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Dr. Trefor Bazett

Calculus II (Integration Methods, Series, Parametric/Polar, Vectors) **Full Course**

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Last updated on Dec 1, 2023
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Welcome to Calculus II
8:48
Intro to Integration By Parts --- Examples: ∫xsinxdx & ∫arctan(x)dx
9:34
Two Tricky Integration By Parts Examples
8:35
Trigonometric Integrals ---  ∫sin^n(x)cos^m(x)dx via Pythagorean or Half-Angle Identities
8:10
Intro to Trigonometric Substitution  --- Ex: Deriving Area of Circle Formula
7:22
Trig Subs  |  How To Choose The Substitution & Deal With Indefinite Integrals
8:10
Deconstructing a messy integral | Trig subs & u-subs combined
11:39
Integration by Partial Fractions | Big Idea + First Example
9:51
Partial Fractions | Repeating and irreducible Quadratic Terms
10:10
Choosing what integration methods to use - Part I
9:28
Choosing what integration methods to use - Challenging Example!
9:04
MATH PROF vs TRICKY INTEGRALS
23:46
Improper Integrals: How to Integrate with Infinities, 2 ways!
8:51
Comparison Test for Improper Integrals
7:55
Arclength Formula | Derivation & Ex: Circumference of a Circle
10:13
Area of Surfaces of Revolution | Derivation & Example
8:29
Infinite Surface Area but Finite Volume!?!?   *Gabriel's Horn*
5:22
Intro to Sequences
4:00
Limits of Sequences, Limit laws & Function Representations
8:26
The Hierarchy of Big Functions || n^n greater than n! greater than e^n greater than n^100
15:49
Intro to Series: What is 1/2+1/4+1/8+1/16+...?
5:38
Geometric Series  | Convergence, Derivation, and Example
6:28
Harmonic Series | It diverges, but insanely slowly!
4:39
Integral Test | Derivation & 1st Example
8:55
Estimating the Remainder of a Series Approximation via the Integral Test
9:03
Comparison Test for Series
4:51
Limit Comparison Test for Series
5:09
Alternating Series Test | Intuition, Statement & Example
4:54
Alternating Series | Estimating the Remainder
5:30
The bizarre world of INFINITE rearrangements  // Riemann Series Theorem
17:38
Absolute Convergence vs Conditional Convergence vs Convergence
3:41
Ratio & Root Tests | Geometric Series Generalized
9:12
Choosing Which Convergence Test to Apply to 8 Series
12:13
Solving Inequalities with Absolute Values: Ex |x-2| less than 3
4:34
Power Series & Intervals of Convergence
9:29
Intro to Taylor Series: Approximations on Steroids
12:43
3 Applications of Taylor Series: Integrals, Limits, & Series
7:22
Why Taylor Series actually work: The Taylor Inequality
9:35
Plotting Parametric Curves
4:59
Tangents to Parametric Curves | Multiple tangents at the same point!!
6:16
Area under a Parametric Curve | Formula, Derivation, & Example
5:39
Arclength of Parametric Curves
6:00
Intro to Polar Coordinates
10:52
Sketching Polar Curves
9:08
Areas in Polar Coordinates
5:01
Example: Area Inside Polar Curves
6:04
Why Exponential Growth?? Intro to Separable Differential Equations
10:14
Defining the Natural Logarithm as an Integral?!?!?
12:23
Intro to COMPLEX NUMBERS // Motivation, Algebraic Definition & Fundamental Theorem of Algebra Ep. 1
12:00
The geometric view of COMPLEX NUMBERS
10:19
The Polar Form of COMPLEX NUMBERS  // Finding the nth roots of -1
15:11
Why hyperbolic functions are actually really nice
16:03