Loyola University Chicago

Mathematics and Statistics

MATH 131: Applied Calculus I

Credit Hours



Math Placement Test or MATH 118


An introduction to differential and integral calculus, with an emphasis on applications. This course is intended for students in the life and social sciences, computer science, and business. Topics include: modeling change using functions including exponential and trigonometric functions, the concept of the derivative, computing the derivative, applications of the derivative to business and life, social, and computer sciences, and an introduction to integration.

(Students may not receive credit for both MATH 131 and 161 without permission of the department chairperson. Math 131 is not a substitute for Math 161.)

See Course Page for additional resources.


Hughes-Hallett, Deborah, et al. Applied & Single Variable Calculus for Loyola University Chicago with WebAssign Custom (packaged with WebAssign). 4th ed. ISBN-13: 9781118762202. Hoboken, NJ: Wiley, 2009. Print.

Common Syllabus for MATH 131

Chapter 1 – A Library of Functions (1.5–2 weeks):

1.1 – Functions and Change
1.2 – Exponential Functions
1.3 – New Functions from Old

  • Skip: the subsection on Shifts and Stretches and Odd and Even Symmetry.
  • Review of composite and inverse functions, framed in a practical, not merely algebraic, setting.

1.4 – Logarithmic Functions
1.5 – Trigonometric Functions
1.6 – Powers, Polynomials, and Rational Functions

  • Skip: the subsection on rational functions (pg 49-50).
  • Power functions, graph properties for both positive and negative exponents.
  • Comparison of long-run behavior of exponentials and polynomials.

1.7 – Introduction to Continuity

  • Skip: the majority of the section.
  • Understand the graphical viewpoint of continuity. (are there holes, breaks, or jumps in the graph?)

1.8 – Limits

  • Skip: the subsection “Definition of Limit” (bottom of pg 58 – 59).
  • Skip: the subsection “Definition of Continuity” (see comment on 1.7 above).
  • Understand the concept, notation, and properties of limits  and one-sided limites at a point and limits at infinity.

Chapter 2 – Key Concept – The Derivative (1.5 weeks)

2.1 – How do we measure speed?
2.2 – The Derivative at a Point

  • Emphasis on observing what happens to the value of the average rate of change as the interval gets smaller and smaller.
  • Emphasis placed on visualizing the derivative as the slope of a tangent.

2.3 – The Derivative Function

  • Focus on the conceptual and practical understanding of the derivative.
  • Sketch the graph of f ’ given the graph of f.

2.4 – Interpretation of the Derivative
2.5 – The Second Derivative

Chapter 3 – Shortcuts to Differentiation  (2.5 weeks)

3.1 – Powers and Polynomials
3.2 – The Exponential Function

  • Emphasis on graphical, not epsilon-delta, definition of derivative.
  • Add: differentiation rule for y=ln(x), from section 3.6.

3.3 – Product and Quotient Rules
3.4 – The Chain Rule
3.5 – The Trigonometric Functions


Chapter 4 – Using the Derivative  (3 weeks)

4.1 – Using First and Second Derivatives
4.2 – Optimization
4.3 – Optimization and Modeling
4.4 – Families of Functions and Modeling
4.5 – Applications to Marginality
4.7 – L’Hopital’s Rule, Growth, and Dominance

Chapter 5 – Key Concept – The Definite Integral  (2 weeks)

5.1 – How Do We Measure Distance Traveled?

  • Skip: accuracy of estimates (pg 277)

5.2 – The Definite Integral

  • Approximation using area and interpretation as accumulated change.

5.3 – The Fundamental Theorem and Interpretations
5.4 – Theorems About Definite Integrals

  • Finding area between curves; using the definite integral to find an average.
  • Skip: the subsection “Comparing Integrals”

Chapter 6 – Constructing Antiderivatives  (1 week)

6.1 – Antiderivatives Graphically and Numerically
6.2 – Constructing Antiderivatives Analytically