This page is part of the 2016 Lane website archive, and is presented for historical reference only.

Math 251

Resources - Math 251 Calculus

Hughes-Hallett, Gleason, McCallum et al., 5th Edition

1. A Library of Functions

1.1 Functions and Change

1.2 Exponential Functions

1.3 New Functions from Old

1.4 Logarithmic Functions

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

1.7 Introduction to Continuity

1.8 Limits

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

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

3.3 The Product and Quotient Rules

3.5 The Trigonometric Functions

3.6 The Chain Rule and Inverse Functions

3.7 Implicit Functions

3.8 Hyperbolic Functions

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"

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

4.8 Parametric Equations