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Defining the Natural Logarithm as an Integral?!?!?
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Classroom Contents
Calculus II - Integration Methods, Series, Parametric-Polar, Vectors
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- 1 Welcome to Calculus II
- 2 Intro to Integration By Parts --- Examples: ∫xsinxdx & ∫arctan(x)dx
- 3 Two Tricky Integration By Parts Examples
- 4 Trigonometric Integrals --- ∫sin^n(x)cos^m(x)dx via Pythagorean or Half-Angle Identities
- 5 Intro to Trigonometric Substitution --- Ex: Deriving Area of Circle Formula
- 6 Trig Subs | How To Choose The Substitution & Deal With Indefinite Integrals
- 7 Deconstructing a messy integral | Trig subs & u-subs combined
- 8 Integration by Partial Fractions | Big Idea + First Example
- 9 Partial Fractions | Repeating and irreducible Quadratic Terms
- 10 Choosing what integration methods to use - Part I
- 11 Choosing what integration methods to use - Challenging Example!
- 12 MATH PROF vs TRICKY INTEGRALS
- 13 Improper Integrals: How to Integrate with Infinities, 2 ways!
- 14 Comparison Test for Improper Integrals
- 15 Arclength Formula | Derivation & Ex: Circumference of a Circle
- 16 Area of Surfaces of Revolution | Derivation & Example
- 17 Infinite Surface Area but Finite Volume!?!? *Gabriel's Horn*
- 18 Intro to Sequences
- 19 Limits of Sequences, Limit laws & Function Representations
- 20 The Hierarchy of Big Functions || n^n greater than n! greater than e^n greater than n^100
- 21 Intro to Series: What is 1/2+1/4+1/8+1/16+...?
- 22 Geometric Series | Convergence, Derivation, and Example
- 23 Harmonic Series | It diverges, but insanely slowly!
- 24 Integral Test | Derivation & 1st Example
- 25 Estimating the Remainder of a Series Approximation via the Integral Test
- 26 Comparison Test for Series
- 27 Limit Comparison Test for Series
- 28 Alternating Series Test | Intuition, Statement & Example
- 29 Alternating Series | Estimating the Remainder
- 30 The bizarre world of INFINITE rearrangements // Riemann Series Theorem
- 31 Absolute Convergence vs Conditional Convergence vs Convergence
- 32 Ratio & Root Tests | Geometric Series Generalized
- 33 Choosing Which Convergence Test to Apply to 8 Series
- 34 Solving Inequalities with Absolute Values: Ex |x-2| less than 3
- 35 Power Series & Intervals of Convergence
- 36 Intro to Taylor Series: Approximations on Steroids
- 37 3 Applications of Taylor Series: Integrals, Limits, & Series
- 38 Why Taylor Series actually work: The Taylor Inequality
- 39 Plotting Parametric Curves
- 40 Tangents to Parametric Curves | Multiple tangents at the same point!!
- 41 Area under a Parametric Curve | Formula, Derivation, & Example
- 42 Arclength of Parametric Curves
- 43 Intro to Polar Coordinates
- 44 Sketching Polar Curves
- 45 Areas in Polar Coordinates
- 46 Example: Area Inside Polar Curves
- 47 Why Exponential Growth?? Intro to Separable Differential Equations
- 48 Defining the Natural Logarithm as an Integral?!?!?
- 49 Intro to COMPLEX NUMBERS // Motivation, Algebraic Definition & Fundamental Theorem of Algebra Ep. 1
- 50 The geometric view of COMPLEX NUMBERS
- 51 The Polar Form of COMPLEX NUMBERS // Finding the nth roots of -1
