# FAQ Mirror

The next few questions represent Math 100 content, to be mirrored on other pages.

Chapter 1: Functions and Algebraic Structure
1.1  What Is A Function?
1.2  Functions and Expressions
1.3  Functions and Equations
1.4  Functions and Change
1.5  Functions, Modeling, and Proportionality

Chapter 2: Linear Functions
2.1  Introduction to Linear Functions
2.2  Linear Expressions
2.3  Linear Equations
2.4  Equations for Lines in The Plane
2.5  Modeling with Linear Functions
2.6  Systems of Linear Equations

3.3  Converting to Factored and Vertex Form

Chapter 4: Power Functions
4.1  Power Functions: Positive Exponents
4.2  Power Functions: Negative Exponents
4.3  Power Functions and Expressions
4.4  Power Functions and Equations
4.5  Modeling with Power Functions

Chapter 5: More on Functions
5.1  Domain and Range
5.2  Composing and Decomposing Functions
5.3  Shifting and Scaling
5.4  Inverse Functions

McCallum, Connally, Hughes-Hallett et al. Algebra: Form and Function. 2nd edition. (with WileyPlus ebook)

Instructions for students to obtain the e-book and to use WileyPlus: Use your Loyola email address to create a WileyPlus account. Your professor will include details on WileyPlus in the syllabus.

The next few questions represent Math 108 content, to be mirrored on other pages.

#### Part I - Management Science

Chapter 1: Urban Services [0.5 Weeks]
Euler Circuits, Finding Euler Circuits, Circuits with Reused Edges

Chapter 2: Business Efficiency [1 Week]
Hamiltonian Circuits, Fundamental Principle of Counting, Traveling Salesman Problem, Strategies for Solution, Nearest-Neighbor Algorithm, Sorted-Edges Algorithm, Minimum-Cost Spanning Trees, Kruskal's Algorithm

Chapter 3: Planning and Scheduling [1 Week]
Scheduling Tasks, Assumptions and Goals, List-Processing Algorithm, When is a Schedule Optimal?, Strange Happenings, Critical-Path Schedules, Independent Tasks, Decreasing-Time Lists

Chapter 4: Linear Programming [1 Week]
Mixture Problems, Mixture Problems Having One Resource, One Product and One Resource: Making Skateboards, Common Features of Mixture Problems, Two Products and One Resource: Skateboards and Dolls, Mixture Charts, Resource Constraints, Graphing the Constraints to Form the Feasible Region, Finding the Optimal Production Policy, General Shape of Feasible Regions, The Role of the Profit Formula: Skateboards and Dolls, Setting Minimum Quantities for Products: Skateboards and Dolls, Drawing a Feasible Region When There are Nonzero Minimum Constraints, Finding Corner Points of a Feasible Region Having Nonzero Minimums, Evaluating the Profit Formula at the Corners of a Feasible Region with Nonzero Minimums, Summary of the Pictorial Method, Mixture Problems Having Two Resources, Two Products and Two Resources: Skateboards and Dolls, The Corner Point Principle, Linear Programming: The Wider Picture, Characteristics of Linear Programming Algorithms, The Simplex Method, An Alternative to the Simplex Method

#### Part III - Voting and Social Choice

Chapter 9: Social Choice: The Impossible Dream [1.5 Weeks]
Elections with Only Two Alternatives, Elections with Three or More Alternatives: Procedures and Problems, Plurality Voting and the Condorcet Winner Criterion, The Borda Count and Independence of Irrelevant Alternatives, Sequential Pairwise Voting and the Pareto Condition, the Hare System and Monotonicity, Insurmountable Difficulties: From Paradox to Impossibility, The Voting Paradox of Condorcet, Impossibility, A Better Approach? Approval Voting

Chapter 11: Weighted Voting Systems [2 Weeks]
How Weighted Voting Works, Notation for Weighted Voting, The Banzhaf Power Index, How to Count Combinations, Equivalent Voting Systems, The Shapley-Shubik Power Index, How to Compute the Shapley-Shubik Power Index, Comparing the Banzhaf and Shapley-Shubik Models

#### Part IV - Fairness and Game Theory

Chapter 13: Fair Division [1.5 Weeks]
The Adjusted Winner Procedure, The Knaster Inheritance Procedure, Divide-and-Choose, Cake-Division Procedures: Proportionality, Cake-Division Procedures: The Problem of Envy

Chapter 14: Apportionment [1.5 Weeks]
The Apportionment Problem, The Hamilton Method, Paradoxes of the Hamilton Method, Divisor Methods, The Jefferson Method, Critical Divisors, The Webster Method, The Hill-Huntington Method, Which Divisor Method is the Best?

Chapter 15: Game Theory: The Mathematics of Competition [as time permits]
Two-Person Total-Conflict Games: Pure Strategies, Two-Person Total-Conflict Games: Mixed Strategies, A Flawed Approach, A Better Idea, Partial-Conflict Games, Larger Games, Using Game Theory, Solving Games, Practical Applications

#### Part V - The Digital Revolution

Chapter 16: Identification Numbers [1 Week]
Check digits, the Zip Code, Bar Codes, Encoding Personal Data

Chapter 17: Transmitting Information [1.5 Weeks]
Binary Codes, Encoding with Parity-Check Sums, Data Compression, Cryptography

Note: Instructors may vary the topics covered, and length of time devoted to each.

Consortium for Mathematics and Its Applications (COMAP), S. Garfunkel, ed., For All Practical Purposes: Mathematical Literacy in Today's World, 9th edition. W. H. Freeman (2011). ISBN-13: 978-1429-25482-3.

MATH 108 Core Problems

The next few questions represent Math 117 content, to be mirrored on other pages.

Chapter 1: Linear Functions and Change

1.1 Functions and Function Notation
1.2 Rates of Change
1.3 Linear Functions
1.4 Formulas for Linear Functions
1.5 Modeling with Linear Functions
1.6 Fitting linear functions to data

Chapter 2: Functions

2.1 Input and Output
2.2 Domain and Range
2.3 Piecewise-defined functions
2.4 Preview of Transformations: Shifts
2.5 Preview of Composite and Inverse Functions
2.6 Concavity

3.1 Introduction to the Family of Quadratic Functions
3.2 The vertex of a Parabola

Chapter 6: Transformations and their graphs

6.1 Shifts, reflections, and symmetry
6.2 Vertical stretches and compressions
6.3 Horizontal stretches and combinations of transformations

Chapter 11: Polynomial and Rational Functions

11.1 Power functions and proportionality
11.2 Polynomial functions
11.3 The short-run behavior of polynomials
11.4 Rational functions
11.5 The short-run behavior of rational functions

Functions Modeling Change: A Preparation for Calculus, 5th Edition, Eric Connally, Deborah Hughes-Hallett, Andrew M. Gleason packaged with WileyPlus.

The next few questions represent Math 118 content, to be mirrored on other pages.

Common Syllabus for MATH 118

Textbook:  Functions Modeling Change(5th ed.) by Connally, Hughes-Hallett, Gleason, et al.

Chapter 4: Exponential functions

4.1 Introduction to the family of exponential function

4.2 Comparing exponential and linear functions

4.3 Graphs of exponential functions

4.4 Applications to compound interest

4.5 The number e

Chapter 5: Logarithmic functions

5.1 Logarithms and their properties

5.2 Logarithms and exponential models

5.3 The logarithmic function and its applications

5.4 Logarithmic scales

Chapter 11: Polynomial and rational functions

11.6 Comparing power, exponential, and log functions

11.7 Fitting exponentials and polynomials to data

Chapter 7: Trigonometry and periodic functions

7.1 Introduction to periodic functions

7.2 The sine and cosine functions

7.4 Graphs of  the sine and cosine

7.5 Sinusoidal functions

7.6 The tangent function

7.7 Trigonometric functions and identities

7.8 Inverse trigonometric functions

Chapter 8: Triangle trigonometry and polar coordinates

8.1 Trig functions and right triangles

8.2 Non-right triangles

8.3 Polar coordinates

Chapter 9: Trigonometric identities, models, and complex numbers

9.1 Trigonometric equations

9.2 Identities, expressions, and equations

9.3 Sum and difference formulas for sine and cosine

9.6 Complex numbers and De Moivre’s theorem

Chapter 10: Compositions, inverses, and combinations of functions

10.1 Composition of functions

10.2 Invertibility and properties of inverse functions

10.3 Combinations of functions

The next few questions represent Math 131 content, to be mirrored on other pages.

Chapter 1: Foundations For Calculus: Functions and Limits
1.1    Functions and Change
1.2    Exponential Functions
1.3    New Functions from Old
1.4    Logarithmic Functions
1.5    Trigonometric Functions
1.6    Powers, Polynomials, and Rational Functions
1.7    Introduction to Continuity
1.8    Limits
Chapter 2: Key Concept: The Derivative
2.1    How Do We Measure Speed?
2.2    The Derivative at a Point
2.3    The Derivative Function
2.4    Interpretations of the Derivative
2.5    The Second Derivative
Chapter 3: Short-Cuts to Differentiation
3.1    Powers and Polynomials
3.2    The Exponential Function
3.3    The Product and Quotient Rules
3.4    The Chain Rule
3.5    The Trigonometric Functions
3.6    The Chain Rule and Inverse Functions
Chapter 4: Using the Derivative
4.1    Using First and Second Derivatives
4.2    Optimization
4.3    Optimization and Modeling
4.4    Families of Functions and Modeling
4.5    Applications to Marginality
4.7    L’Hopital’s Rule, Growth, and Dominance
Chapter 5: Key Concept: The Definite Integral
5.1    How Do We Measure Distance Traveled?
5.2    The Definite Integral
5.3    The Fundamental Theorem and Interpretations
Chapter 6: Constructing Antiderivatives
6.1    Antiderivatives Graphically and Numerically
6.2    Constructing Antiderivatives Analytically
6.3    [Optional] Differential Equations and Motion

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 1. A Library of Functions
1.1 1, 8, 13, 16, 23, 27, 31, 33, 53, 55, 70(No WP*)
1.2 2, 5, 6, 8, 10, 16, 17, 31, 38, 39
1.3 9, 13, 14, 28, 32, 43, 45, 50, 51, 52, 56, 61, 68, 19, 71
1.4 2, 4, 6, 7, 12, 16, 19, 24, 26, 30, 36, 45, 47, 48
1.5 6, 10, 12, 18, 20, 30, 31, 33, 62, 63, 68
1.6 3, 6, 8, 9 , 12, 15, 17, 19, 47 (No WP), 50, 52, 54
1.7 2, 3, 12 (No WP), 14 (No WP), 24( No WP), 26(No WP), 28 (No WP), 31 (No WP), 39 (No WP), 43 (No WP), 49 (No WP)
1.8 4, 6, 31, 33, 38, 45, 52 (No WP)
Chapter 2. Key Concept: The Derivative
2.1 1, 3, 5, 7, 10, 15, 16, 17, 21, 22, 29, 31, 33
2.2 1, 3, 4, 8, 10, 19, 22, 23(No WP), 32, 37, 47, 56, 60, 63
2.3 1, 2, 5, 13, 20, 22, 33, 49, 50, 52
2.4 2, 3, 9, 12(No WP), 17, 19, 24 (No WP), 27, 33, 38, 51, 54 (No WP)
2.5 2, 3, 8, 9, 12, 14, 15, 25, 37, 38, 41
Chapter 3. Short-Cuts to Differentiation
3.1 6, 10, 11, 14, 18, 23, 25, 28, 30, 32, 35, 38, 48, 58, 70, 75, 99
3.2 2, 4, 6, 8, 10, 12, 13, 17, 24, 42, 44, 46, 49, 58
3.3 4, 6, 7, 10, 12, 16, 19, 20, 24, 28, 31, 43, 47, 52, 90
3.4 2, 4, 7, 11, 17, 18, 28, 33, 43, 45, 48, 58, 60, 61, 67, 70, 73, 77, 86
3.5 4, 8, 10, 12, 16, 19, 22, 24, 26, 30, 36, 38, 45, 61
3.6 1, 9, 12, 13, 17, 22, 25, 26, 28, 30, 32, 35, 38, 39, 41, 50
Chapter 4. Using the Derivative
4.1 1, 5, 18, 25, 32, 34, 35, 36, 37, 40, 52, 53, 59
4.2 4, 6, 7, 8, 10, 13, 18, 19, 30, 37, 39, 40, 43
4.3 5, 6, 7, 9, 11, 14, 18, 22, 25, 27, 38, 39, 45
4.4 3, 4, 16, 25, 26, 47, 49, 50, 51, 57, 63
4.5 1, 4, 7, 12, 13, 15, 16, 18
4.7 6, 11, 35, 41, 42, 48, 53, 58, 59, 65, 67, 76, 87
Chapter 5. Using the Derivative
5.1 1, 2, 4, 8, 14 ,15, 23, 25, 28
5.2 4, 8, 12, 24, 29, 30, 32, 36
5.3 1, 2, 3, 4, 5, 7, 9, 10, 12, 14, 16, 18, 22, 30
5.4 1, 2, 3, 4, 6, 7, 8, 11, 14, 16, 19, 25, 26, 28, 30, 33
Chapter 6. Constructing Antiderivatives
6.1 3, 6, 13, 15, 20, 25, 33
6.2 7, 9, 10, 11, 12, 15, 18, 20, 21, 26, 28, 30, 31, 35, 41, 44, 50, 55, 56, 57, 58, 60, 65

* No WP means the problem is not in WileyPlus and should be completed from the textbook.

The next few questions represent Math 108 content, to be mirrored on other pages.

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

The next few questions represent Math 161 content, to be mirrored on other pages.

Chapter 1: Functions and Models
1.1 Four Ways to Represent a Function
1.2 Mathematical Models: A Catalog of Essential Functions
1.3 New Functions from Old Functions
1.4 Exponential Functions and Logarithms
1.5 Inverse Functions and Logarithms
Optional: Graphing with calculators, Mathematica, Wolfram Alpha (pp. xxiv-xxv)

Chapter 2: Limits and Derivatives
2.1 The Tangent and Velocity Problems
2.2 The Limit of a Function
2.3 Calculating Limits Using the Limit Laws
2.4 The Precise Definition of a Limit
2.5 Continuity
2.6 Limits at Infinity; Horizontal Asymptotes
2.7 Derivatives and Rates of Change
2.8 The Derivative as a Function

Chapter 3: Differentiation Rules
3.1 Derivatives of Polynomials and Exponential Functions
3.2  The Product and Quotient Rules
3.3 Derivatives of Trigonometric Functions
3.4 The Chain Rule
3.5 Implicit Differentiation
3.6 Derivatives of Logarithmic Functions
3.7 Rates of Change in Natural and Social Sciences
3.8 Exponential Growth and Decay
3.9 Related Rates
3.10 Linear Approximations and Differentials
3.11 Optional: Hyperbolic Functions

Chapter 4: Applications of Derivatives
4.1 Maximum and Minimum Values
4.2 The Mean Value Theorem
4.3 How Derivatives Affect the Shape of a Graph
4.4 Indeterminate Forms and l'Hospital's Rule
4.5 Summary of Curve Sketching
4.6 Optional: Graphing with Calculus and Calculators
4.7 Optimization Problems
4.8 Optional: Newton's Method
4.9 Antiderivatives

Chapter 5: Integrals
5.1 Areas and Distances
5.2 The Definite Integral
5.3 The Fundamental Theorem of Calculus
5.4 Indefinite Integrals and the Net Change Theorem
5.5 The Substitution Rule

Textbook for MATH 162 and MATH 162: Dwyer and Gruenward. Calculus Resequenced for Students in STEM, preliminary edition. Wiley. ISBN: 978-1119321590.

Note: MATH 162A uses a different textbook. Namely, James Stewart. Calculus, Early Transcendentals (WebAssign eBook) 8th ed. Cengage Learning. Be sure you are reading the correct information.

MATH 161 Core Problems

The next few questions represent Math 162 content, to be mirrored on other pages.

Review of prerequisite Material from MATH 161

Chapter 6. Techniques of Integration
6.2 Integration by Parts
6.3 Trigonometric Substitution
6.4 Integrating Rational Functions
6.5 Improper Integrals
6.6 Approximating Definite Integrals

Chapter 7. Applications of Integration
7.1 Average Value and Area Between Curves
7.2 Arc Length
7.3 Volumes
7.4 Solids of Revolution: Volumes by Shells and Surface Area
7.5 Work

Chapter 8. Vectors and Matrices
8.1 Vectors
8.2 Dot Product
8.3 Matrices
8.4 Determinants and Inverse Matrices
8.5 Cross Product
8.6 Lines and Planes in Space

Chapter 9. Functions of Several Variables
9.1 Introduction to F’ns of Several Variables
9.2 Limits and Continuity
9.3 Partial Derivatives
9.4 Chain Rule
9.6 Tangent Planes and Linear Approximations
9.7 Extrema and the Second Partials Test
9.8 Lagrange Multipliers

Chapter 10. Double Integrals
10.1 Double Integrals Over Rectangles
10.2 Double Integrals Over Regions
10.3 Double Integrals in Polar Coordinates
10.4 Applications of Double Integrals

Chapter 11. Differential Equations
11.1 Introduction to Differential Equations
11.2 Separable Differential Equations
11.2 Optional: Graphical, Numerical Solutions to Differential Equations
11.3 Optional: Linear First-Order Differential Equations

MATH 162 Core Problems

WebAssign is an online, interactive environment for teaching and learning.  Using WebAssign students will complete Core Homework Problems common to all sections; individual instructors may also assign additional homework.  WebAssign also provides access to the text as an e-book.  By department policy, homework will count at least 5% towards students' final course grade.  The ground rules provided by your instructor will have further details.

You may begin using WebAssign on the first day of class. In order to access WebAssign after the 14-day grace period, you must purchase an access code as detailed below. If you purchased an access code in MATH 161 or Math 162 for the Stewart text in a previous semester, do not purchase a new code as the code you previously purchased remains valid.

Instructions for students to obtain the e-book and to use WebAssign: Once your instructor has uploaded the class roster to WebAssign, your personal class page will be activated. You will access it with your Loyola ID and password as detailed below. (Note to returning students: there is a change from previous semesters... you no longer need a class key to use WebAssign.)

1. Go to www.webassign.net/luc/login.html (Note the change in URL from previous semesters.)
2. Use the LOG IN @ LOYOLA UNIVERSITY CHICAGO button in the center of the page. The LOG IN button in the upper right-hand corner should NOT be used.
3. Selecting the Loyola login button will bring you to a standard Loyola login page, where you will enter your Loyola ID and password.
4. Successful login should bring you to a WebAssign home screen from which you can access any of your courses having a WebAssign component.
5. Select the desired course. If you have not already registered an access code for the course, a notice will be displayed with three choices:
• Enter an access code (purchased at the Loyola Bookstore or from the Acadiem website),
• Purchase an access code (online from WebAssign), or
• Continue the free trial.
Select the appropriate choice to access the e-book and homework assignments.
6. If you purchased an access code for the Stewart text in a previous semester, you do not need to purchase another code.
7. If at any time you run into technical difficulty using WebAssign, you can contact WebAssign directly by email or phone.  Visit https://webassign.com/support/student-support/ to get started.

• For Windows users:
• Mozilla Firefox (version 38 or later)
• Internet Explorer/Microsoft Edge (version 11 or later)
• Google Chrome (version 44 or later)
• For Mac users:
• Mozilla Firefox (version 38 or later)
• Google Chrome (version 44 or later)
• Apple Safari (version 8 or later)
• For iPad users (iOS 8 or later):
• Apple Safari (version 8 or later)

As you work WebAssign problems, WebAssign will warn you if you need additional plug-ins.  If you run into issues with system requirements, go to http://www.webassign.net/manual/instructor_guide/c_a_system_requirements.htm or contact WebAssign technical support at https://webassign.com/support/student-support/.

The next few questions represent Math 263 content, to be mirrored on other pages.

Chapter 12: Vectors and the Geometry of Space
12.1    Three-Dimensional Coordinate Systems
12.2    Vectors
12.3    The Dot Product
12.4    The Cross Product
12.5    Equations of Lines and Planes
12.6    Optional: Cylinders and Quadric Surfaces
Chapter 13: Vector Functions
13.1    Vector Functions and Space Curves
13.2    Derivatives and Integrals of Vector Functions
13.3    Arc Length and Curvature
13.4    Motion in Space: Velocity and Acceleration
Chapter 14: Partial Derivatives
14.1    Functions of Several Variables
14.2    Limits and Continuity
14.3    Partial Derivatives
14.4    Tangent Planes and Linear Approximation
14.5    The Chain Rule
14.6    Directional Derivatives and the Gradient Vector
14.7    Maximum and Minimum Values (Optional: Discovery Project “Quadratic Approximations and Critical Points”)
14.8    Lagrange Multipliers
Chapter 15: Multiple Integrals
15.1    Double Integrals over Rectangles
15.2    Double Integrals over General Regions
15.3    Double Integrals in Polar Coordinates
15.4    Applications of Double Integrals
15.5    Surface Area
15.6    Triple Integrals
15.7    Triple Integrals in Cylindrical Coordinates
15.8    Triple Integrals in Spherical Coordinates
15.9    Change of Variables in Multiple Integrals
Chapter 16: Vector Calculus
16.1    Vector Fields
16.2    Line Integrals
16.3    The Fundamental Theorem for Line Integrals
16.4    Green’s Theorem
16.5    Curl and Divergence
16.6    Parametric Surfaces and Their Areas
16.7    Surface Integrals
16.8    Stokes’ Theorem
16.9    The Divergence Theorem

MATH 263 Core Problems

James Stewart. Calculus: Early Transcendentals (WebAssign eBook) 8th edition. Cengage Learning

WebAssign is an online, interactive environment for teaching and learning.  Using WebAssign students will complete Core Homework Problems common to all sections; individual instructors may also assign additional homework.  WebAssign also provides access to the text as an e-book.  By department policy, homework will count at least 5% towards students' final course grade.  The ground rules provided by your instructor will have further details.

You may begin using WebAssign on the first day of class. In order to access WebAssign after the 14-day grace period, you must purchase an access code as detailed below. If you purchased an access code in MATH 161 or MATH 162 or MATH 263 for the Stewart text in a previous semester, do not purchase a new code as the code you previously purchased remains valid.

Instructions for students to obtain the e-book and to use WebAssign: Once your instructor has uploaded the class roster to WebAssign, your personal class page will be activated. You will access it with your Loyola ID and password as detailed below. (Note to returning students: there is a change from previous semesters... you no longer need a class key to use WebAssign.)

1. Go to www.webassign.net/luc/login.html (Note the change in URL from previous semesters.)
2. Use the LOG IN @ LOYOLA UNIVERSITY CHICAGO button in the center of the page. The LOG IN button in the upper right-hand corner should NOT be used.
3. Selecting the Loyola login button will bring you to a standard Loyola login page, where you will enter your Loyola ID and password.
4. Successful login should bring you to a WebAssign home screen from which you can access any of your courses having a WebAssign component.
5. Select the desired course. If you have not already registered an access code for the course, a notice will be displayed with three choices:
• Enter an access code (purchased at the Loyola Bookstore or from the Acadiem website),
• Purchase an access code (online from WebAssign), or
• Continue the free trial.
Select the appropriate choice to access the e-book and homework assignments.
6. If you purchased an access code for the Stewart text in a previous semester, you do not need to purchase another code.
7. If at any time you run into technical difficulty using WebAssign, you can contact WebAssign directly by email or phone.  Visit https://webassign.com/support/student-support/ to get started.

• For Windows users:
• Mozilla Firefox (version 38 or later)
• Internet Explorer/Microsoft Edge (version 11 or later)
• Google Chrome (version 44 or later)
• For Mac users:
• Mozilla Firefox (version 38 or later)
• Google Chrome (version 44 or later)
• Apple Safari (version 8 or later)
• For iPad users (iOS 8 or later):
• Apple Safari (version 8 or later)

As you work WebAssign problems, WebAssign will warn you if you need additional plug-ins.  If you run into issues with system requirements, go to http://www.webassign.net/manual/instructor_guide/c_a_system_requirements.htm or contact WebAssign technical support at https://webassign.com/support/student-support/.

The next few questions represent STAT 103 content, to be mirrored on other pages.

Chapter 1: Getting Started
1.1    What Is Statistics?
1.2    Random Samples
1.3    Introduction to Experimental Design
Chapter 2: Organizing Data
2.1    Frequency, Distributions, Histograms, and Related Topics
2.2    Bar Graphs, Circle Graphs, and Time-Series Graphs
Chapter 3: Averages and Variation
3.1    Measures of Central Tendency: Mode, Median, and Mean
3.2    Measures of Variation
3.3    Percentiles and Box-and-Whisker Plots
Chapter 4: Correlation and Regression
4.1    Scatter Diagrams and Linear Correlation
4.2    Linear Regression and the Coefficient of Determination
Chapter 5: Elementary Probability Theory
5.1    What is Probability?
5.2    Some Probability Rules-Compound Events
Chapter 6: The Binomial Probability Distribution and Related Topics
6.1    Introduction to Random Variables and Probability Distributions
6.2    Binomial Probabilities
6.3    Additional Properties of the Binomial Distribution
Chapter 7: Normal Curves and Sampling Distributions
7.1    Graphs of Normal Probability Distributions
7.2    Standard Units and Areas Under the Standard Normal Distribution
7.3    Areas Under Any Normal Curve
7.4    Sampling Distributions
7.5    The Central Limit Theorem
7.6    Normal Approximation to Binomial Distribution and to p-hat
Chapter 8: Estimation
8.1    Estimating μ When σ is Known
8.2    Estimating μ When σ is Unknown
8.3    Estimating p in the Binomial Distribution
Chapter 9: Hypothesis Testing
9.1    Introduction to Statistical Tests
9.2    Testing the Mean μ
9.3    Testing a Proportion p
10.1    Tests Involving Paired Differences (Dependent Samples)
10.2    Inferences about the Difference of Two Means μ12
10.3    Inferences about the Difference of Two Proportions p1-p2
Chapter 11: Optional: Additional Topics Using Inference
11.1    Optional: Chi-Square: Tests of Independence and a Homogeneity
11.2    Optional: Chi-Square: Goodness-of-Fit

C.H. Brase and C.P. Brase. Understanding Basic Statistics, 7th ed (WebAssign eBook). Cengage.

Instructions for students to obtain the e-book and to use WebAssign:Once your instructor has uploaded the class roster to WebAssign, your personal class page will be activated. You will access it with your Loyola ID and password as detailed below.

1.    Go to www.webassign.net/luc/login.html(Note the change in URL from previous semesters.)

2.    Use the LOG IN @ LOYOLA UNIVERSITY CHICAGObutton in the center of the page. The LOG IN button in the upper right-hand corner should NOTbe used.

3.    Selecting the Loyola login button will bring you to a standard Loyola login page, where you will enter your Loyola ID and password.

4.    Successful login should bring you to a WebAssign home screen from which you can access any of your courses having a WebAssign component.

5.    Select the desired course. If you have not already registered an access code for the course, a notice will be displayed with three choices:

o    Enter an access code (purchased at the Loyola Bookstore or from the Acadiem website),

o    Purchase an access code (online from WebAssign), or

o    Continue the free trial.

Select the appropriate choice to access the e-book and homework assignments.

6.    If you purchased an access code for the Larson text in a previous semester, you do not need to purchase another code.

7.    If at any time you run into technical difficulty using WebAssign, you can contact WebAssign directly by email or phone. Visit https://webassign.com/support/student-support/to get started.

Below are “core problems” that we expect students to be able to solve to ensure understanding of the material in the course syllabus. The WebAssign core homework problems are taken from Understanding Basic Statistics (7th ed.) by C.H. Brase and C.P. Brase (with the exception of three problems that written in italics in the table below).

Chapter 1. Getting Started
1.1 1, 3, 4, 8
1.2 2, 3, 8, 20
1.3 1, 7, 9, Review.7, Review 11
Chapter 2. Organizing Data
2.1 9, 10, 20, OpenStax2.79, 19
2.2 4, 5, 10, Review.5, Review.6, Q.LineGraph
Chapter 3. Averages and Variation
3.1 2, 16, 17, 18
3.2 1, 3, 4, 9, 10, 11, Q.Decision , Review.2, Review.3
3.3 1, 4, 11, Review.8
Chapter 4. Correlation and Regression
4.1 2, 3, 4, 5, 14, 16
4.2 1, 3, 5, 7
Chapter 5. Elementary Probability Theory
5.1 3, 4, 13, 17, 20, 23
5.2 1, 2, 11, 12, 13, 15, 16, 17, 21, 23, 30
Chapter 6. The Binomial Probability Distribution and Related Topics
6.1 1, 3, 10, 14, 16
6.2 2, 3, 7, 8, 15, 16, 19
6.3 1, 11, 17, 18
Chapter 7. Normal Curve and Sampling Distributions
7.1 2, 3, 4, 8, 9
7.2 9, 33, 34, 35, 37, 39, 42, 43, 47
7.3 6, 8, 12, 14, 15, 17, 19, 23, 25, 29
7.4 1, 3, 4, 5, 6, 9
7.5 2, 4, 7, 8, 9, 11, 12, 14, 15, 18
7.6 1, 6, 11
Chapter 8. Estimation
8.1 1, 2, 4, 5, 6, 9, 10, 15, 19
8.2 13, 15, 17, 19, 22
8.3 18, 19, 25
Chapter 9. Hypothesis Testing
9.1 1, 3, 4, 16, 20
9.2 15, 16, 18, 23, 26
9.3 1, 10, 11, 17
10.1 2, 10, 12
10.2 16, 20
10.3 8, 19, 21, 22

### Center for Tutoring and Academic Excellence

The Center for Tutoring & Academic Excellence offers free collaborative learning opportunities that include small group tutoring and tutor-led study halls to Loyola students. To learn more or request tutoring services, visit the Center for Tutoring & Academic Excellence online at http://www.luc.edu/tutoring.

### Loyola Math Club Tutoring

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

## 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.

### Installing Mathematica (free!)

Mathematica is a powerful computing environment that is designed for use in engineering, mathematics, finance, physics, chemistry, biology, and a wide range of other fields. Loyola students and faculty can download and install the latest copy of Mathematica for free. You must be logged on to Loyola VPN, and then visit the following ITS webpage, https://digitalmedia.luc.edu/News/NewsItem/View/4/mathematica-version-9-downloads-available.

### Wolfram Demonstrations Project

From the Wolfram Demonstrations Project.  ". . . the Wolfram Demonstrations Project is an open-code resource that uses dynamic computation to illuminate concepts in science, technology, mathematics, art, finance, and a remarkable range of other fields.

Its daily growing collection of interactive illustrations is created by Mathematica users from around the world who participate by contributing innovative Demonstrations."