Episode Synopsis "Chapter 3.5: Sigma Notation and Areas - 03) Area Under a Curve"

Chapter 3.5: Sigma Notation and Areas

Listen "Chapter 3.5: Sigma Notation and Areas - 03) Area Under a Curve"

More episodes of the podcast Applied Calculus (Chapters 1 - 3) - Course

• Brief Review - 01) Part One
• Brief Review - 02) Part Two
• Brief Review - 03) Part Three
• Brief Review - 04) Part Four
• Chapter 1.1: Extrema of a Function - 01) Continuous Functions and Intervals
• Chapter 1.1: Extrema of a Function - 02) Maximums and Minimums
• Chapter 1.1: Extrema of a Function - 03) Extreme Value Theorem
• Chapter 1.1: Extrema of a Function - 04) Relative Max. and Min.
• Chapter 1.1: Extrema of a Function - 05) Critical Numbers and Points
• Chapter 1.1: Extrema of a Function - 06) Example 2 and 3
• Chapter 1.1: Extrema of a Function - 07) Finding Extreme Values
• Chapter 1.1: Extrema of a Function - 08) Critical Point Test Theroem
• Chapter 1.1: Extrema of a Function - 09) Example 6
• Chapter 1.2: First Derivative Test - 01) First Derivative test
• Chapter 1.2: First Derivative Test - 02) Examples 1 and 2
• Chapter 1.2: First Derivative Test - 03) Example 3
• Chapter 1.2: First Derivative Test - 04) Example 4
• Chapter 1.2: First Derivative Test - 05) Example 5
• Chapter 1.2: First Derivative Test - 06) Example 6
• Chapter 1.3: Concavity and the Second Derivative - 01) Higher Order Derivatives
• Chapter 1.3: Concavity and the Second Derivative - 02) Example 2
• Chapter 1.3: Concavity and the Second Derivative - 03) Example 3
• Chapter 1.3: Concavity and the Second Derivative - 04) Example 4
• Chapter 1.3: Concavity and the Second Derivative - 05) Concavity and Points of Inflection
• Chapter 1.3: Concavity and the Second Derivative - 06) Concavity and 2nd Derivative
• Chapter 1.3: Concavity and the Second Derivative - 07) Example 5
• Chapter 1.3: Concavity and the Second Derivative - 08) 2nd Derivative Test for Relative Extrema
• Chapter 1.3: Concavity and the Second Derivative - 09) Example 6
• Chapter 1.3: Concavity and the Second Derivative - 10) Example 8
• Chapter 1.3: Concavity and the Second Derivative - 11) Example 10
• Chapter 1.3: Concavity and the Second Derivative - 12) Example 11
• Chapter 1.3: Concavity and the Second Derivative - 13) Example 12
• Chapter 1.3: Concavity and the Second Derivative - 14) Implicit Differentiation
• Chapter 1.4: Geometric Optimization Problems - 01) Examples 1 and 2
• Chapter 1.4: Geometric Optimization Problems - 02) Example 3: Rancher
• Chapter 1.4: Geometric Optimization Problems - 03) Example 4: Open Top
• Chapter 1.4: Geometric Optimization Problems - 04) Example 5: River
• Chapter 1.5: Business and Economic Optimization Problems - 01) Example 1
• Chapter 1.5: Business and Economic Optimization Problems - 02) Example 2: Bicycles
• Chapter 1.5: Business and Economic Optimization Problems - 03) Example 3: Average Cost
• Chapter 1.5: Business and Economic Optimization Problems - 04) Example 4: Stereos
• Chapter 1.5: Business and Economic Optimization Problems - 05) Example 5: Theatre
• Chapter 1.5: Business and Economic Optimization Problems - 06) Elasticity of Demand
• Chapter 1.5: Business and Economic Optimization Problems - 07) Elasticity of Demand Revisited
• Chapter 1.5: Business and Economic Optimization Problems - 08) Relative Change
• Chapter 1.6: Linearization and Differentials - 01) Linearization
• Chapter 1.6: Linearization and Differentials - 02) Example 1
• Chapter 1.6: Linearization and Differentials - 03) Examples 2 and 3
• Chapter 1.6: Linearization and Differentials - 04) Differentials
• Chapter 1.6: Linearization and Differentials - 05) Example not in textbook
• Chapter 1.6: Linearization and Differentials - 06) Example 5: Bacteria
• Chapter 1.6: Linearization and Differentials - 07) Relative Change
• Chapter 1.6: Linearization and Differentials - 08) Analysis of E
• Chapter 1.6: Linearization and Differentials - 09) Differential Formulas
• Chapter 2.1: Inverse Functions - 01) intro
• Chapter 2.1: Inverse Functions - 02) Example 1
• Chapter 2.1: Inverse Functions - 03) Composition Property
• Chapter 2.1: Inverse Functions - 04) Example 2
• Chapter 2.1: Inverse Functions - 05) Practice 1
• Chapter 2.1: Inverse Functions - 06) Practice 2
• Chapter 2.1: Inverse Functions - 07) One to One Example
• Chapter 2.1: Inverse Functions - 08) One to One Definition
• Chapter 2.1: Inverse Functions - 09) One to One Practice
• Chapter 2.1: Inverse Functions - 10) Practice with Inverses
• Chapter 2.1: Inverse Functions - 11) Derivative of Inverse Function
• Chapter 2.1: Inverse Functions - 12) Practice of Inverse Prime
• Chapter 2.2: Exponential Functions - 01) A New Function
• Chapter 2.2: Exponential Functions - 02) Exploring Exponential Functions
• Chapter 2.2: Exponential Functions - 03) Practice
• Chapter 2.2: Exponential Functions - 04) Practice 2
• Chapter 2.2: Exponential Functions - 05) Solving Special Exponential Equations
• Chapter 2.2: Exponential Functions - 06) Exponential Functions from Data
• Chapter 2.2: Exponential Functions - 07) Exponential Turtle Example
• Chapter 2.2: Exponential Functions - 08) Growth Decay Formulas
• Chapter 2.3: The Number e - 01) Matching the Graphs of Exp Functions
• Chapter 2.3: The Number e - 02) Compound Interest
• Chapter 2.3: The Number e - 03) Discovering e
• Chapter 2.3: The Number e - 04) Practice Compound Continuously
• Chapter 2.3: The Number e - 05) Graph of e to x
• Chapter 2.4: The Derivative of e - 01) Investigating Derivative of e to x
• Chapter 2.4: The Derivative of e - 02) Example 1
• Chapter 2.4: The Derivative of e - 03) Example 2
• Chapter 2.4: The Derivative of e - 04) Example 3
• Chapter 2.4: The Derivative of e - 05) Example 4
• Chapter 2.4: The Derivative of e - 06) Implicit Differentiation
• Chapter 2.4: The Derivative of e - 07) Extrema and Concave Graphs
• Chapter 2.5: Logarithmic Functions - 01) Introduction to Logs
• Chapter 2.5: Logarithmic Functions - 02) Decay Example: Solve for t, Part 1
• Chapter 2.5: Logarithmic Functions - 03) Decay Example: Solve for t, Part 2
• Chapter 2.5: Logarithmic Functions - 04) Inverse y equals 2 to x
• Chapter 2.5: Logarithmic Functions - 05) Inverse y equals 10 to x
• Chapter 2.5: Logarithmic Functions - 06) Practice evaluating logs
• Chapter 2.5: Logarithmic Functions - 07) Calc. Practice: Napiers Bones
• Chapter 2.5: Logarithmic Functions - 08) Logorithms ph
• Chapter 2.5: Logarithmic Functions - 09) Graphs and transformation
• Chapter 2.5: Logarithmic Functions - 11) y equlas in plus minus e
• Chapter 2.5: Logarithmic Functions - 12) Derivative of f of x
• Chapter 2.5: Logarithmic Functions - 13) Generalized Logorithmic
• Chapter 2.6: Properties of Logarithmic Functions - 01) Properties of Logs
• Chapter 2.6: Properties of Logarithmic Functions - 02) Multiplication Property of Logs
• Chapter 2.6: Properties of Logarithmic Functions - 03) Division Property of Logs
• Chapter 2.6: Properties of Logarithmic Functions - 04) Practice with Properties
• Chapter 2.6: Properties of Logarithmic Functions - 05) Discovering Exponential Property
• Chapter 2.6: Properties of Logarithmic Functions - 06) Using the Property
• Chapter 2.6: Properties of Logarithmic Functions - 07) Derivatives Using Properties
• Chapter 2.6: Properties of Logarithmic Functions - 08) Solving Logarithmic Equations
• Chapter 2.6: Properties of Logarithmic Functions - 09) Solving Exponential Equations
• Chapter 2.6: Properties of Logarithmic Functions - 10) t in Compound Interest Problems
• Chapter 2.6: Properties of Logarithmic Functions - 11) Solving for r and t
• Chapter 2.6: Properties of Logarithmic Functions - 12) Change of Base
• Chapter 2.6: Properties of Logarithmic Functions - 13) Derivative and Change of Base
• Chapter 2.6: Properties of Logarithmic Functions - 14) Logarithmic Differentiation
• Chapter 2.7: Applications of Exponential and Logarithmic Functions - 01) Introduction
• Chapter 2.7: Applications of Exponential and Logarithmic Functions - 02) Investment Example
• Chapter 2.7: Applications of Exponential and Logarithmic Functions - 03) Bacterial Growth Example
• Chapter 2.7: Applications of Exponential and Logarithmic Functions - 04) Radioactive Decay
• Chapter 2.7: Applications of Exponential and Logarithmic Functions - 05) Carbon Dating
• Chapter 2.7: Applications of Exponential and Logarithmic Functions - 06) Logistical Growth and Richtor Scale
• Chapter 2.7: Applications of Exponential and Logarithmic Functions - 07) Sea Lion Hint
• Chapter 3.1: Antidifferentiation - Integration - 01) Antidifferentiation
• Chapter 3.1: Antidifferentiation - Integration - 02) More Differentiation Practice
• Chapter 3.1: Antidifferentiation - Integration - 03) Using the Sum/Difference Rule
• Chapter 3.1: Antidifferentiation - Integration - 04) Results with ln "x" and e
• Chapter 3.2: Applications of Antidifferentiation - 01) Families of Antiderivatives
• Chapter 3.2: Applications of Antidifferentiation - 02) Graphs and Particular Solutions
• Chapter 3.2: Applications of Antidifferentiation - 03) Solving Differential Equations
• Chapter 3.2: Applications of Antidifferentiation - 04) Motion Equations: Part 1
• Chapter 3.2: Applications of Antidifferentiation - 05) Motion Equations: Part 2
• Chapter 3.2: Applications of Antidifferentiation - 06) Marginal Cost and Revenue
• Chapter 3.2: Applications of Antidifferentiation - 07) Separable Differential Equations
• Chapter 3.3: The Substitution Method - 01) The Substitution Method
• Chapter 3.3: The Substitution Method - 02) Examples
• Chapter 3.3: The Substitution Method - 03) Technique of Substitution
• Chapter 3.3: The Substitution Method - 04) Generalized Rules
• Chapter 3.3: The Substitution Method - 05) Practice Using Substitution
• Chapter 3.3: The Substitution Method - 06) More Practice wtih Substitution
• Chapter 3.4: Approximation of Areas - 01) Approximation of Areas
• Chapter 3.4: Approximation of Areas - 02) Endpoints
• Chapter 3.4: Approximation of Areas - 03) Practice with Endpoints and Midpoints
• Chapter 3.5: Sigma Notation and Areas - 01) Sigma Notation and Area
• Chapter 3.5: Sigma Notation and Areas - 02) Practice with Summation
• Chapter 3.5: Sigma Notation and Areas - 03) Area Under a Curve
• Chapter 3.5: Sigma Notation and Areas - 04) Example 1
• Chapter 3.5: Sigma Notation and Areas - 05) Example 2
• Chapter 3.6: The Definite Integral - 01) The Definite Integral and Fundamental Theorem
• Chapter 3.6: The Definite Integral - 02) Practice 1
• Chapter 3.6: The Definite Integral - 03) Practice 2
• Chapter 3.6: The Definite Integral - 04) Properties of the Definite Integral
• Chapter 3.6: The Definite Integral - 05) Area Problem
• Chapter 3.7: Substitution and Properties of the Definite Integral - 01) Substitution and Properties of the Definite Integra
• Chapter 3.7: Substitution and Properties of the Definite Integral - 02) Even and Odd Functions
• Chapter 3.7: Substitution and Properties of the Definite Integral - 03) Average Value
• Chapter 3.7: Substitution and Properties of the Definite Integral - 04) Derivative of Definite Integral
• Chapter 3.8: Applications of the Definite Integral - 01) Introduction
• Chapter 3.8: Applications of the Definite Integral - 02) Example 1
• Chapter 3.8: Applications of the Definite Integral - 03) Example 2
• Chapter 3.8: Applications of the Definite Integral - 04) Example 3
• Chapter 3.8: Applications of the Definite Integral - 05) Consumer Surplus
• Chapter 3.8: Applications of the Definite Integral - 06) Producer Surplus
• Chapter 3.8: Applications of the Definite Integral - 07) Continuous Income Flow
• Chapter 3.8: Applications of the Definite Integral - 08) Probability Density Functions