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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General Calculus I +$69.00

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General Calculus I

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Course Number: MAT250 Download Course Syllabus

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Self Paced
Mathematics
Content by ThinkWell

Online Course

General Calculus I +$69.00

Tutoring (included)

Proctoring (included)

Credits 3

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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	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

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

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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

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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.

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8/22/14 by dreamdungeon613

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8/9/14 by roy.p

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6/4/14 by yaejinkim1030

This was helpful.

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4/6/14 by yaejinkim1030

This was helpful.

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1/10/14 by sbeck.imap

Overall, the course was in line with the curriculum of a calculus 1 class.

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Load More Reviews

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