Mastering Advanced Calculus: Integration to Polar Coordinates
Master Calculus II: Dive into Integrals and Infinite Series with Expert Guidance!
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What you'll learn
Develop proficiency in integration techniques such as parts, trigonometric substitutions, and partial fractions
Apply integration methods to solve improper integrals and series approximations
Analyze parametric and polar curves for calculus problems, including areas and arc lengths
Understand complex numbers and sequences to evaluate limits and convergence tests
This course includes
7.5 hours of video
Certificate of completion
Access on mobile and TV
Course content
1 modules
• 52 lessons
• 7.5 hours of video
Mastering Advanced Calculus: Integration to Polar Coordinates
52 lessons
• 7.5 hours
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Welcome to Calculus II08:48
Intro to Integration By Parts --- Examples: ∫xsinxdx & ∫arctan(x)dx09:34
Two Tricky Integration By Parts Examples08:34
Trigonometric Integrals --- ∫sin^n(x)cos^m(x)dx via Pythagorean or Half-Angle Identities08:09
Intro to Trigonometric Substitution --- Ex: Deriving Area of Circle Formula07:21
Trig Subs | How To Choose The Substitution & Deal With Indefinite Integrals08:10
Deconstructing a messy integral | Trig subs & u-subs combined11:39
Integration by Partial Fractions | Big Idea + First Example09:51
Partial Fractions | Repeating and irreducible Quadratic Terms10:10
Choosing what integration methods to use - Part I09:28
Choosing what integration methods to use - Challenging Example!09:04
MATH PROF vs TRICKY INTEGRALS23:46
Improper Integrals: How to Integrate with Infinities, 2 ways!08:50
Comparison Test for Improper Integrals07:54
Arclength Formula | Derivation & Ex: Circumference of a Circle10:12
Area of Surfaces of Revolution | Derivation & Example08:29
Infinite Surface Area but Finite Volume!?!? *Gabriel's Horn*05:21
Intro to Sequences03:59
Limits of Sequences, Limit laws & Function Representations08:26
The Hierarchy of Big Functions || n^n greater than n! greater than e^n greater than n^10015:49
Intro to Series: What is 1/2+1/4+1/8+1/16+...?05:37
Geometric Series | Convergence, Derivation, and Example06:27
Harmonic Series | It diverges, but insanely slowly!04:39
Integral Test | Derivation & 1st Example08:55
Estimating the Remainder of a Series Approximation via the Integral Test09:03
Comparison Test for Series04:50
Limit Comparison Test for Series05:09
Alternating Series Test | Intuition, Statement & Example04:53
Alternating Series | Estimating the Remainder05:30
The bizarre world of INFINITE rearrangements // Riemann Series Theorem17:37
Absolute Convergence vs Conditional Convergence vs Convergence03:40
Ratio & Root Tests | Geometric Series Generalized09:12
Choosing Which Convergence Test to Apply to 8 Series12:12
Solving Inequalities with Absolute Values: Ex |x-2| less than 304:33
Power Series & Intervals of Convergence09:28
Intro to Taylor Series: Approximations on Steroids12:43
3 Applications of Taylor Series: Integrals, Limits, & Series07:22
Why Taylor Series actually work: The Taylor Inequality09:35
Plotting Parametric Curves04:59
Tangents to Parametric Curves | Multiple tangents at the same point!!06:16
Area under a Parametric Curve | Formula, Derivation, & Example05:38
Arclength of Parametric Curves06:00
Intro to Polar Coordinates10:52
Sketching Polar Curves09:07
Areas in Polar Coordinates05:01
Example: Area Inside Polar Curves06:04
Why Exponential Growth?? Intro to Separable Differential Equations10:14
Defining the Natural Logarithm as an Integral?!?!?12:22
Intro to COMPLEX NUMBERS // Motivation, Algebraic Definition & Fundamental Theorem of Algebra Ep. 112:00
The geometric view of COMPLEX NUMBERS10:19
The Polar Form of COMPLEX NUMBERS // Finding the nth roots of -115:11
Why hyperbolic functions are actually really nice16:03
