Vectors for Math and Calculus

Welcome to this thorough course on vectors for Math and Calculus.

Student Reviews:

"Detailed and clear explanations. Great use of diagrams. Lots of support material. Great Course. I highly recommend it." — Noris Isabel

"Simple and clear." — Karnik Vatsalya Ananta

You will master vectors by solving more than 162 practice problems and you will acquire the knowledge you need for more advanced courses in math, calculus, physics and other fields.

What makes this course really unique is:

- Engaging visuals: If you are a visual learner (like me. ) you will find the lectures very engaging. I’ve designed it to explain vectors for calculus with detailed and colorful slides, animations and diagrams.

- Mathematical Expressions Completely written in LaTeX: This course is completely written in LaTeX, a special software that interprets mathematical expressions and produces nice-looking equations and expressions. Say goodbye to writing with the cursor.

- PDF handouts: On each section you will find PDF handouts with the diagrams presented for you to download and read while you’re on the go. Vectors will always be right there with you.

- Hands-on practice: Each section has practice problems with their corresponding answers.

- Quizzes: Every section has quizzes to check your knowledge and to help you determine the areas you may need to practice a little bit more.

- Discussion Forums: You will have access 24/7 to the course discussion forums. You can ask any questions you may have and I will be very glad to help you.

Learn to love calculus,

Start mastering vectors for math, calculus and physics right now,

See you in class.

What's inside

Learning objectives

Perform operations with 2d and 3d vectors such as addition, subtraction, scalar multiplication, dot product, cross product.
Transform vectors from cartesian coordinates to polar coordinates and vice versa.
Calculate and identify the main properties and elements of vectors: components, magnitude, direction and sense.

Determine if vectors are orthogonal, linearly dependent or linear combinations of other vectors.
Find a unit vector from any vector.

Perform operations with 2d and 3d vectors such as addition, subtraction, scalar multiplication, dot product, cross product.
Transform vectors from cartesian coordinates to polar coordinates and vice versa.
Calculate and identify the main properties and elements of vectors: components, magnitude, direction and sense.
Determine if vectors are orthogonal, linearly dependent or linear combinations of other vectors.
Find a unit vector from any vector.

Syllabus

You will be introduced to the course and familiarize yourself with the platform.

Welcome | Introduce Yourself and Set Your Goals

You will learn:

How to use our virtual classroom.
How to access and navigate course content.
How to use the discussion forums and ask new questions.

After this lecture you will know the fundamental aspects of 2D vectors.

After this lecture you will be able to identify what the origin is and where it is located.

After this lecture you will know how to denote vectors using two types of notations.

After this lecture you will be able to identify vector components and what they represent graphically.

After this lecture you will be able to identify the three main properties of vectors: Magnitude, Direction and Sense.

After this lecture you will be able to determine if two vectors are equal based on three criteria.

Test your knowledge with this quiz.

After this lecture you will be able to identify and find the components of a vector that starts at the origin.

After this video you will be able to identify and find the components of a vector that doesn't start at the origin.

In this lecture you will practice how to find vector components.

After this lecture you will be able to add vectors graphically using two methods:

Connecting the ending point with the starting point
Parallelogram Law of Vector Addition.

After this lecture you will learn how to add vectors using their components.

After this lecture you will be able to identify the opposite vector of any vector both graphically and using components.

After this lecture you will be able to subtract vectors graphically and understand the concept of vector subtraction.

After this lecture you will be able to subtract vectors using their components.

In this lecture you will learn the main properties of vector addition and we will prove them graphically.

After this lecture you will be able to identify when a vector is in Polar coordinates and the elements needed to describe it.

In this lecture you will learn what it means to multiply a scalar by a vector and how to calculate it.

After this lecture you will know how vectors change when they are multiplied by numbers between 0 and 1 and negative numbers.

In this lecture you will learn the general properties of multiplying a scalar by a vector.

After this lecture you will be able to rewrite a vector expressed in Cartesian coordinates in Polar Coordinates.

After this lecture you will be able to rewrite a vector expressed in Polar coordinates in Cartesian Coordinates.

After this lecture you will know what the magnitude of a vector represents graphically.

In this lecture you will learn how to calculate the magnitude of a vector using a formula derived from the Pythagorean Theorem.

In this lecture you will learn what the direction of a vector is, how it is measured and two notations used to describe it.

After this lecture you will be able to find the direction of a vector located in the first quadrant using a formula.

In this lecture you will learn how to find the direction of vectors located in the 2nd, 3rd or 4th quadrants.

After this lecture you will be able to find the dot product of two vectors using their components.

In this lecture you will learn how to convert an angle from Degrees to Radians and from Radians to Degrees.

After this lecture you will know what the dot product is and how it is based on the orthogonal projection of a vector onto another.

After this lecture you will be able to determine when two vectors are orthogonal both graphically and using the dot product.

After this lecture you will be able to solve problems that combine all the previous operations you learned during the course.

After this lecture you will be able to identify if two vectors are linearly dependent both graphically and using systems of linear equations.

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Read about what's good

what should give you pause

and possible dealbreakers

Taught by Estefania Cassingena Navone, who are recognized for their work in math and calculus

Develops skills and knowledge that are core for trigonometry, physics, and higher math

Provides hands-on practice with 162 practice problems and quizzes

Involves engaging visuals and colorful slides, animations, and diagrams

Includes PDF handouts with easy access to material

Utilizes LaTeX software to present nice-looking equations and expressions

Reviews summary

Mastering vectors for calculus and physics

According to learners, this is a highly recommended course for anyone looking to master vectors for math, calculus, and physics. Students consistently praise the instructor's ability to explain complex concepts in a clear, concise, and structured manner. A standout feature is the extensive use of engaging visuals, including detailed animations and diagrams, which are particularly beneficial for visual learners and help to bring abstract ideas to life. The course provides an abundance of practice problems with solutions and helpful quizzes, ensuring a thorough understanding and building confidence. While some more experienced learners found the pace occasionally slow or desired deeper advanced applications, it is widely considered an excellent and complete foundation, especially for beginners. The professional LaTeX formatting and responsive instructor support also contribute to a strong learning experience.

High-quality LaTeX equations and helpful resources enhance the learning experience.

"The LaTeX equations look very professional."

"The LaTeX formatting for equations is a small but significant detail that makes the material so much easier to read and follow."

"The PDF handouts are a nice touch for quick review."

"The instructor is very responsive in the discussion forums."

Extensive practice and quizzes reinforce understanding and build confidence.

"I especially appreciated the numerous practice problems with detailed solutions. It's great for solidifying understanding and building confidence."

"The practice problems are well-chosen and essential. This course helped me bridge gaps in my understanding..."

"The quizzes after each section were helpful to check my progress. This course has greatly improved my understanding of vectors."

"The sheer volume of practice problems with solutions ensures thorough understanding. A must-take for students."

Diagrams and animations greatly enhance learning for visual learners.

"The use of animations and diagrams is super helpful for visual learners like myself."

"The visual aids truly make a difference. This one's approach to breaking down topics with clear diagrams and animations is unparalleled."

"Excellent course! I particularly enjoyed the visual explanations and the step-by-step approach to solving problems."

"The visual explanations, especially the animated diagrams, are incredibly effective."

Complex topics are broken down and made easy to understand.

"The instructor explains complex concepts in a very clear and concise manner, making it easy to understand."

"A gem of a course! The explanations are so clear, and the visual aids truly make a difference."

"The material is presented in a very structured and logical way. I particularly enjoyed the visual explanations..."

"I struggled with vectors in college, but this course finally made sense of it all. The teaching style is incredibly patient and thorough."

Excellent for beginners, but pace can be slow for those with prior knowledge.

"Sometimes I wished for a bit more advanced application examples or perhaps a slightly faster pace in some sections, as I already had some prior knowledge."

"For a complete beginner, it's excellent. A more experienced learner might find some parts a bit slow."

"The course covers the basics of vectors, but I felt some explanations could have been more concise. The pace was a bit slow for me..."

"It's a decent starting point, but perhaps not for those seeking advanced insights."

Activities

Be better prepared before your course. Deepen your understanding during and after it. Supplement your coursework and achieve mastery of the topics covered in Vectors for Math and Calculus: A Complete & Practical Course with these activities:

Review Cartesian Coordinates

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Refresh your knowledge of Cartesian Coordinates. Reviewing Cartesian Coordinates will help you better understand the material covered in this course.

Browse courses on Coordinate Systems

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Review your notes on Cartesian Coordinates.
Take a practice quiz on Cartesian Coordinates.

Visualizing Vectors in Polar Coordinates

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Understand Polar Coordinates of Vectors by watching a guided videos. Watching a guided video tutorial on how to visualize vectors in Polar Coordinates is a great way to improve your understanding of the material.

Browse courses on Polar Coordinates

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Find a guided video tutorial on how to visualize vectors in Polar Coordinates.
Watch the video tutorial and take notes.
Try to visualize vectors in Polar Coordinates on your own.

Vector Problem-Solving Workshop

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Gain problem-solving techniques by participating in Vector Problem-Solving Workshop. Working with other students on a Vector Problem-Solving Workshop will enhance your understanding of the material.

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Find a group of students to work with.
Choose a vector problem to work on.
Work together to solve the problem.

One other activity

Expand to see all activities and additional details

Show all four activities

Vector Calculation Practice Problems

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Obtain more Vector Calculation Practice. Solving Vector Calculation Practice Problems will improve your skill and knowledge.

Browse courses on Vector Math

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Identify the type of Vector Calculation problem you need to solve.
Gather the necessary information from the problem.
Apply the appropriate formulas and techniques to solve the problem.
Check your answer to ensure it is correct.

Career center

Learners who complete Vectors for Math and Calculus: A Complete & Practical Course will develop knowledge and skills that may be useful to these careers: