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Calculus I

MAT250 | 4 Credits

Calculus I will introduce the basic calculus principles. You’ll gain experience using and applying calculus methods in practical applications, and get familiar with topics like limits, derivatives, and computational techniques.

Professor: Ms. Sayali Desphande

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$79 + membership
97% Average Pass Rate
29 Day Average Completion
$2.6 Million Saved on Tuition
ACE-RECOMMENDED 2024

About This Course

What You’ll Learn

General Calculus I acquaints you with calculus principles such as derivatives, integrals, limits, approximation, applications and integration, and curve sketching.

  • Demonstrate the continuity or discontinuity of the function.
  • Solve the limit problems by using various limit laws.
  • Demonstrate various rules of derivatives.
  • Compute derivatives.
  • Demonstrate derivatives for trigonometric, exponential, and logarithmic functions
  • Apply Implicit differentiation
  • Apply L’Hôpital’s Rule to find the limit of indeterminate forms.
  • Sketch the graphs using the derivatives.
  • Compute area between the curves using integration.
  • Solve vertical motion problems.
  • Illustrate the Fundamental Theorem of Calculus.
  • Demonstrate convergence and divergence of improper integrals.

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Course Details

MAT250
Calculus I
4 Credits

This course is designed to acquaint students with calculus principles such as derivatives, integrals, limits, approximation, applications and integration, and curve sketching. 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 Special Functions, Limits, Derivatives, Computational Techniques, Applications of Differentiations, and Applications of Integration.

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The American Council on Education (ACE) evaluates and recommends college credit for courses taken outside traditional degree programs. StraighterLine courses are ACE Credit®-recommended, which means they are transferable to over 3,000 colleges and universities nationwide.

ACE Code:

OOSL-0012

Flexible Schedule

29-day Average Course Completion

Transferred 2,300 times

$2,600,000 Saved on Tuition

Prerequisites

Precalculus is a required prerequisite for Calculus I. If you enroll, the assumption is made that you have previously completed Precalculus for credit with a passing score.

Course Text 

This course does not require a textbook.

 

Course Checkpoints

Preliminaries and Functions

  • Welcome to Calculus
  • The Two Questions of Calculus
  • Average Rates of Change
  • How to Do Math
  • Functions
  • Graphing Lines
  • Parabolas
  • Some Non–Euclidean Geometry
  • Limits and Continuity

  • 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
  • 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 Function
  • Computational Techniques

  • 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
  • Implicit Differentiation

  • An Introduction to Implicit Differentiation
  • Finding the Derivative Implicitly
  • Using Implicit Differentiation
  • Applying Implicit Differentiation
  • Dealing with Indeterminate Forms

  • Indeterminate Forms
  • An Introduction to L’Hôpital’s Rule
  • Basic Uses of L’Hôpital’s Rule
  • More Exotic Examples of Indeterminate Forms
  • L’Hopital’s rule and Indeterminate Products
  • L’Hôpital’s rule and Indeterminate Differences
  • L’Hôpital’s rule and One to the Infinite Power
  • Another example of One to the Infinite Power
  • Applications of Differentiation

  • 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 Slope and Optimization
  • The Fence Problem
  • The Box Problem
  • The Can Problem
  • The Wire–Cutting Problem
  • The Ladder Problem
  • The Baseball Problem
  • The Blimp Problem
  • Math Anxiety
  • Curve Sketching

  • 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 Tests
  • Magic Math
  • Concavity and Inflection Points
  • Using the Second Derivative to Examine Concavity
  • The Mobius Band
  • Graphs of Polynomial Functions
  • Cusp Points and the Derivative
  • Domain–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
  • Introduction to Integrals

  • 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
  • Approximating Areas of Plane Regions
  • Areas, Riemann Sums, and Definite Integrals
  • The Fundamental Theorem of Calculus, Part I
  • The Fundamental Theorem of Calculus, Part II
  • Illustrating the Fundamental Theorem of Calculus
  • Evaluating Definite Integrals
  • Applications of Integration

  • 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
  • 3 Techniques of Integration

  • 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
  • Special 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
  • 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
  • Defining the Hyperbolic Functions
  • Hyperbolic Identities
  • Derivatives of Hyperbolic Functions
  • Assignments & Grading 

    Your score provides a percentage score and letter grade for each course. A passing percentage is 70% or higher.

    Assignments for this course include:

    • 4 Graded Topic Reviews
    • 4 Graded Quizzes
    • 4 Graded Exams
    • 1 Graded Final

    This course has an open book proctored Final Exam. Scientific and/or graphing calculators are allowed throughout the course.

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    • Basic computer skills
    • Any required course materials

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    Course Professor

    Ms. Sayali Deshpande

    Passionate math educator, specializing in algebraic reasoning and mathematical foundations for college learners.

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    Starting Your STEM Career with Calculus I

    Calculus I is the foundation for many careers in science or engineering. That’s because it allows you to model change in a way that other math disciplines don’t! Whether you go on to become a data scientist, mechanical engineer, or financial manager, getting a grasp on calculus will serve you well.

    Why it matters:

    • New jobs for mathematicians and statisticians are expected to grow 3x faster than average with 11% job growth between 2023 – 2032
    • Calculus will help you understand rates of change and results of change — a valuable skill in many STEM jobs.

    How this course sets you up for success:

    Data Scientist, Actuary, Statistician, Operations Research Analyst, Quantitative Analyst, Mathematical Modeler, Cryptographer, Financial Analyst, Market Research Analyst, Software Engineer

    How this course sets you up for success:

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