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Loyola University Chicago

Mathematics and Statistics

MATH 131: Applied Calculus I

Credit Hours

3

Prerequisites

Math Placement Test or MATH 118

Description

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.

Textbook

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

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

1.7 – Introduction to Continuity

1.8 – Limits

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

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

2.3 – The Derivative Function

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

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?

5.2 – The Definite Integral

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


Chapter 6 – Constructing Antiderivatives  (1 week)

6.1 – Antiderivatives Graphically and Numerically
6.2 – Constructing Antiderivatives Analytically

Loyola

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