Math 152 - Summer 2020

Online Resources

This page contains all of the resources that I made for the asynchronous summer 2020 Calculus 2 class.

Chapter 5

Section Title	Video List	Video Notes	Worksheet (html)	Worksheet (pdf)
Section 5.7 - The Substitution Method	Video 1: Definition of the Method	Blank Notes	Worksheet 1	Worksheet 1
	Video 2: Definite Integrals by Substitution	Filled Notes
	Video 3: Complicated Substitutions

Chapter 6

Section Title	Video List	Video Notes	Worksheet (html)	Worksheet (pdf)
Section 6.1 - Area between curves	Video 1: Introduction	Blank Notes	Worksheet 2	Worksheet 2
	Video 2: Region Bounded by Two Curves
	Video 3: Curves that Cross Multiple Times	Filled Notes
	Video 4: Multiple Vertically Simple Regions
	Video 5: Horizontally Simple Regions
Section 6.2 - Setting up Integrals	Video 1: Applications of Integrals	Blank Notes	Worksheet 3	Worksheet 3
	Video 2: Volume of Simple Objects
	Video 3: Volumes from Cross-Sectional Area	Filled Notes
	Video 4: Mass of Objects
	Video 5: Average Value of Functions
Section 6.3 - Solids of Revolution - Washer Method	Video 1: Solids of Revolusion	Blank Notes	Worksheet 4	Worksheet 4
	Video 2: Disk Method
	Video 3: Washer Method	Filled Notes
	Video 4: Rotation around other lines
	Video 5: Rotation around vertical lines
Section 6.4 - Solids of Revolution - Shell Method	Video 1: Another Method	Blank Notes	Worksheet 5	Worksheet 5
	Video 2: Multiple Functions and Different Lines
	Video 3: Rotating around Horizontal Lines	Filled Notes
	Video 4: Choosing a Method

Chapter 7

Section Title	Video List	Video Notes	Worksheet (html)	Worksheet (pdf)
Section 7.1 - Integration by Parts	Video 1: Basic Formula	Blank Notes	Worksheet 6	Worksheet 6
	Video 2: Using Integration by Parts
	Video 3: Circular Integration by Parts	Filled Notes
	Video 4: Definite Integration by Parts
	Video 5: Other Integration by Parts
Section 7.2 - Trigonometric Integrals	Video 1: Trigonometric Identities	Blank Notes	Worksheet 7	Worksheet 7
	Video 2: Trigonometric Integrals by Substitution
	Video 3: Trigonometric Integrals by Reduction Formulas
	Video 4: Derivation of Reduction Formulas	Filled Notes
	Video 5: Integrals of Tangent and Secant
	Video 6: Integrals of Products with Different Frequencies
Section 7.3 - Trigonometric Substitution	Video 1: Pythagorean Identities and Potential Use	Blank Notes	Worksheet 8	Worksheet 8
	Video 2: Choosing a Substitution
	Video 3: Converting Expressions back to x	Filled Notes
	Video 4: Completing the Square
Section 7.5 - Method of Partial Fractions	Video 1: Partial Fraction Decompositions	Blank Notes	Worksheet 9	Worksheet 9
	Video 2: Value Substitution and Integrals
	Video 3: Irreducible Quadratics
	Video 4: Repeated Factors	Filled Notes
	Video 5: Long Division
	Video 6a: Combining Adjustments (short version)
	Video 6b: Combining Adjustments (full version)
Section 7.6 - Strategies for Integration	Video 1: Summary of Methods	Blank Notes	Worksheet 10	Worksheet 10
	Video 2: Substitution Methods
	Video 3: Integration by Parts	Filled Notes
	Video 4: Special Techniques
Section 7.7 - Improper Integrals	Video 1: Definitions	Blank Notes	Worksheet 11	Worksheet 11
	Video 2: Infinite Intervals
	Video 3: Unbounded Integrands	Filled Notes
	Video 4: p-Integrals and the Comparison Test
	Video 5: Multiple Issues
Section 7.8 - Numerical Integration	Video 1: Why Numerical Integration?	Blank Notes	Worksheet 12	Worksheet 12
	Video 2: Midpoint and Trapezoid Rule
	Video 3: Simpson's Rule	Filled Notes
	Video 4: Error Bounds

Chapter 10

Section Title	Video List	Video Notes	Worksheet (html)	Worksheet (pdf)
Section 10.1 - Sequences	Video 1: Definition of a Sequence	Blank Notes	Worksheet 13	Worksheet 13
	Video 2: Geometric and Recursive Sequences
	Video 3: Limit Laws and Theorems for Sequences	Filled Notes
	Video 4: Functions of Sequences
	Video 5: Bounded Sequences
Section 10.2 - Infinite Series	Video 1: Infinite Series	Blank Notes	Worksheet 14	Worksheet 14
	Video 2: Telescoping Series
	Video 3: Geometric Series	Filled Notes
	Video 4: Limit Laws for Series
	Video 5: Divergence Test
Section 10.3 - Series with Positive Terms	Video 1: Series with Positive Terms	Blank Notes	Worksheet 15	Worksheet 15
	Video 2: Integral Test and p-Series
	Video 3: Direct Comparison Test	Filled Notes
	Video 4: Limit Comparison Test
Section 10.4 - Conditional Convergence and Alternating Series	Video 1: Absolute and Conditional Convergence	Blank Notes	Worksheet 16	Worksheet 16
	Video 2: Alternating Series
	Video 3: Proof of the Alternating Series Test	Filled Notes
	Video 4: Error Bound on Alternating Series
Section 10.5 - Ratio and Root Tests	Video 1: Ratio Test	Blank Notes	Worksheet 17	Worksheet 17
	Video 2: Root Test
	Video 3: Proof of the Root Test	Filled Notes
	Video 4: Choosing Convergence Tests
Section 10.6 - Power Series	Video 1: Definition of Power Series	Blank Notes	Worksheet 18	Worksheet 18
	Video 2: Convergence of Power Series
	Video 3: Power Series Expansions	Filled Notes
	Video 4: Differentiation and Integration of Power Series
	Video 5: A Famous Example
Section 10.8 - Taylor Series	Video 1: Definition of Taylor Series	Blank Notes	Worksheet 19	Worksheet 19
	Video 2: Convergence of Taylor Series
	Video 3: Proving Convergence	Filled Notes
	Video 4: Finding and Using Taylor Series
	Video 5: Other Uses of Taylor Series
Section 10.7 - Taylor Polynomials	Video 1: Truncation of Taylor Series	Blank Notes	Worksheet 20	Worksheet 20
	Video 2: Extension of Linear Approximation
	Video 3: Error Bound	Filled Notes
	Video 4: Using the Error Bound

Chapters 8 and 11

Section 8.2 - Arc Length and Surface Area	Video 1: Arc Length	Blank Notes	Worksheet 21	Worksheet 21
	Video 2: Surface Area
	Video 3: More Examples	Filled Notes
	Video 4: Gabriel's Horn Example
Section 11.1 - Parametric Equations	Video 1: Definition of Parametric Equations	Blank Notes	Worksheet 22	Worksheet 22
	Video 2: Eliminating the Parameter
	Video 3: Multiple Parametrizations	Filled Notes
	Video 4: Tangent Lines to Parametric Curves
	Video 5: Area under a Parametric Curve
Section 11.2 - Arc Length and Speed for Parametric Equations	Video 1: Arc Length for Parametric Equations	Blank Notes	Worksheet 23	Worksheet 23
	Video 2: Distance Traveled and Displacement	Filled Notes
	Video 3: Surface Area
Section 11.3 - Polar Coordinates	Video 1: Polar Coordinates	Blank Notes	Worksheet 24	Worksheet 24
	Video 2: Conversion Formulas
	Video 3: Polar Equations	Filled Notes
	Video 4: Converting Equations from Polar
	Video 5: Graph Sketching
Section 11.4 - Arc Length and Area in Polar Coordinates	Video 1: Area for Polar Functions	Blank Notes	Worksheet 25	Worksheet 25
	Video 2: More Examples	Filled Notes
	Video 3: Arc Length

Complex Numbers

Complex Numbers Day 1	Video 1: Algebra of Complex Numbers	Blank Notes	Worksheet 26	Worksheet 26
	Video 2: Complex Conjugate and Division
	Video 3: Geometry of Complex Numbers
	Video 4: Exponential Form and Euler's Formula
	Video 5: Applications to Partial Fractions	Filled Notes
	Video 6: Applications to Power Series
	Example 1: Partial Fractions Application
	Example 2: Power Series Application
Complex Numbers Day 2	Video 1: Powers of Complex Numbers	Blank Notes	Worksheet 27	Worksheet 27
	Video 2: Roots of Complex Numbers
	Video 3: Roots of Unity	Filled Notes
	Video 4: De Moivre's Formulas
	Video 5: Polynomials and Complex Numbers