General Calculus I

General Calculus I

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$79

General Calculus I

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About this course.

MAT250

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General Calculus I

General Calculus I acquaints you with calculus principles such as derivatives, integrals, limits, approximation, applications and integration, and curve sketching. During this online General Calculus I course, gain experience using calculus methods and learn how calculus methods may be applied to practical applications. Become familiar with topics like special functions, limits, derivatives, computational techniques, applications of differentiations, and applications of integration.

ACE Approved 2021

Outcomes

After completing this course students will be able to:

Solve the limit problems by using various limit laws.

Demonstrate the continuity or discontinuity of the function

Demonstrate various rules of derivatives

Compute derivatives

Demonstrate derivatives for trigonometric, exponential, and logarithmic functions

Apply implicit differentiation

Use tangent line approximation

Use derivatives to solve optimization and related rates problem

Sketch the graphs using the derivatives

Solve integration using substitution method

Illustrate the Fundamental Theorem of Calculus

Compute area between the curves using integration

Apply L’Hôpital’s Rule to find the limit of indeterminate forms

Use logarithmic differentiation

Apply various techniques to evaluate integration

Demonstrate convergence and divergence of improper integrals

Solve First Order linear differential equation

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
  • Functions
  • 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 Function
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
  • Some Special Derivatives
  • An Introduction to Implicit Differentiation
  • Finding the Derivative Implicitly
  • Using Implicit Differentiation
  • Applying Implicit Differentiation
Applications of Differentiations
  • 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 Slope and Optimization
  • Solving Word Problems on Optimization (The Fence Problem, The Box Problem, The Can Problem, The Wire-Cutting Problem, etc.)
  • Solving Word Problems on Related Rates (The Pebble Problem, The Ladder Problem, The Baseball Problem, The Blimp Problem, etc.)
  • 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 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
The Basics of Integration
  • Antiderivative
  • Integration by Substitution
  • Illustrating Integration by Substitution
  • The Fundamental Theorem of Calculus
  • 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
  • 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 I
  • Finding Areas by Integrating with Respect to Y, Part II
  • Area, Integration by Substitution, and Trigonometric Substitution
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 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 Function
Techniques of Integration
  • An Introduction to Integration by Partial Fractions
  • Integration by Part
  • 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 Equation
  • Solving Separable Differential Equations
  • Finding a Particular Solution
  • Direction Fields
  • Euler’s Method for Solving Differential Equations Numerically
  • First-Order Linear Differential Equations


StraighterLine suggests, though does not require, that students take Precalculus or its equivalent before enrolling in General Calculus I.



The required eTextbook for this course is included with your course purchase at no additional cost.

Prefer the hard copy? Simply purchase from your favorite textbook retailer; you will still get the eTextbook for free.


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.

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