Loyola University Chicago

Mathematics and Statistics

MATH 132: Applied Calculus II

Course Details
Credit Hours: 3
Prerequisites: MATH 131 or MATH 161 with a grade of C- or higher
Description:  A continuation of MATH 131. Topics include: the definition and interpretations of the integral, basic techniques for computing anti-derivatives, applications to economics, probability and statistics, an introduction to multi-variable calculus and optimization for functions of several variables, and mathematical modeling using differential equations. This course is not a substitute for MATH 162.

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

Review of Chapters 5 and 6

Chapter 7: Integration
    7.1    Integration by Substitution
    7.2    Integration by Parts
    7.6    Improper Integrals
Chapter 8: Using the Definite Integral
    8.6  Optional: Applications to Economics
    8.7  Distribution Functions
    8.8  Probability, Mean, and Median
Chapter 9: Functions of Several Variables 
    9.1  Understanding Functions of Two Variables
    9.2  Contour Diagrams
    9.3  Partial Derivatives
    9.4  Computing Partial Derivatives Algebraically
    9.5  Critical Points and Optimization
    9.6  Constrained Optimization
Chapter 10: Differential Equations
    10.1    What is a Differential Equation?
    10.2    Slope Fields
    10.3    Euler’s Method
    10.4    Separation of Variables
    10.5    Growth and Decay
    10.6    Applications and Modeling
    10.7    The Logistic Model
    10.8    Systems of Differential Equations
    10.9    Analyzing the Phase Plane

Chapter 5 Review: The Definite Integral

5.1 How We Measure Distance Traveled?: 5, 38, 41

5.2 The Definite Integral: 7, 35, 38

5.3 The Fundamental Theorem and Interpretations: 3, 14, 28, 43

5.4 Theorems About Definite Integrals: 17, 53, 69

 

Chapter 6 Review: Antiderivatives

6.1 Antiderivatives Graphically and Numerically: 4, 13, 35, 38, 40

6.2 Constructing the Antiderivative Analytically: 24, 33, 47, 50, 52, 63, 64, 82, 84,

99

 

Chapter 7: Integration

7.1 Integration by Substitution: 2, 4, 8, 9, 10, 14, 16, 17, 19, 21, 22, 26, 29, 31, 32,

37, 44, 61, 64, 74, 88 , 115, 124, 148, 152

7.2 Integration by Parts: 3, 4, 5, 6, 8, 10, 13, 19, 21,  31, 40, 46, 58, 60, 63, 78, 84

7.6 Improper Integrals: 3, 4, 6, 7, 9, 11, 13, 14, 18, 20, 25 (No WP) , 28, 36,

50 (No WP)

 

Chapter 8: Using the Definite Integral

8.6 (Optional) Applications to Economics : 1, 8, 9, 27, 36, 37, 41, 44

8.7 Distribution Functions: 1, 5, 6, 7, 8, 9, 11, 14, 15, 16, 17, 23

8.8 Probability, Mean and Median: 2, 4 (No WP), 5 (No WP), 8 (No WP), 9 (No WP),

13, 14, 15, 16, 17 (No WP) , 18 (No WP), 19 (Problem 10 in WP) , 21, 24

 

Chapter 9: Functions of Several Variables

9.1 Understanding Functions of Two Variables: 1, 8, 13, 15, 20

9.2 Contour Diagrams: 4, 5, 18, 21, 27, 32, 39, 40

9.3 Partial Derivatives: 7, 9, 11, 12, 14, 16, 20, 25, 34, 39

9.4 Computing Partial Derivatives Algebraically: 1, 5, 7, 10, 15, 25, 31, 33, 35, 43 (Problem ITQ 43 in WP)

9.5 Critical Points and Optimization: 2, 16, 19, 20, 22, 26, 30, 32

9.6 Constrained Optimization: 1, 3, 7, 8, 12, 14, 27

 

Chapter 10: Differential Equations

10.1 What is a Differential Equation?: 1, 8, 10, 11, 15, 18, 20, 22, 25, 28,  30, 34, 35

10.2 Slope Fields: 4(a)(c)(e) 6, 8, 12(a)(b), 24, 26, 28, 29

10.3 Euler's Method: 8, 9(ab), 11a, 12, 20 (No WP)

10.4 Separation of Variables: 2, 3, 4, 5, 11, 12, 13, 15, 18, 20, 21, 29, 30, 32, 33, 34,

35, 55, 59

10.5 Growth and Decay: 1, 2, 9, 13, 21 WP (36 in text), 30, 32, 41, 46, 50 (No WP)

10.6 Applications and Modeling: 1, 2, 7, 13, 14, 17 (No WP), 22, 26 (No WP), 29

10.7 The Logistic Model: 8 (No WP), 9, 11, 12, 13, 16 (No WP) , 18 (No WP), 20 (No WP) , 22 (No WP), 32 (No WP), 34 (No WP), 38

10.8 Systems of Differential Equations: 1, 2, 3, 4, 22, 24, 28, 30, 31, 32, 34, 35

10.9 (Optional) Analyzing the Phase Plane: 1 (No WP), 2, 5 (No WP), 12 (12a,12b in WP), 16**, 20 (No WP), 21 (No WP)

 

 

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

 

**For problem 16 in Section 10.9 use software to generate the phase plane. Here is an example website https://www.bluffton.edu/homepages/facstaff/nesterd/java/slopefields.html

See Course Page for additional resources.