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.

Deborah Hughes-Hallett, et al. Applied & Single Variable Calculus for Loyola University Chicago with WileyPlus eBook.

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 11: Differential Equations
    11.1    What is a Differential Equation?
    11.2    Slope Fields
    11.3    Euler’s Method
    11.4    Separation of Variables
    11.5    Growth and Decay
    11.6    Applications and Modeling
    11.7    The Logistic Model
    11.8    Systems of Differential Equations
    11.9    Analyzing the Phase Plane

Chapter 5: Review

5.1How We Measure Distance Traveled?: 1, 25, 37

5.2The Definite Integral:5, 7, 34, 37

5.3The Fundamental Theorem and Interpretations:2, 6, 34

5.4Theorems About Definite Integrals 14, 32, 57

 

Chapter 6:Review

6.1Antiderivatives Graphically and Numerically: 3, 15, 31, 33, 34

6.2Constructing the Antiderivative Analytically: 26, 46, 49, 51, 55, 65, 76, 92, 116

 

Chapter 7: Integration

7.1Integration by Substitution: 2, 4, 8, 9, 10, 12, 14, 16, 17, 19, 20, 26, 29, 31, 32, 33 (No WP*), 37, 44, 61, 64, 70, 79 (No WP) , 118, 132

7.2Integration by Parts: 3, 4, 5, 6, 8, 10, 13, 19, 32, 44, 47, 55, 57, 60, 74, 77, 78

7.6Improper Integrals: 2, 3, 5, 6, 8, 10, 12, 13, 15 (No WP), 17, 24 (No WP) , 27, 35, 48 (No WP)

 

Chapter 8A: Using the Definite Integral

8A.6 (Optional) Applications to Economics :1, 4, 8, 9, 10, 21, 30, 31, 33, 36

8A.7Distribution Functions: 1, 5, 6, 7, 8, 9, 10, 11, 14, 15, 16, 17, 21

8A.8Probability, Mean and Median: 2, 4, 5, 6, 8, 9, 11, 13, 14, 15, 16, 17, 18, 19, 20, 23

 

Chapter 8B: Functions of Several Variables

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

8B.2Contour Diagrams: 4, 5, 18, 21, 27, 32, 39, 40

8B.3Partial Derivatives: 7, 9, 11, 12, 14, 16, 20, 25, 34, 39

8B.4Computing Partial Derivatives Algebraically: 1, 5, 7, 10, 15, 25, 31, 33, 34, 44

8B.5Critical Points and Optimization: 2, 16, 17, 22, 23, 31, 32

8B.6Constrained Optimization: 1, 3, 7, 8, 12, 14, 27

 

Chapter 11: Differential Equations

11.1What is a Differential Equation?: 1, 8, 10, 11, 15, 18, 20, 22, 25, 28, 29, 30, 31

11.2Slope Fields: 4(a)(c)(e) 6, 8, 12(a)(b), 19, 21, 23, 24

11.3Euler's Method: 7, 8, 10, 11, 18

11.4Separation of Variables: 2, 3, 4, 5, 6, 7, 8, 10, 13, 15, 16, 24, 25, 27, 28, 29, 30, 32, 49, 51, 53

11.5 Growth and Decay: 1, 2, 9, 11, 20 WP (30 in text), 24, 26, 34, 39, 43

11.6 Applications and Modeling: 1, 2, 6, 8, 14, 15, 18, 22, 24, 28 (No WP)

 

Chapter 11- Rev Ex 45a (Only in WP)

11.7The Logistic Model: 8 (No WP), 9, 11, 12, 14, 16, 18, 20, 22, 31, 33, 37

11.8Systems of Differential Equations: 1, 2, 3, 4, 20, 22, 25, 27, 28, 31, 32

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

 

 

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

 

**For problem 16 in Section 11.9 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.