Joel Mueller

Ohio University - Main Campus
Professor

Biography

Math is one of my favorite things and I strive to communicate a love for the subject when I teach.

Education

MS Mathematics
Ohio University - Main Campus
BS Mathematics
West Virginia University

Educator Statistics

Numerade tutor for 5 years
288 Students Helped

Topics Covered

Differential Equations Made Simple: Expert Tips & Resources
Discover the Best Series to Binge-Watch | Your Ultimate Guide
Mastering Partial Derivatives: Essential Techniques and Tips
Vector Functions: Understanding the Basics
Mastering Polynomials: Essential Tips and Tricks | [Brand Name]
Master Algebra Basics: Your Introduction to Algebra
Exploring the Functions of Multiple Variables
Mastering the Basics of Parametric Equations: A Comprehensive Guide
Polar Coordinates: Understanding the Basics and Applications
Master Vector Calculus with Our Comprehensive Guide
Unlock the Power of Vectors: Discover Their Limitless Possibilities

Joel's Textbook Answer Videos

12:31
Thomas Calculus

In Exercises $1-8,$ find the eccentricity of the ellipse. Then find andgraph the ellipse's foci and directrices.
$$16 x^{2}+25 y^{2}=400$$

Chapter 11: Parametric Equations and Polar Coordinates
Section 7: Conics in Polar Coordinates
Joel Mueller
03:08
Elementary Linear Algebra: Applications Version

A problem on a Babylonian tablet requires finding the length and width of a rectangle given that the length and the width add up to $10,$ while the length and one-fourth of the width add up to $7 .$ The solution provided on the tablet consists of the following four statements:
Multiply 7 by 4 to obtain 28 Take away 10 from 28 to obtain $18 .$ Take one-third of 18 to obtain $6,$ the length. Take away 6 from 10 to obtain $4,$ the width.
Explain how these steps lead to the answer.

Chapter 10: Applications of Linear Algebra
Section 2: The Earliest Applications of Linear Algebra
Joel Mueller
12:15
Thomas Calculus in SI Units

Which of the series, and which diverge? Use any method, and give reasons for your answers.
$$\sum_{n=1}^{\infty} \frac{\sqrt[n]{n}}{n^{2}}$$

Chapter 10: Infinite Sequences and Series
Section 4: Comparison Tests
Joel Mueller
15:00
Thomas Calculus in SI Units

Use the surface integral in Stokes' Theorem to calculate the flux of the curl of the field $\mathbf{F}$ across the surface $S$ in the direction of the outward unit normal $\mathbf{n}$. $$\begin{aligned}
&\mathbf{F}=(x-y) \mathbf{i}+(y-z) \mathbf{j}+(z-x) \mathbf{k}\\
&S: \quad \mathbf{r}(r, \theta)=(r \cos \theta) \mathbf{i}+(r \sin \theta) \mathbf{j}+(5-r) \mathbf{k}\\
&0 \leq r \leq 5, \quad 0 \leq \theta \leq 2 \pi
\end{aligned}$$

Chapter 16: Integrals and Vector Fields
Section 7: Stokes’ Theorem
Joel Mueller
10:24
Mathematical Methods in the Physical Sciences

Let $f(z)=u+i v$ be an analytic function, and let $\mathbf{F}$ be the vector $\mathbf{F}=v \mathbf{i}+u \mathbf{j}$. Show that the equations div $\mathbf{F}=0$ and $\operatorname{curl} \mathbf{F}=0$ are equivalent to the Cauchy-Riemann equations.

Chapter 14: Functions of a Complex Variable
Section 2: Analytic Functions
Joel Mueller
1 2

Joel's Quick Ask Videos

03:16
Algebra

For the complex exponential function f (z) = ez,
describe the image of the vertical line Re z = 2 and the image of
the horizontal line Im z = ∏/2.

Joel Mueller
07:19
Calculus 1 / AB

A company has a price-demand function given by p = -3√x + 60, where x is the number of items sold at a price of $p per item. The company also has a cost function given by C(x) = 90√x + 12x + 5000 dollars when x items are made. If P(x) represents the company's profit function, in dollars, when x items are made and sold, find P'(144). Interpret your answer.

Joel Mueller
03:58
Calculus 3

Concept 2: Volumes of Solids with Known Cross Sections 3.
The base of a solid is the region in the first quadrant bounded
by the line x = -2y + 6 and the coordinate axes. What is the
volume of the solid if every cross-section perpendicular to the
y-axis is a square.

Joel Mueller
08:19
Algebra

Use the Intermediate Value Theorem and Rolle's Theorem to show that there exists a unique solution to the equation x^3 + x^2 - 1 = 0 between x = 2/3 and x = 1.

Joel Mueller
08:06
Calculus 3

Determine how many distinct left cosets of H in U30 with
H = {1, 11}.
a. Find all distinct left cosets of H in U30.
b. Is the left coset equal to the right coset? Prove or disprove.
c. By Lagrange's theorem, the order of each subgroup is a divisor
of the order of the finite group. Construct a subgroup H with |H| =
4 of U30. Show using Cayley Table.

Joel Mueller
08:39
Calculus 3

During the midday at 2 pm, the temperature of the water that is left out on a table is 18°C. If the temperature of the surroundings is 35°C and the water's temperature heated up to 26°C at 2:25 pm, after how many minutes will the water's temperature be 32°C?

Joel Mueller
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