Math 251 - Calculus Lecture Notes

Go to: Chapter 1 | Chapter 2 | Chapter 3 | Chapter 4 | Chapter 5 | Chapter 6

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Chapter 1 - Functions & Models

  1. Chapter 1 Lecture Notes
  2. §1.1 Four Ways to Represent a Function
  3. §1.2 Mathematical Models: A Catalog of Essential Functions
  4. §1.3 New Functions from Old Functions
  5. §1.4 Graphing Calculators & Computers
  6. §1.5 Exponential Functions
  7. §1.6 Inverse Functions & Logarithms

Chapter 2 - Limits & Derivatives

  1. Chapter 2 Lecture Notes
  2. §2.1 Tangent & Velocity Problems
  3. §2.2 The Limit of a Function
  4. §2.3 Calculating Limits Using the Limit Laws
  5. §2.4 The Precise Definition of a Limit
  6. §2.5 Continuity
  7. §2.6 Limits at Infinitiy; Horizontal Asymptotes
  8. §2.7 Derivatives and Rates of Change
  9. §2.8 Derivative as a Function

Chapter 3 - Differentiation Rules

  1. Chapter 3 Lecture Notes
  2. §3.1 Derivatives of Polynomials and Exponential Functions
  3. §3.2 The Product and Quotient Rules
  4. §3.3 Derivatives of Trigonometric Functions
  5. §3.4 The Chain Rule
  6. §3.5 Implicit Differentiation
  7. §3.6 Derivatives of Logarithmic Functions
  8. §3.7 Rates of Change in the Natural and Social Sciences
  9. §3.8 Exponential Growth & Decay
  10. §3.9 Related Rates
  11. §3.10 Linear Approximations & Differentials
  12. §3.11 Hyperbolic Functions

Chapter 4 - Applications of Differentiation

  1. Chapter 4 Lecture Notes
  2. §4.1 Maximum & Minimum Values
  3. §4.2 The Mean Value Theorem
  4. §4.3 How Derivatives Affect the Shape of a Graph
  5. §4.4 Indeterminant Forms and L'Hospital's Rule
  6. §4.5 Summary of Curve Sketching
  7. §4.6 Graphing with Calculus and Calculators
  8. §4.7 Optimization Problems
    Links to Optimization Examples
  9. §4.8 Newton's Method
  10. §4.9 Antiderivatives

Chapter 5 - Integrals

  1. Chapter 5 Lecture Notes
  2. §5.1 Areas and Distances
  3. §5.2 The Definite Integral
  4. §5.3 The Fundamental Theorem of Calculus
  5. §5.4 Indefinite Integrals and the Net Change Theorem
  6. §5.5 The Substitution Rule

Chapter 6 - Applications of Integration

  1. §6.1 Areas between Curves
  2. §6.2 Volumes
  3. §6.3 Volumes by Cylindrical Shells
  4. §6.4 Work
  5. §6.5 Average Value of a Funciton

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