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