CALCULUS I : Βιντεομαθήματα από το πανεπιστήμιο της πολιτείας Νεμπράσκα

   PreCalculus Review

• Functions

  • Functions

  • Describing and Transforming Functions

  • Compositions and Inverses

• Exponential and Logarithmic Functions

  • Introduction

  • Half Life

  • Logarithm

  • Examples

• Trigonometric Functions

  • Periodic Functions

  • Measring Angles

  • Trigonometric and Inverse Trigonometric Functions

  • Generalized Trigonometric Functions

Chapter 1 Understanding the Derivative

• Introduction to Continuity

  • Introduction to Continuity

  • Continuity

  • Piecewise Functions

  • Intermediate Value Theorem

  • Continuity at a Point

• Introduction to Limits

  • Intuition of Limits

  • Defining Limits

  • Single-Sided Limits and Limits at Infinity

  • Continuity

• How do we Measure Velocity?

  • Introduction

  • Limits and Velocity

• The Derivative of a Function at a Point

  • Defining Derivatives at Points

  • Approximating and Computing Derivatives at a Point

• The Derivative Function

  • Tangent Line Approximations

  • The Derivative Function

  • Some Derivatives

• Interpreting, Estimating, and Using the Derivative

  • Using the Derivative

• The Second Derivative

  • The Second Derivative

  • Concavity

  • Acceleration

• Differentiability

  • Definition and Graphical Examples

  • Continuity and Differentiability

Chapter 2 Computing Derivatives

• Elementary Derivative Rules

  • Elementary Rules

  • Tangent Lines

  • Exponential Functions

• The Sine and Cosine Functions

  • Derivative Rules

• The Product and Quotient Rules

  • Product and Quotient

  • Product Rule Examples

  • The Quotient Rule

  • Quotient Rule Examples

• Derivatives of Other Trigonometric Functions

  • Deriving Derivative of Tangent

  • Deriving Derivative of Secant

• The Chain Rule

  • The Chain Rule

  • The Chain Rule Examples

  • The Chain Rule More Examples

• Derivatives of Inverse Functions

  • Using Inverse Functions to Find Derivatives

  • Derivatives of Exponential and Logarithmic Functions

  • Derivatives of Inverse Trigonometric Functions

  • Derivatives of General Inverse Functions

• Derivatives of Functions Given Implicitly

  • Implicit Differentiation

  • Implicit Differentiation Examples

• Hyperbolic Functions

  • Introduction to Hyperbolic Functions

  • Extension to Hyperbolic Tangent

• The Tangent Line Approximation

  • Tangent Line Approximations

  • Error Approximation

  • Tangent Line Approximation Examples

• The Mean Value Theorem

  • Statement and Graphical Intuition

  • Computational Example

  • Additional Theorems

Chapter 3 Using Derivatives

• Using Derivatives to Identify Extreme Values

  • Extreme Values

  • Derivative Tests

  • Examples

• Global Optimization

  • Global Maxima and Minima

  • The Extreme Value Theorem

  • Example on Closed Interval

  • Example on Open Interval

• Applied Optimization

  • How to Solve It

  • Initial Example

  • Advanced Example

• Using Derivatives to Describe Families of Functions

  • Families of Functions

• Related Rates

  • Related Rates

  • Sliding Ladder Problem

  • Drifting Boat Problem

  • Rising Hot Air Balloon Problem

• Using Derivatives to Evaluate Limits

  • L'Hopital's Rule

  • Additional Examples

  • L'Hopital's Rule at Infinity

  • Applications of L'Hopital's Rule

• Parametric Equations

  • Introduction to Parametric Equations

  • Curve Sketching

  • Tangent Lines and Parametric Equations

  • Speed and Velocity in Parametric Equations

  • Concavity

Chapter 4 The Definite Integral

• Determining Distance Traveled from Velocity

  • Estimating Distance Traveled

  • Refining Estimates to Determine Exact Distance

  • Area Beneath Velocity Curve Represents Distance

• Riemann Sums

  • Riemann Sums Part 1

  • Riemann Sums Part 2

  • Riemann Sums Examples

• The Definite Integral

  • Introduction to the Definite Integral

  • Computing Definite Integrals Using Area

  • Properties of the Definite Integral

  • Definite Integrals and Symmetry

  • Definite Integrals and Averages

• The Fundamental Theorem of Calculus

  • FTC

  • FTC Examples

Chapter 5 Evaluating Integrals

• Constructing Accurate Graphs of Antiderivatives

  • Graphs of Antiderivatives

  • From Derivative Graph to Antiderivative Information

  • The Integral Function

• Antiderivatives from Formulas

  • Antiderivatives From Formulas

  • Antiderivatives of Other Functions

  • Using Antiderivatives to Compute a Definite Integral

  • Computing Area Between Two Curves

• Differential Equations

  • What is a Differential Equation?

  • Initial Conditions

  • Initial Value Problem Examples

• The Second Fundamental Theorem of Calculus

  • Introduction

  • Examples Part 1

  • Examples Part 2

• Integration by Substitution

  • Motivation

  • Indefinite Substitution Integrals

  • Definite Substitution Integrals

  • Challenging Substitution Integrals