EXAMPLE 1 11:26 Formula 5 35:42

Theorem 2 1:18 EXAMPLE 1 17:11 - Independence of Path 18:42 Theorem 3 25:42

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Formula 2: Integration by parts formula 3:08 EXAMPLE 1 3:23 Integration by parts order 9:45 EXAMPLE 2 12:26 EXAMPLE 4 27:13 EXAMPLE 5 39:35

Equations 7 0:58 Equation 8 (remember) 2:23 4:46 EXAMPLE 4 5:36 Formula 9 15:23 - Line Integrals in Space 16:06 Formula 9 18:58 Equation 10 21:40 EXAMPLE 5 22:19

EXAMPLE 1 12:18 EXAMPLE 2 17:22 EXAMPLE 3 26:59

Equation 5 2:55 Recall: The Fundamental Thm of Calculus (110A chapter 5) 6:05 Equation 6 9:05 Equation 7 9:33 Equation 8 10:26 recall: arc length formulas 12:19 EXAMPLE 4 15:22

The Arc Length Formula 14:22 15:40 19:40 EXAMPLE 1 22:21 EXAMPLE 2 39:11

- Combining Vectors 21:03

EXAMPLE 1 14:40 EXAMPLE 2 23:38 Practice 1 (HW#1) 28:28 Practice 2 (HW#3) 30:37 Practice 3 (HW#6) 33:35 EXAMPLE 3 37:33 EXAMPLE 4 39:33 EXAMPLE 5 45:00 EXAMPLE 6 48:28 Practice 4 (HW#2) 52:48 Practice 5 (HW#7) 1:01:05

#1 0:20 0:32 #2 0:34 #3 6:09 #4 7:18 How to simplify from v/5sin(5) - v/5sin(-5) --> 2v/5sin(5) 7:20 #5 7:22

EXAMPLE 1 7:15 Jacobian 13:56 EXAMPLE 2 22:58 EXAMPLE 3 28:53 - Triple Integrals 38:13 EXAMPLE 4 40:05

- Spherical Coordinates EXAMPLE 1 9:18 EXAMPLE 2 10:45 - Evaluating Triple Integrals with Spherical Coordinates 12:45 EXAMPLE 3 20:11 EXAMPLE 4 23:08

- Cylindrical Coordinates EXAMPLE 1 5:08 - Evaluating Triple Integrals with Cylindrical Coordinates EXAMPLE 3 19:39 Recap 29:19

EXAMPLE 1 (3) 0:05 EXAMPLE 2 (5) 4:18 EXAMPLE 3 (6) 11:22 EXAMPLE 4 (7) 16:31 EXAMPLE 5 (8) 22:43

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cube formula (a+b)^3=a^3+3a^2b+3ab^2+b^3 17:31

a) Trig functions: i: (sin^m)x(cos^n)x 5:19

moment of the entire lamina about the x-axis/y-axis 15:05 16:09 EXAMPLE 1 21:53 EXAMPLE 2 30:30 - SAVE Method to find the antiderivative of trig function 35:55

EXAMPLE 3 22:23 EXAMPLE 4 35:18

EXAMPLE 7 8:22

Theorem 2 4:00 EXAMPLE 1 14:33 EXAMPLE 2 20:55 Formula 3: Second Derivative Test 26:18

Formula 2 - Change to Polar Coordinates in a Double Integral 13:58 EXAMPLE 1 17:55 EXAMPLE 2 24:19

Review Inverse Trig Functions 0:20 - 5:23

EXAMPLE 3 29:08

Thank you so much! You made it make perfect sense

- The Midpoint Rule EXAMPLE 3 2:48 - Iterated Integrals EXAMPLE 4 9:48 !!! Fubini's Theorem, EXAMPLE 5, 6 are presented in class EXAMPLE 7 14:43 EXAMPLE 8 25:15

EXAMPLE 2 x^3 + y^3 = 6xy a. Find y' 11:58 b. Find slope of tangent @ point (3,3) on x^3+y^3=6xy 14:28 c. At which point in the 1st quadrant is the tangent horizontal? 15:35 EXAMPLE 4 x^4 + y^4 = 16 Find y', y'' 27:23

EXAMPLE 3 2:25 EXAMPLE 4 11:56 !!! EXAMPLE 5 19:49 EXAMPLE 6 29:13

The Gradient Vector - Equation 9 7:30 Functions of Three Variables - Def. 12 11:28 - Ex.5 13:45 Maximizing the Directional Derivatives Theorem 15 23:28

- Length of a Curve 0:11 formula 1 3:35 formula 2 4:12 formula 3 5:12 Example 1 9:45 - The Arc Length Function 17:48 Equation 6 17:52 Equation 7 23:07 Example 2 28:00

- Equation 1 35:00 - Theorem 2 44:23 - Example 1 46:15 Differentiation Rules 57:39 - Theorem 3 57:50 - Example 4 1:00:23 Integrals 1:10:15 - Example 5 1:13:30

NOTE: - Definition 1 16:18 - Example 1 25:00 - Equation 2 (Squeeze Theorem) 28:10 Continuity 32:20 - Example 5 37:45

NOTE: Graphs 6:31 - linear function 9:55 - Example 6 11:50 Level Curves 15:26 - isothermals 24:12 Functions of Three or More Variables 26:13 - Example 14 28:08 - Equation 3 35:55

NOTE: 1) Where does the ball land? 3:33 2) With what speed does the ball hit the ground? 9:10

Equation 1 0:26 Equation 2 2:13 Example 1 6:33 Newton's Second Law of Motion 15:58 - Projectile Motion 16:20 EXAMPLE 5 16:58 Equation 3 (The position vector of the projectile) 23:25 Equation 4 (The parametric equations of the trajectory) 27:02

Want some voice, 34:33 here we go! 😉I can't wait to finish learning calculus, because I want to understand the different if a person have learned cal before, and someone who have never learn calculus before.

20:38 |a dot (bxc)| = |(bxc)dot a |

16:28 只要croos product 是零那么两个向量就是三维水平？

the goat

This is very helpful! Thank you!

you just randomly picked u = y-2x? why not v?

bro thank you so much this was making me lose my mind.

Thank you so much!!! It's such a simple problem but I was losing my mind over finding u and v. You explained it very clearly in a way I haven't seen in any other videos.

wonderful!

💯

Sir, I've found that Alan S. Tussy's books are very helpful for beginners like me. Can you recommend another math book on calculus for a complete beginner?

Thank you so much!

thank you for breaking this down in a simple way

I love the design :)