# MATH 131: Applied Calculus I

Course Details
Credit Hours: 3
Prerequisites: MATH 118 with a grade C- or higher, or Math Placement Assessment Students who plan to take MATH 263 later should register for MATH 161 instead of MATH 131
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.)

Deborah Hughes-Hallett, et al. Applied Calculus for Loyola University Chicago Custom (packaged with WileyPlus).

Chapter 1: Foundations For Calculus: Functions and Limits
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
2.1    How Do We Measure Speed?
2.2    The Derivative at a Point
2.3    The Derivative Function
2.4    Interpretations of the Derivative
2.5    The Second Derivative
Chapter 3: Short-Cuts to Differentiation
3.1    Powers and Polynomials
3.2    The Exponential Function
3.3    The Product and Quotient Rules
3.4    The Chain Rule
3.5    The Trigonometric Functions
3.6    The Chain Rule and Inverse Functions
Chapter 4: Using the Derivative
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
5.1    How Do We Measure Distance Traveled?
5.2    The Definite Integral
5.3    The Fundamental Theorem and Interpretations
Chapter 6: Constructing Antiderivatives
6.1    Antiderivatives Graphically and Numerically
6.2    Constructing Antiderivatives Analytically
6.3    [Optional] Differential Equations and Motion

Chapter 1: Foundation For Calculus: Functions and Limits

1.1 Functions and Change: 1, 4, 10, 16, 23, 27, 31, 33, 54, 55, 56 72

1.2 Exponential Functions: 2, 5, 6, 8, 10, 16, 17, 31, 38, 40, 50

1.3 New Functions From Old: 9, 17, 18, 23, 32, 36, 47, 49, 54, 55, 56, 60, 65, 75

1.4 Logarithmic Functions: 2, 4, 6, 7, 12, 16, 19, 24, 26, 30, 37, 46, 49, 50

1.5 Trigonometric Functions: 6, 10, 12, 18, 20, 30, 31, 33, 63, 64

1.6 Powers, Polynomials and Rational Functions: 3, 6, 8, 9, 12, 15, 17, 19, 54, 56, 58

1.7 Introduction to Limits and Continuity: 3, 12, 14, 24( No WP), 26(No WP), 28,

31, 39, 42, 46 (No WP), 62

1.8 Extending the Idea of a Limit: 4, 6, 37, 38, 39, 42, 44, 55, 62

Chapter 2: Key Concept: The Derivative

2.1 How Do We Measure Speed?: 3, 4, 6, 8, 11, 18, 19, 20, 21, 25, 26, 34 (GTP 34 in WP), 36, 38

2.2 The Derivative at a Point: 1, 3, 5, 9, 11, 21, 24, 26, 33, 36 51, 57, 61, 64

2.3 The Derivative Function: 1, 2, 5, 13, 20, 22, 37, 52, 53, 56

2.4 Interpretations of the Derivative: 3, 5, 6, 12, 21, 26, 31, 37, 49, 56

2.5 The Second Derivative: 2, 4, 8, 9, 12, 14, 15, 27, 40, 44

Chapter 3: Short-Cuts to Differentiation

3.1 Powers and Polynomials: 10, 12, 14, 18, 23, 25, 28, 29, 30, 33, 36, 46, 60, 61, 67, 80, 94

3.2 The Exponential Function: 2, 4, 6, 8, 10, 12, 13, 17 21, 42, 44, 46, 51, 60

3.3 The Product and Quotient Rules: 4, 6, 7, 10, 12, 13, 19, 20, 26, 28, 31, 43, 47,

52 (No WP), 97

3.4 The Chain Rule: 2, 4, 7, 11, 17, 18, 28, 33, 43, 45, 48, 58, 60, 61, 68, 73, 77, 81,

94

3.5 The Trigonometric Functions: 4, 8, 12, 17, 19, 22, 24, 26, 29,  31, 36, 40, 45, 63

3.6 The Chain Rule and Inverse Functions: 1, 9, 12, 13, 17, 22, 25, 26, 28, 30, 32,

35, 38, 39, 41, 53

Chapter 4: Using the Derivative

4.1 Using First and Second Derivatives: 1, 5, 8, 10, 18, 33, 35, 37, 38, 39, 40, 43, 54, 55, 61

4.2 Optimization: 4, 6, 7, 8, 10, 13, 18, 19, 34, 42, 45, 46, 49

4.3 Optimization and Modeling: 5, 6, 7, 9, 11, 14, 24, 28, 43

4.4 Families of Functions and Modeling: 3, 4, 16, 21, 28, 49, 51, 52, 53, 58, 64

4.5 Applications to Marginality: 1, 4, 7, 12, 14, 17, 19

4.7 L’Hopital’s Rule, Growth, and Dominance: 6, 11, 35, 41, 42, 50, 55, 60, 61, 67,

68, 89

Chapter 5: Key Concept: The Definite Integral

5.1 How We Measure Distance Traveled?: 1, 2, 4, 16, 20, 22 ,23, 27, 29, 32

5.2 The Definite Integral: 4, 8,  9, 12, 25, 27, 30, 31, 33, 37

5.3 The Fundamental Theorem and Interpretations: 2, 4, 6, 7, 10, 11, 13, 15, 21,

23, 29, 39

5.4 Theorems About Definite Integrals: 1, 2, 4, 6, 7, 8, 11, 14, 16, 19, 25 (No WP),

26, 28, 31, 44

Chapter 6: Constructing Antiderivatives

6.1 Antiderivatives Graphically and Numerically: 3, 13, 15, 24, 29, 32, 37

6.2 Constructing the Antiderivative Analytically: 7, 10,  12, 15, 16, 18, 20, 26, 28,

31, 35, 41, 45, 50, 53, 56, 57, 58, 59, 60, 66

* No WP means the problem is not in WileyPlus and should be completed from the textbook.

Math 131 Common Final Study Materials

The Math 131 common final exam is scheduled for Thursday, May 4, 2023, 7:00 pm – 9:00 pm. Calculators will be permitted on the exam, however no internet-capable devices will be permitted during the exam. CAS (computer algebra system) calculator features will not be needed on the exam.We provide sample exams and study materials here from previous academic years. Please note that some of these exams were administered online. We plan for the Spring 2023 final exam to be administered in person on the Loyola campus.

We provide the following pdf files:

See Course Page for additional resources.