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Intro to COMPLEX NUMBERS // Motivation, Algebraic Definition & Fundamental Theorem of Algebra Ep. 1
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- 1Welcome to Calculus II
- 2Intro to Integration By Parts --- Examples: ∫xsinxdx & ∫arctan(x)dx
- 3Two Tricky Integration By Parts Examples
- 4Trigonometric Integrals --- ∫sin^n(x)cos^m(x)dx via Pythagorean or Half-Angle Identities
- 5Intro to Trigonometric Substitution --- Ex: Deriving Area of Circle Formula
- 6Trig Subs | How To Choose The Substitution & Deal With Indefinite Integrals
- 7Deconstructing a messy integral | Trig subs & u-subs combined
- 8Integration by Partial Fractions | Big Idea + First Example
- 9Partial Fractions | Repeating and irreducible Quadratic Terms
- 10Choosing what integration methods to use - Part I
- 11Choosing what integration methods to use - Challenging Example!
- 12MATH PROF vs TRICKY INTEGRALS
- 13Improper Integrals: How to Integrate with Infinities, 2 ways!
- 14Comparison Test for Improper Integrals
- 15Arclength Formula | Derivation & Ex: Circumference of a Circle
- 16Area of Surfaces of Revolution | Derivation & Example
- 17Infinite Surface Area but Finite Volume!?!? *Gabriel's Horn*
- 18Intro to Sequences
- 19Limits of Sequences, Limit laws & Function Representations
- 20The Hierarchy of Big Functions || n^n greater than n! greater than e^n greater than n^100
- 21Intro to Series: What is 1/2+1/4+1/8+1/16+...?
- 22Geometric Series | Convergence, Derivation, and Example
- 23Harmonic Series | It diverges, but insanely slowly!
- 24Integral Test | Derivation & 1st Example
- 25Estimating the Remainder of a Series Approximation via the Integral Test
- 26Comparison Test for Series
- 27Limit Comparison Test for Series
- 28Alternating Series Test | Intuition, Statement & Example
- 29Alternating Series | Estimating the Remainder
- 30The bizarre world of INFINITE rearrangements // Riemann Series Theorem
- 31Absolute Convergence vs Conditional Convergence vs Convergence
- 32Ratio & Root Tests | Geometric Series Generalized
- 33Choosing Which Convergence Test to Apply to 8 Series
- 34Solving Inequalities with Absolute Values: Ex |x-2| less than 3
- 35Power Series & Intervals of Convergence
- 36Intro to Taylor Series: Approximations on Steroids
- 373 Applications of Taylor Series: Integrals, Limits, & Series
- 38Why Taylor Series actually work: The Taylor Inequality
- 39Plotting Parametric Curves
- 40Tangents to Parametric Curves | Multiple tangents at the same point!!
- 41Area under a Parametric Curve | Formula, Derivation, & Example
- 42Arclength of Parametric Curves
- 43Intro to Polar Coordinates
- 44Sketching Polar Curves
- 45Areas in Polar Coordinates
- 46Example: Area Inside Polar Curves
- 47Why Exponential Growth?? Intro to Separable Differential Equations
- 48Defining the Natural Logarithm as an Integral?!?!?
- 49Intro to COMPLEX NUMBERS // Motivation, Algebraic Definition & Fundamental Theorem of Algebra Ep. 1
- 50The geometric view of COMPLEX NUMBERS
- 51The Polar Form of COMPLEX NUMBERS // Finding the nth roots of -1
- 52Why hyperbolic functions are actually really nice