Course Materials for WvEB Calculus (Math 153/154)
(August 2018)
|
Textbook: Essential Calculus, by J. Stewart (8th ed.) |
|
Math 153: Calculus 1A with Precalculus, Fall 2019 |
|
Administration |
Math 153 Syllabus
Math 154 Syllabus
Cheating Policy
Homework Problems
eCampus Homework Problems
Grading Break-Down
|
Chapter 1: Functions and Models |
|
Section 1.1: Four Ways to Represent a Function |
Notes
Simple Definition
Vertical Line Test
Increasing/Decreasing Functions
Even and Odd Functions
Examples, Notation
Examples, Domain and Range
Examples, Odd/Even; Interpretation
|
Section 1.2: Mathematical Models: A Catalog of Essential Functions |
Notes
The Function Families
Trigonometric Families
Parent Function Graphing 1
Parent Function Graphing 2
Domain Combinations
|
Section 1.3: New Functions from Old Functions |
Composite Functions
Examples of Composite Functions
|
Section 1.4: Exponenial Functions |
Notes
Exponential Functions
Graphing to Evaluate Limits
What is 'e'?
|
Section 1.5: Inverse Functions and Logarithms |
Notes
Inverse Functions
Calculating an Inverse Function
Useful Theorems
Log Rules and Notation
Managing Numbers in Logs
Solving Equations with Logs
|
Chapter 2: Limits and Derivatives |
|
Section 2.1: The Tangent and Velocity Problems |
Notes
Tangent Lines
Position/Vellocity/Acceleration
|
Section 2.2: The Limit of a Function |
Notes
Definition of Limit
Finding Limits using a Table
Finding Limits using a Picture
One-Sided Limits
Limits Involving Infinity
Vertical Asymptotes
|
Section 2.3: Calculating Limits Using the Limit Laws |
Notes
Algebraic Limit Rules
Finding Limits with Direct Substitution
Finding Limits with Squeeze Theorem
Finding Limits by Forcing Known Forms
Limits Using Trig
|
Section 2.4: The Precise Definition of a Limit |
Notes
|
Section 2.5: Continuity |
Notes
Definition of Continuity
Classifying Discontinuity
Continuity on an Interval
Managing Continuous Functions
Intermediate Value Theorem
|
Section 2.6: Limits at Infinity; Horizontal Asymptotes |
Notes
Horizontal Asymptotes
Unusual Use of Infinity
Managing Unusual Limits
|
Section 2.7: Derivatives and Rates of Change |
Definition of Derivative
Applications
|
Section 2.8: The Derivative as a Function |
Notes
Derivative at x
Graphing the Derivative
Differentiability
|
Chapter 3: Differentiation Rules |
|
Section 3.1: Derivatives of Polynomials and Exponential Functions |
Notes
Basic Rules
Basic Examples
Tangent Lines
Derivatives of Exponentials
|
Section 3.2: The Product and Quotient Rules |
Notes
Product Rule
Product Rule Examples
Quotient Rule
Quotient Rule Examples
|
Section 3.3: Derivatives of Trigonometric Functions |
Controlling Domain
Derivatives of Inverse Trig
Finding Values
Simplification Problems
Mannaging Derivatives
|
Section 3.4: The Chain Rule |
Notes
Chain Rule
Chain Rule with Product Rule
Chain Rule with Quotient Rule
Chain Rule with Chain Rule (Trig?)
|
Section 3.5: Implicit Differentiation |
Notes
Implicit Differentiation Rules
Implicit Differentiation Examples
Tangent Lines
|
Section 3.6: Derivatives of Logarithmic Functions |
Notes
Derivatives of Logarithms
Examples
Logarithmic Differentiation 1
Logarithmic Differentiation 2
|
Section 3.7: Rates of Change in the Natural and Social Sciences |
|
Section 3.8: Exponential Growth and Decay |
Notes
Differential Equation Structure
Bacteria Growth
Census
Half Life
|
Section 3.9: Related Rates |
Notes
Solving Strategy - Easy (Spheres)
Solving Strategy - Moderate (Rectangles)
Solving Strategy - Moderate (Triangles - Pythagorean Theorem)
Solving Strategy - Hard (Triangles - Similar Triangles)
|
Section 3.10: Linear Approximations and Differentials |
Notes
Linearization and Tangent Lines
Linearization as a Tool
What are Differentials?
Using Differentials in Applications
|
Section 3.11: Hyperbolic Functions |
Notes
Definitions and Graphs
Derivatives
Finding Values
Managing Derivatives
|
Chapter 4: Applications of Differentiation |
|
Section 4.1: Maximum and Minimum Values |
Notes
Definitions of Max and Min
Extreme Value Theorem
Critical Numbers
Critical Numbers Example
Absolute Min and Max Example
Appication Examples
|
Section 4.2: The Mean Value Theorem |
Notes
Rolle's Theorem
Mean Value Theorem
|
Section 4.3: How Derivatives Affect the Shape of a Graph |
Notes
Increasing and Decreasing Functions
First Derivative Test
Inflection Points and Concavity
Second Derivative Test
|
Section 4.4: Indeterminate Forms and l'Hospital's Rule |
Notes
Weak Theorem
Strong Theorem
More Examples
|
Section 4.5: Summary of Curve Sketching |
Notes
Curve Sketching - Making a Table of Data
Curve Sketching - Transforming the Table into a Sketch
Example 1 - Part 1
Example 1 - Part 2
Example 2 - Part 1
Example 2 - Part 2
|
Section 4.7: Optimization Problems |
Notes
Example 1
Example 2
Example 3
|
Section 4.9: Antiderivatives |
Notes
Antiderivatives
Basic Antiderivative Rules
Finding 'C'
Applications
|
Chapter 5: Integrals |
|
Section 5.1: Areas and Distances |
Notes
Areas and Distances
Estimating Area Under a Curve
Right-Hand, Left-Hand, Mid-Point
Riemann Sums
Applications
|
Section 5.2: The Definite Integral |
Notes
Definition of Definite Integral
Definition of Integrable
Definite Integral Properties
Notation
Examples
|
Section 5.3: The Fundamental Theorem of Calculus |
Notes
Fundamental Theorem of Calculus
Functions as Upper/Lower Limits
Examples
Averages with Integrals
Mean Value Theorm for Integrals
|
Section 5.4: Indefinite Integrals and the Net Change Theorem |
Notes
Evaluating Integrals
Indefinite Integrals
Examples - Multiplication
Examples - Division
Applications
|
Section 5.5: The Substitution Rule |
Notes
U-Substitution
U-Substitution - Indefinite Integrals
U-Substitution - Definite Integrals
Symmetry and Integrals
|
Calc 2 Materials |
|
Chapter 7: Techniques of Integration |
|
Section 7.1: Integration By Parts |
Integration By Parts
Trig Example
Exponential Example
Logarithmic and Exponential/Trig Examples
Fraction Examples
|
Section 7.3: Trig Substitution |
Basic Trigonometry Properties
Integration with Trigonometry
Even-Powered Trig Integrals
Odd-Powered Trig Integrals
Using the Pythagorean Theorem
Examples