Alejandro Ruiz

Carnegie Mellon University
Math Tutor

Biography

I am freshman studying Electrical and Computer Engineering. I completed BC calculus in high school and also completed Calc I and Calc II my freshman year of college. I posses a great amount of math knowledge and enjoy teaching to students!

Education

BS Electrical and Computer Engineering
Carnegie Mellon University

Educator Statistics

Numerade tutor for 7 years
68 Students Helped

Topics Covered

Mastering the Basics of Parametric Equations: A Comprehensive Guide
Polar Coordinates: Understanding the Basics and Applications
Mastering Quadratic Functions: Unlocking Their Power
Mastering Polynomials: Essential Tips and Tricks | [Brand Name]
Rational Functions: Understanding Their Properties and Applications
Differential Equations Made Simple: Expert Tips & Resources

Alejandro's Textbook Answer Videos

02:51
Calculus Early Transcendentals

Sketch the curve by using the parametric equations to plot points. Indicate with an arrow the direction in which the curve is traced as $t$ increases.
$x=5 \sin t, \quad y=t^{2}, \quad-\pi \leqslant t \leqslant \pi$

Chapter 10: Parametric Equations and Polar Coordinates
Section 1: Curves Defined by Parametric Equations
Alejandro Ruiz
01:00
Calculus Volume 2

For the following problems, use the direction field below from the differential equation $y^{\prime}=-2 y .$ Sketch the graph of the solution for the given initial conditions.
$$y(0)=0$$

Chapter 4: Introduction to Differential Equations
Section 2: Direction Fields and Numerical Methods
Alejandro Ruiz
01:09
Calculus Volume 2

For the following problems, use the direction field below from the differential equation $y^{\prime}=-2 y .$ Sketch the graph of the solution for the given initial conditions.
Are there any equilibria? What are their stabilities?

Chapter 4: Introduction to Differential Equations
Section 2: Direction Fields and Numerical Methods
Alejandro Ruiz
01:02
Calculus Volume 2

For the following problems, use the direction field below from the differential equation $y^{\prime}=y^{2}-2 y .$ Sketch the graph of the solution for the given initial conditions.
$$y(0)=1$$

Chapter 4: Introduction to Differential Equations
Section 2: Direction Fields and Numerical Methods
Alejandro Ruiz
00:30
Calculus Volume 2

For the following problems, use the direction field below from the differential equation $y^{\prime}=y^{2}-2 y .$ Sketch the graph of the solution for the given initial conditions.
Are there any equilibria? What are their stabilities?

Chapter 4: Introduction to Differential Equations
Section 2: Direction Fields and Numerical Methods
Alejandro Ruiz
00:49
Calculus Volume 2

Draw the direction field for the following differential equations, then solve the differential equation. Draw your solution on top of the direction field. Does your solution follow along the arrows on your direction field?
$$y^{\prime}=e^{t}$$

Chapter 4: Introduction to Differential Equations
Section 2: Direction Fields and Numerical Methods
Alejandro Ruiz
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