General Calculus I

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Course Number: MAT250
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This course is designed to acquaint students with calculus principles such as derivatives, integrals, limits, approximation, applications and modeling, and sequences and series. During this course students will gain experience in the use of calculus methods and learn how calculus methods may be applied to practical applications. Topics covered include Functions & Graphs, Limits & Continuity, Derivatives, the Application of Derivatives, Antiderivatives and definite Integrals.  

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3
college credits
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Self Paced
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Mathematics
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12 Reviews
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  • 10/1/14 by sbeck.imap
    Overall, the course was in line with the curriculum of a calculus 1 class.
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  • 9/8/14 by roy.p
    More examples
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  • 8/31/14 by george.b
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  • 8/31/14 by george.b
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  • 8/25/14 by jinchunzi10
    First of all, I liked the professor very much. In addition, I think the system is very efficient
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  • 8/25/14 by jinchunzi10
    First of all, I liked the professor very much. In addition, I think the system is very efficient
    Content Rating
    Overall Rating
  • 8/22/14 by dreamdungeon613
    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.
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  • 8/22/14 by dreamdungeon613
    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.
    Content Rating
    Overall Rating
  • 8/9/14 by roy.p
    More examples
    Content Rating
    Overall Rating
  • 6/4/14 by yaejinkim1030
    This was helpful.
    Content Rating
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  • 4/6/14 by yaejinkim1030
    This was helpful.
    Content Rating
    Overall Rating
  • 1/10/14 by sbeck.imap
    Overall, the course was in line with the curriculum of a calculus 1 class.
    Content Rating
    Overall Rating

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 Non-Euclidean 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
  • One-Sided 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
  • Higher-Order 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 Wire-Cutting 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
  • Romain-Restricted 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 Quotients

  • 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

  • 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 First-Order Linear Differential Equations
  • An Introduction to Differential Equations
  • Solving Separable DIfferential Equations
  • Finding a Particular Solution
  • Direction Fields
  • Euler’s Method
  • First-Order Linear Differential Equations

Review and Final Exam

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

150

9

Graded Exam 3

125

13

Graded Exam 4

125

Final Exam

350

Total

1000


You are required to take an online proctored final exam in order to be eligible for transfer credit. You can take your proctored final exam at home or anywhere you have access to a webcam with a microphone and a reliable, high-speed internet connection. For additional questions, please refer to the FAQ on Online Proctoring or contact your student advisors at 877-787-8375.

This course is designed to acquaint students with calculus principles such as derivatives, integrals, limits, approximation, applications and modeling, and sequences and series. During this course students will gain experience in the use of calculus methods and learn how calculus methods may be applied to practical applications. Topics covered include Functions & Graphs, Limits & Continuity, Derivatives, the Application of Derivatives, Antiderivatives and definite Integrals.  

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