.6. Practice

3.8.1. Introduction to Applications of Partial Derivatives1 min

3.9.1. Maximums, Minimums, and Critical Points5 min

3.9.2. Example5 min

3.9.3. Example5 min

3.9.4. Practice4 min

3.9.5. Practice3 min

3.10.1. Absolute Max and Min2 min

3.10.2. Example3 min

3.10.3. Example6 min

3.10.4. Practice6 min

3.11.1. Lagrange Multipliers3 min

3.11.2. Example3 min

3.11.3. Example

3.11.4. Practice3 min

3.11.5. Practice4 min

3.Q. Checkpoint Quiz10 Qns

4. Multiple Integrals

1.7hr

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. Triple Integrals over Rectangular Regions1 min

4.4.2. Triple Integrals over Regions of General Shape2 min

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

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

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

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

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

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

4.5.1. Double Integrals in Polar Coordinates2 min

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

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

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

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

4.6.1. Triple Integrals in Cylindrical Coordinates2 min

4.6.2. Triple Integrals in Spherical Coordinates1 min

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

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

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

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

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

4.Q. Checkpoint Quiz2 Qns

5. Differential Equations

1.2hr

5.1.1. Differential Equations8 min

5.1.2. Direction Fields/Slope Fields5 min

5.1.3. Practice Question: DE Solution Graphs3 min

5.2.1. Separable First Order Differential Equations3 min

5.2.2. Practice (separable DE)2 min

5.2.3. Practice (IVP)3 min

5.2.4. Practice (IVP)3 min

5.2.5. Practice (IVP*)5 min

5.2.6. Practice (separable DE)1 min

5.3.1. Linear First Order Differential Equations7 min

5.3.2. Practice (integrating factor)1 min

5.3.3. Practice (linear DE)3 min

5.3.4. Practice (IVP)3 min

5.3.5. Practice (IVP)4 min

5.4.1. Exponential Growth and Decay3 min

5.4.2. Example4 min

5.4.3. Example5 min

5.4.4. Practice5 min

5.4.5. Practice (population)3 min

5.4.6. Practice (population)4 min

5.5.1. Second-Order Reducible DE

5.5.2. Practice: Dependent Variable Missing

5.5.3. Practice: Independent Variable Missing

5.Q. DE Quiz4 Qns

I Welcome

Free Activity

Welcome to Calculus!
My name is Corey and I'm the instructor for this course. Feel free to go through this course at your own pace.
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Answered

Anonymous

What are the conecpts to focus on for midterm 1 at western 

Corey M

Instructor

Likely limits and differentiation techniques through the chain rule, but double-check with your instructor to see exactly what will be covered.

Unanswered

Layan E

Use the Intermediate Value Theorem to show that thereis a root of the given equation in the specified interval.Use the Intermediate Value Theorem to show that thereis a root of the given equation in the specified interval.
sin(x)=x2−x, x∈(1,2)

Corey M

Instructor

While this isn't quite the place for this question (please refer to the IVT section in the course), and we can't really just solve random problems for you, I can give you a bit of a hint:  You could try moving everything to one side of the equation and treating it like a function, and then see if you can't find function values within your specified range that return a positive value and a negative value (another hint: try the endpoints of your interval first).  If you're able to do that, then the IVT tells us that there should exist a function input between those two points that returns 0 or, in other words, that is a root.

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