# MATH 132: Applied Calculus II

Credit Hours

3

Prerequisites

MATH 131

Description

A continuation of MATH 131. Topics include: properties of the definition and interpretations of the integral, basic techniques for computing anti-derivatives, applications to probability, 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.)

See Course Page for additional resources.

## Textbook

Hughes-Hallett, Deborah, et al. Applied & Single Variable Calculus for Loyola University Chicago with WebAssign Custom (packaged with WebAssign). 4th ed. ISBN-13: 9781118762202. Hoboken, NJ: Wiley, 2009. Print.

## Common Syllabus for MATH 132

Review of Chapters 5 & 6.  Definite and Indefinite Integrals [1.5 to 2 Weeks]
(Prerequisite Material from MATH 131)
5
.1 – How Do We Measure Distance Traveled?
Skip: accuracy of estimates (pg 277)

5.2 – The Definite Integral
5.3 – The Fundamental Theorem and Interpretations
5.4 – Theorems About Definite Integrals
properties of definite integrals; area between curves; using the definite integral to find an average
Skip: the subsection “Comparing Integrals”

6.1 – Antiderivatives Graphically and Numerically
6.2 – Constructing Antiderivatives Analytically
Skip: Sections 6.3-6.4

Chapter 7.  Integration [1.5 to 2 Weeks]
7.1 – Integration by Substitution
7.2 – Integration by Parts
7.6 – Improper Integrals
consider only those where limits of integral are infinite
Skip: cases where value of integrand becomes infinite (pp. 398–400)
Skip: Sections 7.3, 7.4, 7.5 & 7.7

Chapter 8.  Using the Definite Integral [2 Weeks]

8.6 – Applications to Economics
8.7 – Distribution Functions
8.8 – Probability, Mean, and Median
Skip: Sections 8.1–8.5

Chapter 9.  Functions of Several Variables [2.5 to 3 Weeks]
9.1 – Understanding Functions of Two Variables
9.2 – Contour Diagrams
9.3 – Partial Derivatives
9.4 – Computing Partial Derivatives
9.5 – Critical Points and Optimization
9.6 – Constrained Optimization

Chapter 11.  Differential Equations [3.5 Weeks]
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 (time permitting)