General Calculus 1
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GeneralCalculusI_V31.pdf
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MAT250: General Calculus I
General Calculus I
Course Text
● This course does not require a text.
Course Description and Objectives
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.
Course Prerequisites
StraighterLine does not require prerequisites, however it is suggested that students take
Precalculus or its equivalent before enrolling in General Calculus I.
Important Terms
In this course, different terms are used to designate tasks:
● Proctoring: all final exams require proctoring which can be completed conveniently from your home. A webcam is required.
● Tutoring: memberships include online tutoring for students to access with any content/subject related questions in the place of faculty. If your tutor is not able to
answer your questions please contact a student advisor.
● Exam: A graded online test. ● Exercises: ungraded practice exercises and quiz questions.
Course Evaluation Criteria
StraighterLine provides a percentage score and letter grade for each course. See Academic Questions section in FAQ for further details on percentage scores and grading scale. 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
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MAT250: General Calculus I
3 Graded Exam 1 125
6 Graded Exam 2 125
7 Midterm Exam 200
9 Graded Exam 3 125
11 Graded Exam 4 125
12 Final Exam 300
Total 1000
Course Topics and Objectives
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
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MAT250: General Calculus I
● 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
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 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
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MAT250: General Calculus I
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
● Antiderivativ es
● 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
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MAT250: General Calculus I
● Finding Areas by Integrating with Respect to y: Part Two
● Area, Integration by Substitution, and Trigonometric
L’Hôpital’s
Rule
● Indeterminat e 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 Function
s
● The Calculus of
Inverse
Functions
● Inverse Trigonomet
ric
Functions
● The Calculus of Inverse
Trigonometri
c 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 Introductio
n 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 Differenti
● An Introduction to Differential Equations ● Solving Separable DIfferential Equations
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MAT250: General Calculus I
al
Equations
● Solving First-Order
Linear
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
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