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Business Calculus with Excel
Mike May, S.J., Anneke Bart
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Frontmatter
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Colophon
Acknowledgements
Preface
Notes for Instructors
Notes for Students
1
Functions Graphs and Excel
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1.1
Linear Functions and models
1.1.1
Equations of a line
1.1.2
Reading Check
1.1.3
Exercises 1.1 Linear Functions and models
1.2
Functions in the Business setting
1.2.1
Quadratic Functions
1.2.2
Exponential functions
1.2.3
Logistic Functions
1.2.4
Sinusoidal Functions
1.2.5
Normal Distribution Functions
1.2.6
Inversely Proportional Functions
1.2.7
Logarithmic Functions
1.2.8
Reading Check
1.2.9
Exercises Functions in the Business Setting
1.3
Introduction to Excel Spreadsheets
1.3.1
Basic Arithmetic, show formulas and quick fill.
1.3.2
Absolute and Relative Cell References
1.3.3
Named Cell References
1.3.4
Getting Help
1.3.5
Other Details
1.3.6
Reading Check
1.3.7
Exercises Introduction to Excel Spreadsheets
1.4
Graphing functions with Excel
1.4.1
A basic graph
1.4.2
A graph with parameters
1.4.3
Controlling the viewing window
1.4.4
Graphing more than one function
1.4.5
Formatting a chart
1.4.6
Online graphing tools: Wolfram Alpha
1.4.7
Reading Check
1.4.8
Exercises 1.4 Graphing functions with Excel
1.5
Using Excel to find best-fit curves
1.5.1
Using Excel to find a best-fit line
1.5.1.1
Find the line
1.5.1.2
Produce the equation of the line
1.5.1.3
Bring the equation of the line back to the chart
1.5.2
Checking and improving our equations
1.5.3
Fitting the Consumer Price Index (
CPI
) to a best fitting curve; an extended example
1.5.3.1
Number of significant digits for equation constants
1.5.3.2
Setting the base point of a variable
1.5.3.3
Selecting data for one model
1.5.4
Reading Check
1.5.5
Exercises: Using Excel to find best fit curves
1.6
Finding Numerical Solutions with Goal Seek
1.6.1
A linear example
1.6.2
A quadratic example and concern with precision
1.6.3
More realistic examples: finding the intersection of two curves
1.6.4
Using Goal Seek for financial computations
1.6.5
Looking under the hood and understanding Goal Seek’s limitations
1.6.6
Reading Check
1.6.7
Finding Numerical Solutions with Goal Seek
2
Business Applications
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2.1
Market Equilibrium Problems
2.1.1
Supply and Demand and Market Equilibrium
2.1.2
Reading Check
2.1.3
Exercises 2.1 Equilibrium Problems
2.2
Modeling Revenue, Costs, and Profit
2.2.1
Revenue and a review of demand price
2.2.2
Cost
2.2.3
Profit
2.2.4
Break-Even Point
2.2.5
Technical note
2.2.6
Reading Check
2.2.7
Exercises: Modeling Revenue, Costs, and Profit
2.3
Nonlinear Functions
2.3.1
Algebraic Functions
2.3.2
Discontinuous Functions
2.3.3
Reading Check
2.3.4
Exercises 2.3 Nonlinear functions
3
Rate of Change and Derivatives
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3.1
Marginal Functions and Difference Quotients
3.1.1
Marginal Functions
3.1.2
Difference Quotients and Average Rate of Change
3.1.3
An Excel Trick for Difference Quotients
3.1.4
Reading Check
3.1.5
Exercises: Marginal Functions and Difference Quotients Problems
3.2
Numeric Derivatives and Limits
3.2
Reading Check
3.2
Exercises: Numeric Derivatives and Limits
3.3
Local Linearity
3.3
Reading Check
3.3
Exercises: Local Linearity
3.4
Optimization
3.4
Reading Check
3.4
Exercises: Optimization
3.5
An Introduction to Solver
3.5
Reading Check
3.5
Exercises: An Introduction to Solver
4
Symbolic Differentiation
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4.1
Elementary Derivatives
4.1.1
Definition and Notation
4.1.2
Derivatives of monomials
4.1.3
Derivatives of Exponential Functions
4.1.4
Derivatives of Logarithmic Functions
4.1.5
Reading Check
4.1.6
Exercises: Elementary Derivatives Problems
4.2
Derivative Rules for Combinations of Functions
4.2.1
Derivatives of scalar products
4.2.2
Derivatives of sums and differences
4.2.3
Derivatives of products
4.2.4
Derivatives of quotients
4.2.5
Reading Check
4.2.6
Exercises: Derivative Rules for Combinations of Functions Problems
4.3
The Chain Rule
4.3
Reading Check
4.3
Exercises: The Chain Rule
4.4
Differentiation Using Computer Algebra
4.4
Reading Check
4.4
Exercises: Differentiation Using Computer Algebra Problems
4.5
The Second Derivative and Concavity
4.5
Reading Check
4.5
Exercises: The Second Derivative and Concavity Problems
5
Differentiation Techniques and Applications
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5.1
Implicit Differentiation
5.1
Reading Check
5.1
Exercises: Implicit Differentiation Problems
5.2
Related Rates
5.2
Reading Check
5.2
Exercises: Related Rates Problems
5.3
Elasticity
5.3.1
Point Elasticity
5.3.2
Arc Elasticity
5.3.3
Reading Check
5.3.4
Exercises: Elasticity Problems
6
Functions of Several Variables
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6.1
Evaluating and Graphing Functions of Several Variables
6.1
Reading Check
6.1
Exercises: Evaluating and Graphing Functions of Several Variables Problems
6.2
Wire Frames, Partial Derivatives, and Tangent Planes
6.2.1
Wire frames
6.2.2
Partial Derivatives
6.2.3
Tangent Planes and Linear Approximation
6.2.4
Reading Check
6.2.5
Exercises: Wire Frames, Partial Derivatives, and Tangent Planes Problems
6.3
Critical Points and Extrema
6.3.1
Critical Points
6.3.2
Second Partial Derivatives
6.3.3
Using the Discriminant to Test Critical Points
6.3.4
Reading Check
6.3.5
Exercises: Critical Points and Extrema Problems
6.4
Optimization and Best Fitting Curves
6.4
Reading Check
6.4
Exercises: Optimization and Best Fitting Curves Problems
7
Integration
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7.1
Approximating Definite Integrals as Sums
7.1
Reading Check
7.1
Exercises: Approximating Definite Integrals as Sums Problems
7.2
The Fundamental Theorem of Calculus
7.2
Reading Check
7.2
Exercises: The Fundamental Theorem of Calculus Problems
7.3
Basic Antidifferentiation
7.3
Reading Check
7.3
Exercises: Basic Antidifferentiation Problems
7.4
Integration by Change of Variables or Substitution
7.4.1
Change of variables for indefinite integrals
7.4.2
Change of variables for definite integrals
7.4.3
Reading Check
7.4.4
Exercises: Integration by Change of Variables or Substitution Problems
7.5
Integration using Computer Algebra
7.5.1
Definite integrals
7.5.2
Initial value problems
7.5.3
Riemann Sums
7.5.4
Reading Check
7.5.5
Exercises: Integration using Computer Algebra Problems
7.6
The Normal Distribution: An extended numeric example
7.6.1
Background from probability
7.6.2
Examples
7.6.3
Reading Check
7.6.4
Exercises: Normal Distribution Problems
7.7
Applications of the integral: Investment and depreciation
7.7.1
Basic Accumulation
7.7.2
Boundary value problems
7.7.3
Depreciation
7.7.4
Reading Check
7.7.5
Exercises: Applications of the integral: Investment and depreciation Problems
7.8
Economics Applications of the Integral
7.8.1
Consumer and Producer Surplus
7.8.2
Lorenz Curves and the Gini Index
7.8.3
Reading Check
7.8.4
Exercises Business Applications of the Integral Problems
Spreadsheet Appendices
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A
Spreadsheet Skills introduced in chapter 1
A.1
From Section 1-3 - Entering and Copying Formulas
A.2
From Section 1.4 Graphing Functions in a Spreadsheet
A.3
From Section 1.5 Adding and Using Best Fit Curves (Trendlines)
A.4
From Section 1.6 Using Goal Seek
A.5
Google Sheets Notes for Chapter 1 skills
B
Spreadsheet Skills Introduced in Chapter 2
C
Spreadsheet Skills introduced in chapter 3
C.1
From Section 3.1- Comparing Functions and Related Marginal Functions
C.1.1
Marginal Functions with
q
increasing by 1
C.1.2
Marginal Functions using Columns
C.1.3
Marginal Functions using Quick Fill
C.2
From Section 3.2- Comparing Functions and Numeric Derivatives
C.2.1
Derivatives from the Intuitive Approach
C.2.2
Derivatives from Numerical Limits
C.2.3
Graphing a Function with its Numeric Derivative
C.2.4
Using Trendline to find Derivative Formulas
C.3
From Section 3.3- Building Linear Approximations
C.4
From Section 3.5 - An introduction to Solver 3.5
C.5
Google Sheets Notes for Chapter 3 Skills
D
Spreadsheet Skills introduced in chapter 6
D.1
From Section 6.1 - Evaluating and graphing functions of several varaibles
D.1.1
Evaluating a function of several variables
D.1.2
Making a table for a function of 2 variable
D.1.3
Turning a table of a function of 2 variables into a surface graph
D.2
From Section 6.3 - Critical points and extrema
D.3
Google Sheets Notes for Chapter 6 Skills
E
Spreadsheet Skills introduced in chapter 7
Section
C.3
From Section 3.3- Building Linear Approximations
using skills from earlier sections, I compute
f
(
a
)
and
f
′
(
a
)
for a given function and value
a
> I then use the point-slope formula:
🔗
L
i
n
e
a
r
f
(
x
)
=
f
′
(
a
)
∗
(
x
−
a
)
+
f
(
a
)
🔗
A screencast of linear approximation of square roots 3.3.3
.
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of
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