# MATH 132

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

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

Below are “core problems” that we expect students to be able to solve to ensure understanding of the material in the course syllabus. The problems are taken from Applied & Single Variable Calculus for Loyola University Chicago (packaged with WebAssign), 4th ed., Hughes-Hallett, Deborah, et al.

Chapter 5 Review
5.1 1, 25, 37
5.2 5, 7, 34, 37
5.3 2, 6, 34
5.4 14, 32, 57
Chapter 6 Review
6.1 3, 15, 31, 33, 34
6.2 26, 46, 49, 51, 55, 65, 76, 92, 116
Chapter 7. Integration
7.1 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
7.2 3, 4, 5, 6, 8, 10, 13, 19, 32, 44, 47, 55, 57, 60, 74, 77, 78
7.6 2, 3, 5, 6, 8, 10, 12, 13, 15 (No WP) 17, 24 (No WP) , 27, 35, 48 (No WP)
Chapter 8. Using the Definite Integral
8A.6 (Optional) 1, 4, 8, 9, 10, 21, 30, 31, 33, 36
8A.7 1, 5, 6, 7, 8, 9, 10, 11, 14, 15, 16, 17, 21
8A.8 2, 4, 5, 6, 8, 9, 11, 13, 14, 15, 16, 17, 18, 19, 20, 23
8B.1 1, 8, 13, 15, 20
8B.2 4, 5, 18, 21, 27, 32, 39, 40
8B.3 7, 9, 11, 12, 14, 16, 20, 25, 34, 39
8B.4 1, 5, 7, 10, 15, 25, 31, 33, 34, 44
8B.5 2, 16, 17, 22, 23, 31, 32
8B.6 1, 3, 7, 8, 12, 14, 27
Chapter 11. Differential Equations
11.1 1, 8, 10, 11, 15, 18, 20, 22, 25, 28, 29, 30, 31
11.2 4(a)(c)(e) 6, 8, 12(a)(b), 19, 21, 23, 24
11.3 7, 8, 10, 11, 18
11.4 2, 3, 4, 5, 6, 7, 8, 10, 13, 15, 16, 24, 25, 27, 28, 29, 30, 32, 49, 51, 53
11.5 1, 2, 9, 11, 20 WP (30 in text), 24, 26, 34, 39, 43
11.6 1, 2, 6, 8, 14, 15, 18, 22, 24, 28 (No WP), Chapter 11- Rev Ex 45a (Only in WP)
11.7 8 (No WP), 9, 11, 12, 14, 16, 18, 20, 22, 31, 33, 37
11.8 1, 2, 3, 4, 20, 22, 25, 27, 28, 31, 32
11.9 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

## Should you choose Math 161/162 or Math 131/132?

Any questions about placement in calculus or other 100-level courses that remain after reading that section should be directed to John Houlihan, Mathematics Placement Director. Please e-mail him to set up an appointment.

Math 161/162 (Calculus I, Calculus II) is a traditional calculus sequence covering all the basic topics of one-variable calculus. This sequence is a prerequisite for Multivariable Calculus (Math 263) as well as for almost all higher-level math courses. It is required for all students majoring in Chemistry, Engineering Science, Mathematics, Physics and Statistics. It is highly recommended, although not required, for students majoring in Biology, Computer Science and Economics.

Math 131/132 (Applied Calculus I, Applied Calculus II) is more of a survey sequence covering many of the basic topics in one-variable calculus as well as some topics in multivariable calculus and differential equations. It is a terminal sequence in that it does not satisfy the prerequisites of upper-level mathematics and statistics courses. Students who enjoyed mathematics in high school and earned ACT math scores of 28 and higher or SAT math scores of 660 and higher are encouraged to choose the Math 161/162 sequence.

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### Loyola Math Club Tutoring

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