# 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 8A: Using the Definite Integral
8A.6  Optional: Applications to Economics
8A.7  Distribution Functions
8A.8  Probability, Mean, and Median
Chapter 8B: Functions of Several Variables
8B.1  Understanding Functions of Two Variables
8B.2  Contour Diagrams
8B.3  Partial Derivatives
8B.4  Computing Partial Derivatives Algebraically
8B.5  Critical Points and Optimization
8B.6  Constrained Optimization
Chapter 11: Differential Equations
11.1    What is a Differential Equation?
11.2    Slope Fields
11.3    Eulerâ€™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.