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Loyola University Chicago

Mathematics and Statistics

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)

Loyola

Department of Mathematics and Statistics
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