# 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 Calculus, 7th Edition (packaged with WileyPlus). ISBN: 978-1-119-799085.

Chapter 5: Accumulated Change: The Definite Integral

5.1 Distance and Accumulated Change

5.2 The Definite Integral

5.3 The Definite Integral as Area

5.4 Interpretations of the Definite Integral

5.5 Total Change and the Fundamental Theorem of Calculus

5.6 Average Value

Chapter 6: Antiderivatives and Applications

6.1 Analyzing Antiderivatives Graphically and Numerically

6.2 Antiderivatives and the Indefinite Integral

6.3 Using the Fundamental Theorem of Calculus to Find Definite Integrals

6.6 Integration by Substitution

6.7 Integration by Parts

Chapter 7: Probability

7.1 Density Functions

7.2 Cumulative Distribution Functions and Probability

7.3 The Median and the Mean

Chapter 8: Functions of Several Variables

8.1 Understanding Functions of Two Variables

8.2 Contour Diagrams

8.3 Partial Derivatives

8.4 Computing Partial Derivatives Algebraically

8.5 Critical Points and Optimization

8.6 Constrained Optimization

Chapter 9: Mathematical Modeling Using Differential Equations

9.1 Mathematical Modeling: Setting Up a Differential Equation

9.2 Solutions of Differential Equations

9.3 Slope Fields

9.4 Exponential Growth and Decay

9.5 Applications and Modeling

9.6 Modeling the Interaction of Two Populations

9.7 Modeling the Spread of a Disease

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.