Loyola University Chicago

Mathematics and Statistics

MATH 132

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    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

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

The Loyola Math Club offers free tutoring to students in 100-level MATH courses (and others). 

Click here to see when it is offered this semester.