Chapter  Topics  Subtopics 
The Basics   Overview
 Precalculus Review
  Welcome to Calculus
 The Two Questions of Calculus
 Average Rates of Change
 How to Do Math
 Functions
 Rational functions
 Complex number
 Zeros of polynomial
 Graphing Lines
 Parabolas
 Some NonEuclidean Geometry

Limits   The Concept of the Limit
 Evaluating Limits
  Finding Rate of Change over an Interval
 Finding Limits Graphically
 The Formal Definition of a Limit
 The Limit Laws, Part I
 The Limit Laws, Part II
 OneSided Limits
 The Squeeze Theorem
 Continuity and Discontinuity
 Evaluating Limits
 Limits and indeterminate Forms
 Two Techniques for Evaluating Limits
 An Overview of Limits

An Introduction to Derivatives   Understanding the Derivative
 Using the Derivative
 Some Special Derivatives
  Rates of Change, Secants, and Tangents
 Finding Instantaneous Velocity
 The Derivative
 Differentiability
 The Slope of a Tangent Line
 Instantaneous Rate
 The Equation of a Tangent Line
 More on Instantaneous Rate
 The Derivative of the Reciprocal Function
 The Derivative of the Square Root

Computational Techniques   The Power Rule
 The Product and Quotient Rules
 The Chain Rule
  A Shortcut for Finding Derivatives
 A Quick Proof of the Power Rule
 Uses of the Power Rule
 The Product Rule
 The Quotient Rule
 An Introduction to the Chain Rule
 Using the Chain Rule
 Combining Computational Techniques

Special Functions   Trigonometric Functions
 Exponential Functions
 Logarithmic Functions
  A Review of Trigonometry
 Graphing Trigonometric Functions
 The Derivatives of Trigonometric Functions
 The Number Pi
 Graphing Exponential Functions
 Derivatives of Exponential Functions
 The Music of Math
 Evaluating Logarithmic Functions
 The Derivative of the Natural Log Function
 Using the Derivative Rules with Transcendental Functions

Implicit Differentiation   Implicit Differentiation Basics
 Applying Implicit Differentiation
  An Introduction to Implicit Differentiation
 Finding the Derivative Implicitly
 Using Implicit Differentiation
 Applying Implicit Differentiation

Applications of Differentiation   Position and Velocity
 Linear Approximation
 Optimization
 Related Rates
  Acceleration and the Derivative
 Solving Word Problems Involving Distance and Velocity
 HigherOrder Derivatives and Linear Approximation
 Using the Tangent Line Approximation Formula
 Newton’s Method
 The Connection Between Slopes and Optimization
 The Fence Method
 The Box Problem
 The Can Problem
 The WireCutting Problem
 The Pebble Problem
 The Ladder Problem
 The Baseball Problem
 The Blimp Problem
 Math Anxiety

Curve Sketching   Introduction
 Critical Points
 Concavity
 Graphing Using the Derivative
 Asymptotes
  An Introduction to Curve Sketching
 Three Big Theorems
 Morale Moment
 Critical Points
 Maximum and Minimum
 Regions Where a Function Increases or Decreases
 The First Derivative Test
 Magic Math
 Concavity and Inflection Points
 Using the Second Derivative to Examine Concavity
 The Möbius Band
 Graphs of Polynomial Functions
 Cusp Points and the Derivative
 RomainRestricted Functions and the Derivative
 The Second Derivative Test
 Vertical Asymptotes
 Horizontal Asymptotes and Infinite Limits
 Graphing Functions with Asymptotes
 Functions with Asymptotes and Holes
 Functions with Asymptotes and Critical Points

The Basics of Integration   Antiderivatives
 Integration by Substitution
 Illustrating Integration by Substitution
 The FUndamental Theorem of Calculus
  Antidifferentiation
 Antiderivatives of Powers of x
 Antiderivatives of Trigonometric and Exponential Functions
 Undoing the Chain Rule
 Integrating Polynomials by Substitution
 Integrating Composite Trigonometric Functions by Substitution
 Integrating Composite Exponential and Rational Functions by Substitution
 More Integrating Trigonometric Functions by Substitution
 Choosing Effective Function Decompositions

Applications of Integration   Motion
 Finding the Area between Two Curves
 Integrating with Respect to y
  Antiderivatives and Motion
 Gravity and Vertical Motion
 Solving Vertical Motion Problems
 The Area between Two Curves
 Limits of Integration and Area
 Common Mistakes to Avoid When Finding Areas
 Regions Bound by Several Curves
 Finding Areas by Integrating with Respect to y: Part One
 Finding Areas by Integrating with Respect to y: Part Two
 Area, Integration by Substitution, and Trigonometry

L’Hôpital’s Rule    Indeterminate Forms
 An Introduction to L’Hôpital’s Rule
 Basic Uses of L’Hôpital’s Rule
 More Exotic Examples of Indeterminate Forms

Elementary Functions and Their Inverses   Inverse Functions
 The Calculus of Inverse Functions
 Inverse Trigonometric Functions
 The Calculus of Inverse Trigonometric Functions
  The Exponential and Natural Log Functions
 Differentiating Logarithmic Functions
 Logarithmic Differentiation
 The Basics of Inverse Functions
 Finding the Inverse of a Function
 Derivatives of Inverse Functions
 The Inverse Sine, Cosine, and Tangent Functions
 The Inverse Secant, Cosecant, and Cotangent Functions
 Evaluating Inverse Trigonometric Functions
 Derivatives of Inverse Trigonometric Functions
 More Calculus of Inverse Trigonometric Functions

Techniques of Integration   An Introduction to Integration by Partial Fractions
 Integration by Parts
  Finding Partial Fraction Decompositions
 Partial Fractions
 Long Division
 An Introduction to Integration by Parts
 Applying Integration by Parts to the Natural Log Function
 Inspirational Examples of Integration by Parts
 Repeated Application of Integration by Parts
 Algebraic Manipulation and Integration by Parts

Improper Integrals    The First Type of Improper Integral
 The Second Type of Improper Integral
 Infinite Limits of Integration, Convergence, and Divergence

Differential Equations   Separable Differential Equations
 Solving FirstOrder Linear Differential Equations
  An Introduction to Differential Equations
 Solving Separable DIfferential Equations
 Finding a Particular Solution
 Direction Fields
 Euler’s Method
 FirstOrder Linear Differential Equations

Review and Final Exam  Review and Final Exam  
StraighterLine suggests, though does not require, that students take Precalculus or its equivalent before enrolling in General Calculus I.
This course does not require a text.
StraighterLine provides a percentage score and letter grade for each course. A passing percentage is 70% or higher.
If you have chosen a Partner College to award credit for this course, your final grade will be based upon that college's grading scale. Only passing scores will be considered by Partner Colleges for an award of credit.
There are a total of 1000 points in the course:
Chapter  Assessment  Points Available 
3  Graded Exam 1  125 
6  Graded Exam 2  125 
7  Midterm Exam  200 
9  Graded Exam 3  125 
13  Graded Exam 4  125 
 Final Exam  300 
Total 
 1000 
Final Proctored Exam
The final exam is developed to assess the knowledge you learned taking this course. All students are required to take an online proctored final exam in order complete the course and be eligible for transfer credit.
Learn more about Proctored Exams
Overall, the course was in line with the curriculum of a calculus 1 class.
More examples
First of all, I liked the professor very much. In addition, I think the system is very efficient
First of all, I liked the professor very much. In addition, I think the system is very efficient
Eleven chapters on differential and integral calculus in which one should give themselves lots and lots of time to understand and practice. Not a course one should take if one is pressed for time. Many of the test questions are far removed from the content put forward by the instructor, Prof. Edward Burger of Williams College.
Eleven chapters on differential and integral calculus in which one should give themselves lots and lots of time to understand and practice. Not a course one should take if one is pressed for time. Many of the test questions are far removed from the content put forward by the instructor, Prof. Edward Burger of Williams College.
More examples
This was helpful.
This was helpful.
Overall, the course was in line with the curriculum of a calculus 1 class.