Calculus II (Integration Methods, Series, Parametric/Polar, Vectors) **Full Course**
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
Mastering Advanced Calculus: Integration to Polar Coordinates
52 lessons
• 7.5 hours
- Welcome to Calculus II 08:48
- Intro to Integration By Parts --- Examples: ∫xsinxdx & ∫arctan(x)dx 09:34
- Two Tricky Integration By Parts Examples 08:35
- Trigonometric Integrals --- ∫sin^n(x)cos^m(x)dx via Pythagorean or Half-Angle Identities 08:10
- Intro to Trigonometric Substitution --- Ex: Deriving Area of Circle Formula 07:22
- Trig Subs | How To Choose The Substitution & Deal With Indefinite Integrals 08:10
- Deconstructing a messy integral | Trig subs & u-subs combined 11:39
- Integration by Partial Fractions | Big Idea + First Example 09:51
- Partial Fractions | Repeating and irreducible Quadratic Terms 10:10
- Choosing what integration methods to use - Part I 09:29
- Choosing what integration methods to use - Challenging Example! 09:04
- MATH PROF vs TRICKY INTEGRALS 23:46
- Improper Integrals: How to Integrate with Infinities, 2 ways! 08:51
- Comparison Test for Improper Integrals 07:55
- Arclength Formula | Derivation & Ex: Circumference of a Circle 10:13
- Area of Surfaces of Revolution | Derivation & Example 08:29
- Infinite Surface Area but Finite Volume!?!? *Gabriel's Horn* 05:22
- Intro to Sequences 04:00
- Limits of Sequences, Limit laws & Function Representations 08:26
- 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+...? 05:38
- Geometric Series | Convergence, Derivation, and Example 06:28
- Harmonic Series | It diverges, but insanely slowly! 04:39
- Integral Test | Derivation & 1st Example 08:55
- Estimating the Remainder of a Series Approximation via the Integral Test 09:03
- Comparison Test for Series 04:51
- Limit Comparison Test for Series 05:09
- Alternating Series Test | Intuition, Statement & Example 04:54
- Alternating Series | Estimating the Remainder 05:30
- The bizarre world of INFINITE rearrangements // Riemann Series Theorem 17:38
- Absolute Convergence vs Conditional Convergence vs Convergence 03:41
- Ratio & Root Tests | Geometric Series Generalized 09:12
- Choosing Which Convergence Test to Apply to 8 Series 12:13
- Solving Inequalities with Absolute Values: Ex |x-2| less than 3 04:34
- Power Series & Intervals of Convergence 09:29
- Intro to Taylor Series: Approximations on Steroids 12:43
- 3 Applications of Taylor Series: Integrals, Limits, & Series 07:22
- Why Taylor Series actually work: The Taylor Inequality 09:35
- Plotting Parametric Curves 04:59
- Tangents to Parametric Curves | Multiple tangents at the same point!! 06:16
- Area under a Parametric Curve | Formula, Derivation, & Example 05:39
- Arclength of Parametric Curves 06:00
- Intro to Polar Coordinates 10:52
- Sketching Polar Curves 09:08
- Areas in Polar Coordinates 05:01
- Example: Area Inside Polar Curves 06:04
- 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
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