Overview of Calculus Topics

Limits

Types of Problems:

  • Limits and their properties
  • Calculate one and two sided limits
  • Calculate limits at infinity
  • Use a limit to show continuity 
  • The variety of definitions of a limit
  • Weird and special cases related to a limit
  • Connection to limits to the derivative and slopes of tangent and normal line

Practice and Solutions

Paul's Online Notes and Practice Problems.
This is an excellent review of the topics that we have covered over the course of the year 
PAUL'S ONLINE NOTES PRACTICE
Solutions to Paul's Online Practice Problems
WORKED OUT SOLUTIONS

Video and other resources

Link to Paul's Online Notes on Limits Chapter
LIMITS CHAPTER
Professor Leonard Video
Intro to Limits
Professor Leonard Video
Properties of Limits
Professor Leonard Video
Continuity of Functions
Professor Leonard Video
Rates of Change Introduction

Derivatives and Differentiation

​Types of Problems:

  • Definition of a derivative
  • What does a derivative tell us?
  • Basic Rules of differentiation
  • Use of product and quotient rules
  • Use of chain rule
  • Implicit Differentiation
  • Related Rates 

​Practice and Solutions

Paul's Online Notes and Practice Problems.
This is an excellent review of the topics that we have covered over the course of the year 
PAUL'S ONLINE NOTES PRACTICE
Solutions to Paul's Online Practice Problems
WORKED OUT SOLUTIONS

Video and other resources

Paul's Online Notes on Derivative
DERIVATIVE CHAPTER
Professor Leonard Video
INTRO TO Derivatives
Professor Leonard Video
Techniques of Differentiation
Professor Leonard Video
Product and Quotient Rule
Professor Leonard Video
​Chain Rule
Professor Leonard Video
Trigonometric Functions Derivatives
Professor Leonard Video
Implicit Differentiation
Professor Leonard Video
​Related Rates

Applications of Derivative

​​Types of Problems:

  • Using the derivative to discuss the behavior of function
  • Using this derivative to determine rates of change with respect to time
  • Finding critical values (local maximums and minimum (sometimes called relative min and maximum)
  • Determining points of inflection (where concavity switches)
  • Finding Absolute Extremes
  • The Mean Value Theorem and Rolle's Theorem (MVT)
  • Optimization
  • Applications of derivative in the business world

​​Practice and Solutions

Paul's Online Notes and Practice Problems.
This is an excellent review of the topics that we have covered over the course of the year 
PAUL'S ONLINE NOTES PRACTICE
Solutions to Paul's Online Practice Problems
WORKED OUT SOLUTIONS

Video and other resources

Paul's Online Notes on Derivative Application
Applications of Derivative
Professor Leonard Video
Applications of Derivative 
Professor Leonard Video
Functions Increasing Decreasing and Concavity
Professor Leonard Video
MVT and Rolle's Theorem
Professor Leonard Video
First Derivative Test
Professor Leonard Video
Second Derivative Test
Professor Leonard Video
Limits at Infinity
Professor Leonard Video
Curve Sketching
Professor Leonard Video
Optimization

Integrals and Integration

​Types of Problems:

  • Determine indefinite integrals 
  • Determine definite integrals
  • Using u-substitution
  • Using Limits and Riemann Sums to approximate are under a curve
  • Using integrals to determine ara between x axis and a function's graph
  • Using integrals to determine ara between y axis and a function's graph
  • Using the integral as an inverse of derivative
  • Fundamental Theorem of Calculus (FTC) 

​​​Practice and Solutions

Paul's Online Notes and Practice Problems.
This is an excellent review of the topics that we have covered over the course of the year 
PAUL'S ONLINE NOTES PRACTICE
Solutions to Paul's Online Practice Problems
WORKED OUT SOLUTIONS

​Video and other resources

Paul's Online Notes on Integrals
Integrals Chapter
Professor Leonard Video
INTRO to integrals
Professor Leonard Video
U Substitution
Professor Leonard Video
Limits and Riemann Sums for Area Under Curve
Professor Leonard Video
Calculating Definite Integrals
Professor Leonard Video
Fundamental Theorem of Calculus

Application of Integration

​​Types of Problems:

  • Using integrals to determine area between two functions
  • Using integrals to find an average function value
  • Using integrals to find volume using disk and washer methods about the x axis
  • Using integrals to find volume using disk and washer methods about the y axis
  • Using integrals to find volume using disk and washer methods about a horizontal line or a vertical line
  • Using integrals to find volume using cross sections perpendicular to the x axis based on a common given geometric shape (square, rectangle, semicircle, right isosceles triangle, equilateral triangle

​​​​Practice and Solutions

Paul's Online Notes and Practice Problems.
This is an excellent review of the topics that we have covered over the course of the year 
PAUL'S ONLINE NOTES PRACTICE
Solutions to Paul's Online Practice Problems
WORKED OUT SOLUTIONS

​Video and other resources

​Paul's Online Notes on Application of Integrals
Applications of Integrals 
Professor Leonard Video
Area between two Curves
Professor Leonard Video
Volume using disks and washers

Additional Resources