Math 153 - Differentital and Integral Calculus for Non-Science - Majors


Table of Contents


Chapter 1: Functions, Graphs and Limits

Section 1.1: Functions
  1. Functions
  2. Vertical Line Test
  3. One-to-One Function
  4. Horizontal Line Test
  5. Piecewise Functions
  6. Functions Used in Economics
  7. Composite Functions
  8. Decomposing a Composite Function
  9. Difference Quotient
Section 1.2: Graphs of a Function

Section 1.3: Linear Functions
  1. Linear Functions
  2. Properties of Linear Functions
  3. Slope of a Line
  4. Different Forms of the Equation of a Line
  5. Parallel and Perpendicular Lines
Section 1.4: Functional Models
  1. Mathematical Models
  2. Proportionality
  3. Business Concepts
  4. Example 1: Spread of an epidemic
  5. Example 2: Auction buyers premium
  6. Example 3: Break even analysis
Section 1.5: Limits
  1. Numerical Experiment
  2. Limit Symbology
  3. Properties and Rules of Limits
  4. Example 1:  Find the limit
  5. Example 2:  Find the limit - 0/0
Section 1.6: One-Sided Limits and Continuity
  1. One-Sided Limits
  2. Infinite Limits
  3. Limits at Infinity
  4. Example 1:  Find the limit as x approaches infinity
  5. Example 2:  Find the limit as x approaches infinity
  6. Example 3:  Find the limit as x approaches infinity
  7. Continuity at a point
  8. Example 4:  Continuity at a Point
  9. Continuity of Functions
  10. Example 5:  Continuity of a piecewise function
  11. Algebra of Continuous Functions
  12. Example 6:  Continuity of a function
  13. Intermediate Value Theorem
  14. Example 7:  Intermediate Value Theorem

Chapter 2: Differentiation:  Basic Concepts

Section 2.1: The Derivative
  1. Basic Concept
  2. Example 1
  3. Secant and Tangent Lines
  4. Example 2
  5. Example 3
  6. The Derivative
  7. Example 4

Chapter 3: Additional Applications of the Derivative

Section 3.1: Increasing and Decreasing Functions; Relative Extrema