Total Differentials #calculus3

# Calculus 3 Playlist: https://youtube.com/playlist?list=PL3Kq77Wcurj6w2CMP-0blhVyeAk_m1wQN&si=x8uR9odyAP6ChyfD ## Chapter 1: Parametric Equations and Polar Coordinates ### 1.1 Parametric Equations - Eliminating the Parameter https://youtu.be/LQQqJh3HSzA - Sketching and Orientation https://youtu.be/7CXPuFplGCY - Finding the Slope of the Tangent Line https://youtu.be/uORC3RWIkRo - Equation of a Tangent Line at a Point https://youtu.be/knyINc5oTfg ### 1.2 Polar Coordinates - Converting Rectangular to Polar Coordinates https://youtu.be/QTWQiot3S0I - Converting Equations to Rectangular Form https://youtu.be/haBbkIjId0c - Identifying a Curve from a Polar Equation https://youtu.be/Ak8D9KlA-WE ### 1.3 Polar Curves - Sketching and Identifying Curves https://youtu.be/xqw8fvFNv28 - Working with Cardioids https://youtu.be/W1W0kxYP8vU ### 1.4 Tangent Lines and Arc Length for Parametric and Polar Curves - Tangent Line of a Parametric Curve https://youtu.be/tboYwwpBgnA - Arc Length of a Polar Curve https://youtu.be/djO1Rg9AIyU - Arc Length Inside a Cardioid https://youtu.be/pMv7K4AxpiQ - Setting Up Arc Length https://youtu.be/ZISweqspt9A ## Chapter 2: Three-Dimensional Space; Vectors ### 2.1 Rectangular Coordinates in 3-Space - Finding Distance and Midpoint https://youtu.be/DBAuu0ZLedc - Finding the Equation of a Sphere https://youtu.be/EKwaQkrM7iI ### 2.2 Vectors - Finding Components and Magnitude https://youtu.be/v6j507LFzec - Unit Vectors and Orthogonality https://youtu.be/FLEQnQ1s960 ### 2.3 Dot Products; Projections - Finding the Angle Between Vectors https://youtu.be/5IrxpSUYAk4 - Vector Projection https://youtu.be/GiJjymrAgf0 ### 2.4 Cross Products - Computing the Cross Product https://youtu.be/4pAwwT9iqqY - Area of a Triangle https://youtu.be/buzb5YMWl1Y - Volume of a Parallelepiped https://youtu.be/L0r4GPT48F4 ### 2.5 Parametric Equations of Lines - Finding Equations of a Line https://youtu.be/vURReUb5wLw - Intersection of Two Lines https://youtu.be/U0JEiwK4osw ### 2.6 Planes in 3-Space - Finding the Equation of a Plane https://youtu.be/EfVTqdHl7qA - Plane Perpendicular to a Line https://youtu.be/U6sGsQp4KEY - Distance from a Point to a Plane https://youtu.be/CpqwnHUX96U ### 2.7 Cylindrical and Quadric Surfaces - Identifying a Surface https://youtu.be/QkIcF-gPoVY - Reducing to Standard Form https://youtu.be/Q_iE3pQt9b8 ## Chapter 3: Partial Derivatives ### 3.1 Functions of Two or More Variables - Finding and Sketching the Domain https://youtu.be/9EhC-BwtE9s - Sketching Level Curves https://youtu.be/BHHHwHePMyg ### 3.2 Limits and Continuity - Showing a Limit Does Not Exist https://youtu.be/o-X1ZK0pS_o - Continuity and Piecewise Functions https://youtu.be/2k0VB2U0dGM ### 3.3 Partial Derivatives - Finding First Partial Derivatives https://youtu.be/LXIB3JEqKCY - Mixed Partial Derivatives https://youtu.be/yckKT7Pyi6E - Mixed Partials Not Equal (Continuity Fails) https://youtu.be/CW5M5Tv-JEQ ### 3.4 Chain Rule - Single Parameter https://youtu.be/L95DEGr6xbo - Multiple Parameters https://youtu.be/TSfGVv_wZHc - Implicit Partial Differentiation https://youtu.be/bNaPXfM471M ### 3.5 Tangent Plane; Total Differentials - Finding the Equation of a Tangent Plane https://youtu.be/i9r7cyx3jFI - Total Differentials (Numerical Approximation) https://youtu.be/Q-wC4KjrA48 ### 3.6 Directional Derivatives - Calculating a Directional Derivative https://youtu.be/jmKeYWEfQf4 - Maximum Rate of Change https://youtu.be/1g4dqFgMPj4 - Zero Directional Derivative and Level Curves https://youtu.be/rp8TO4C5DY4 ### 3.7 Maxima and Minima of Functions of Two Variables - Classifying Critical Points https://youtu.be/19pjpABv550 - An Inconclusive Case (D = 0) https://youtu.be/9sOqS2-fYu0 ## Chapter 4: Multiple Integrals ### 4.1 Double Integrals in Rectangular Coordinates - Evaluating an Iterated Integral https://youtu.be/_jd9u3GTfBk - Calculating Volume Over a Rectangle https://youtu.be/WNXD4EbO0tU ### 4.2 Double Integrals Over Non-rectangular Regions - Evaluating a Type I Integral https://youtu.be/iph_pXfwgPs - Reversing the Order of Integration https://youtu.be/PJj5Fvj9wp8 ### 4.3 Double Integrals in Polar Coordinates - Evaluating a Basic Polar Integral https://youtu.be/oxhrtPoPYf0 - Region Above the x-axis https://youtu.be/3mNTSnTAlQs ### 4.4 Triple Integrals in Rectangular Coordinates - Evaluating a Basic Triple Integral https://youtu.be/r6d6BvL3UG8 - Volume of a Solid https://youtu.be/J4iSl1fY6Do ### 4.5 Triple Integrals in Cylindrical and Spherical Coordinates - Evaluating a Triple Integral in Spherical Coordinates https://youtu.be/ueuEt84QEVI - Volume of an Ice Cream Cone https://youtu.be/yVifveYaSg4