Resources - Math 251 Calculus
Hughes-Hallett, Gleason, McCallum et al., 5th Edition
1. A Library of Functions
1.1 Functions and Change
- Finding the Domain of a Function
- Finding the Domain of a Function Algebraically
- Reading the Domain and Range from a Graph
- Linear Relationships Some Examples of Linear Function Problems
- Recognizing Linear Functions
- Graphing Linear Functions by Finding the X, Y Intercepts
- Proportionality 1 Introduction to Direct and Inverse Proportionality (Variation)
- Proportionality 2 Recognizing Direct and Inverse Proportionality (Variation)
1.2 Exponential Functions
- Exponential Growth Functions y = 3x, Chain Letter Problem
1.3 New Functions from Old
- Function Inverse Examples 1 How To Take the Inverse of a Function
- Function Inverse Examples 2 Find the Inverse of f(x) = (x + 2)2 + 1
- Function Inverse Examples 3 Find the Inverse of f(x) = (x - 1)2 -2
1.4 Logarithmic Functions
- Properties of Logarithms 1 Lots of Examples!
- Properties of Logarithms 2 How to Use the Cancellation Laws,
Examples:
2 ln x = 1
log ex
e2x+3 - 7 = 0
ln (2x +1) = 2 - ln x
log (ab) = log a + log b
log (a / b) = log a - log b
1.5 Trigonometric Functions
1.6 Powers, Polynomials, and Rational Functions
- Finding X- and Y- Intercepts, Vertical and Horizontal Asymptotes, Plotting Points, Examples:
- Graphing Rational Functions 1 f(x) = 1 / x
- Graphing Rational Functions 2 h(x) = (3x + 12)(x - 2) / (x - 1)(x + 5)
- Graphing Rational Functions 3 f(x) = (x2 - 9) / (x - 3)
- Graphing Rational Functions 4 g(x) = (x-3) / (x2 - 9)
- Graphing Rational Functions 5 h(x) = (x2 + 4x) / (x2 - 16)
1.7 Introduction to Continuity
- Continuity 1 Definition of Continuity
- Continuity 2 Is the Function Continuous?
1.8 Limits
- Introduction to Limits
- Step-by-Step Limit Examples 1 Lim (2x + 2) / (x + 1) as x approaches -1
- Step-by-Step Limit Examples 2 Lim (1 / x) as x approaches 0
- Step-by-Step Limit Examples 3 Lim (x2 - 6x + 9) / (x2-9) as x approaches 3
- The Squeeze Theorem
- The Limit of (sin x / x) as x Approaches Zero
- More Limits Lim (x - 2|x|) / (|x|) as x approaches 0
2. Key Concept: The Derivative
2.1 How Do We Measure Speed
- Covered in "2.3 The Derivative Function"
2.2 The Derivative at a Point
- Covered in "2.3 The Derivative Function"
2.3 The Derivative Function
- Derivatives 1 Introduction to Derivatives, The Derivative as the Slope of a Line
- Derivatives 2 The Derivative Formula
- The Derivative of y = x2
2.4 Interpretations of the Derivative
- Covered in "2.3 The Derivative Function"
2.5 The Second Derivative
- Covered in "2.3 The Derivative Function" and "4.1 Using First and Second Derivatives"
2.6 Differentiability
- Covered in "2.3 The Derivative Function"
- Review of "1.7 An Introduction To Continuity" may be helpful!
3. Short-Cuts to Differentiation
3.1 Powers and Polynomials
- Covered in "2.3 The Derivative Function" and "4.3 Families of Functions"
3.2 The Exponential Function
- Derivatives of Exponential Functions
- Derivatives of Logarithmic Functions
- Also Covered in "4.3 Families of Functions"
3.3 The Product and Quotient Rules
3.5 The Trigonometric Functions
- Covered in "More Derivative Examples"
3.6 The Chain Rule and Inverse Functions
- Derivatives of Inverse Trigonometric Functions 1 The Basics
- Derivatives of Inverse Trigonometric Functions 2 More Complicated Examples
- Derivatives of Inverse Trigonometric Functions 3 Using the Chain Rule
3.7 Implicit Functions
3.8 Hyperbolic Functions
- The Basics of Hyperbolic Functions
- Derivatives of Hyperbolic Functions Lots of Examples
- Inverse Hyperbolic Functions Lots of Examples
3.9 Linear Approximation and the Derivative
3.10 Theorems About Differentiable Functions
4. Using the Derivative
4.3 Families of Functions
Some examples covered in "2.3 The Derivative Function"
- Derivative of xn
- Derivative of x1/2 [The square root of x]
- Derivative ln x
- Derivative of ex
- Derivatives of ln x and ex together
4.4 Optimization, Geometry and Modeling
- Covered in "Optimization"
4.5 Applications to Marginality
- Covered in "Optimization"
4.6 Rates and Related Rates
4.7 L'Hopitals Rule, Growth, and Dominance
- L'Hopital's Rules 1 Introduction to L'Hopital's Rules
- L'Hopital's Rules 2 Lim (2 sin x - sin 2x) / (x - sin x) as x approaches 0
- L'Hopital's Rules 3 Lim (4x2 -5x) / (1-3x2) as x approaches infinite
- L'Hopitals Rules 4 Lim (x/x-1 - 1/lnx) as x approaches 1
4.8 Parametric Equations