Calculus 3 with the Math Sorcerer
Learn Calculus 3 with the Math Sorcerer:)
What you will learn
Understand Vectors in the Plane
Understand the Three Dimensional Coordinate System
How to Plot Points in Three Dimensions
Find the Magnitude of Vectors in Two Dimensions and Three Dimensions
How to Find the Vector Given the Initial and Terminal Points
How to Sketch a Vector in Standard Position
Understand what a Unit Vector Actually Is
How to Find a Unit Vector in the Direction of Another Vector
How to Construct a Vector with a Given Magnitude in the Direction of Another Vector
How to Find the Terminal Point of a Vector Given the Vector and its Initial Point
How to Find a Unit Vector in the Direction Opposite of a Vector
How to Compute the Dot Product
How to Determine if Vectors are Orthogonal
How to Find the Angle Between Two Vectors
How to Compute the Dot Product Given the Magnitudes of Vectors and the Angle Between Them
How to Find Two Vectors in Opposite Directions Orthogonal to a Given Vector
Understand What Direction Cosines and Direction Angles Are
How to Derive the Formulas for Direction Cosines and Direction Angles
How to Find Direction Cosines
How to Find Direction Angles
How to Find the Cross Product
How to Find a Unit Vector Orthogonal to Two Vectors
How to Find the Distance Between Two Points in Space
How to Find the Equation of a Sphere Given the Center and Radius
How to Find the Equation of a Sphere Given the Endpoints of the Diameter
How to Write the Equation of the Sphere in Standard Form by Completing the Square and Find the Center and Radius
How to Derive the Formulas for the Parametric and Symmetric Equations of a Line in Space
How to Find the Equation of a Line in Space Given a Point and a Parallel Vector
How to Find the Equation of a Line in Space Passing through Two Points
How to Find the Equation of a Line in Space Given a Point and a Parallel Line
How to Find the Equation of the Plane Given a Point and a Normal Vector
How to Find the Equation of a Plane Given Three Points
How to Find the Equation of the Plane that is Parallel to the z-axis Given Two Points
How to Find the Equation of a Plane Given a Point and a Line on the Plane
How to Find the Equation of a Plane Given Two Points and a Perpendicular Plane
Understand Cylindrical Coordinates and Why they Are Useful
How to Convert from Cylindrical Coordinates to Rectangular Coordinates
How to Convert from Rectangular Coordinates to Cylindrical Coordinates
How to Convert Rectangular Equations to Cylindrical Equations
How to Convert Cylindrical Equations to Rectangular Equations
Understand Spherical Coordinates
How to Convert Spherical Coordinates to Rectangular Coordinates
How to Convert Rectangular Coordinates to Spherical Coordinates
How to Convert Spherical Equations to Rectangular Equations
How to Convert Rectangular Equations to Spherical Equations
Understand Vector-Valued Functions
How to Graph a Vector-Valued Function, Find the Orientation of the Graph, and Write it in Rectangular Form
How to Represent Plane Curves as Vector-Valued Functions
How to Represent Any Circle as a Vector-Valued Function
How to Represent Any Ellipse as a Vector-Valued Function
How to Represent Any Hyperbola as a Vector-Valued Function
How to Evaluate Limits involving Vector-Valued Functions
How to Determine the Intervals on which a Vector-Valued Function is Continuous
How to Find the Derivative of a Vector-Valued Function
How to Find the Second Derivative of a Vector-Valued Function
How to Find the Intervals where a Vector-Valued Function is Smooth
How to Solve Differential Equations with Vector-Valued Functions
How to Evaluate Indefinite Integrals with Vector-Valued Functions
How to Evaluate Definite Integrals with Vector-Valued Functions
How to Find the Velocity, Speed, and Acceleration Given a Position Function as a Vector-Valued Function
How to Find the Position Function Given the Velocity and Acceleration
Understand the Unit Tangent Vector
How to Compute the Unit Tangent Vector
How to Find the Equation of a Tangent Line in Space
Understand the Principal Unit Normal Vector
How to Find the Principal Unit Normal Vector
Understand Arc Length
Understand the Arc Length Function
How to Compute Arc Length
Understand Curvature
Understand the Curvature of a Circle Intuitively
How to Compute the Curvature of a Circle
How to Compute Curvature using Various Formulas
Understand Functions of Several Variables
How to Evaluate Functions of Several Variables
How to Find the Domain and Range of Functions of Several Variables
How to Find the Level Curves of a Function
How to Find Limits for Functions of Several Variables
How to Show a Multivariate Limit Does Not Exist
How to Use Polar Coordinates to Evaluate Limits for Functions of Several Variables
Understand Partial Derivatives
How to Compute Partial Derivatives
Understand the Notation for Higher Order Partial Derivatives
How to Compute Higher Order Partial Derivatives
How to Show a Function Satisfies Laplace's Equation
How to Show a Function Satisfies the Heat Equation
How to Show a Function Satisfies the Wave Equation
How to Show a Function Satisfies the Cauchy Riemann Equations
How to Compute the Total Differential
How to Use the Total Differential To Approximate a Function of Several Variables
Understand the Chain Rule for One Independent Variable
How to use the Chain Rule to Find the Derivative in the One Independent Variable Case
Understand the Chain rule for Two Independent Variables
How to use the Chain Rule to Find the Derivative in the Two Independent Variable Case
How to Find dy/dx using Calculus 3 Methods
How to Differentiate Multivariable Functions Implicity
Understand Directional Derivatives
How to Compute Directional Derivatives
Understand the Gradient
How to Compute the Gradient
How to Find the Maximum Value of the Directional Derivative
How to Find a Unit Normal Vector Given a Surface
Understand Tangent Planes and Normal Lines
How to Find the Equation of a Tangent Plane and the Equation of the Normal Line
How to use the Second Partials Test to Find Relative Extrema and Saddle Points
How to Find the Minimum Distance from a Point to a Plane
How to use Lagrange Multipliers to Find Relative Extrema
How to use Lagrange Multipliers in the Case with Two Constraints
How to Integrate Multivariable Functions with respect to One Variable
Understand Iterated Integrals
How to Evaluate Iterated Integrals
How to Switch the Order of Integration in Iterated Integrals
Understand Double Integrals
How to Write Both Orders of Integration in Double Integrals
Understand Triple Integrals
How to Evaluate Triple Integrals
Understand Vector Fields
How to Determine if a Vector Field is Conservative
How to Find the Potential Function for a Conservative Vector Field
How to Compute the Divergence of a Vector Field
How to Compute the Curl of a Vector Field
How to Evaluate a Line Integral
How to Evaluate the Line Integral of a Vector Field
How to Evaluate a Line Integral in Differential Form
How to Compute the Work Done by a Force Field
Understand Projections
How to find the Projection of u onto v
How to find the Vector Component of u along v
Why take this course?
🚀 Dive into the World of Calculus 3 with the Math Sorcerer! 🧙♂️
Course Overview: Get ready to unlock the secrets of Calculus 3 with the guidance of the Math Sorcerer, your friendly and expert guide through this enchanting realm of mathematics. This comprehensive online course is packed with hundreds of videos designed to make learning calculus as enjoyable and interactive as possible. Whether you're a beginner or someone who's brushed up on Calculus 1 and perhaps skimmed through Calculus 2, this course is for you!
Why Take This Course?
- Accessible Learning: With a focus on short, digestible videos, you can learn math at your own pace. Spend as little or as much time as you like each day—even just one video can make a significant difference in your understanding.
- Interactive Approach: Follow along with the Sorcerer using your pencil and paper, take detailed notes, and tackle problems before he does. This hands-on approach ensures you're actively engaged in the learning process.
- Enjoyable Experience: Calculus 3 is not just about formulas and functions; it's about exploring the beauty of mathematics. The Math Sorcerer aims to make your journey through calculus as exciting and rewarding as possible.
Course Highlights:
- Engaging Videos: Each video is a carefully crafted lesson, designed to build your knowledge step by step. You'll cover topics such as sequences and series, multivariable calculus, and partial differential equations.
- Real-World Applications: Discover how the concepts you learn can be applied in real life scenarios, from physics to engineering and beyond.
- Supportive Learning Environment: With a community of fellow learners and the Math Sorcerer's expert guidance, you'll never feel lost or overwhelmed.
- Flexible Schedule: Learn at your own pace. Whether it's one video a day or a marathon session, this course adapts to your lifestyle.
What You'll Learn:
- Sequences and Series: Master the art of understanding infinite sequences, series, convergence, and divergence.
- Multivariable Calculus: Explore functions of several variables, partial derivatives, multiple integrals, and surface area and volume computations.
- Partial Differential Equations (PDEs): Tackle the fundamentals of PDEs, their types, and how to solve them using various methods.
Join the Adventure: With the Math Sorcerer as your mentor, you'll embark on a journey through the mystical land of Calculus 3. Whether it's for academic advancement, professional development, or personal enrichment, this course is your gateway to mastering one of mathematics' most profound subjects.
📚 Enroll Now and let the Math Sorcerer guide you through an unforgettable calculus adventure! ✨
Key Takeaways:
- Hundreds of Short Videos: Learn at your own pace with bite-sized lessons.
- Interactive Learning: Engage with the material by solving problems first.
- Real-World Application: Apply calculus concepts to practical scenarios.
- Supportive Community: Get help and encouragement from fellow learners and the Math Sorcerer.
- Flexible Schedule: Learn when it suits you best, without the pressure of rigid timetables.
Ready to Master Calculus 3? 🎩 Let's cast that spell together! Enroll in this course today and transform your approach to mathematics forever.
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Our review
🌟 Course Review Summary: 🌟
Overall Rating: 4.77/5
Pros:
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Excellent Teaching Approach: Math Scorcher's approach to teaching mathematics is highly praised, with particular emphasis on his ability to explain complex ideas in an accessible manner.
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Comprehensive Explanations: The course breaks down mathematical concepts thoroughly, providing step-by-step explanations that are especially beneficial for students preparing for college-level math courses.
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Practical Demonstrations: The instructor's method of working through examples for each definition is considered very applicable and practical, which is appreciated by students who aim to understand the material in a university context.
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Concept Emphasis: The instructor does an excellent job of explaining the need-to-know concepts and emphasizing those that will be important later in the course, enhancing the learning experience.
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Engaging Content: Math Scorcher's ability to follow and explain concepts in an easy-to-understand manner makes him an engaging and effective instructor.
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Great for Introduction: The course is ideal for students looking to introduce themselves to the subject matter before diving deeper into textbooks or more comprehensive learning materials.
Cons:
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Content Coverage: While the content provided in the course is generally aligned with recent reviews, a few students have mentioned that it stops a bit early compared to their college course material, suggesting that the course may not cover every topic required for some academic courses.
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Practice Oriented: The course is heavily oriented towards practice, which is great for learning but might require supplemental resources if a more theoretical approach is needed.
Additional Notes:
- YouTube Channel Recommendation: The student who recommended this course also pointed out that Math Scorcher's YouTube channel is a valuable resource, suggesting that students might benefit from checking it out as an additional learning tool.
In conclusion, the online course "Math Scorchers Approach to Mathematics" is highly recommended by recent reviewers for its clear and practical teaching style, thorough explanations, and emphasis on foundational concepts that are crucial for understanding higher-level mathematics. While it may not cover the entire curriculum of some college courses, the content provided is solid and beneficial for students preparing for Calculus or similar advanced math subjects. It's a great starting point and can be supplemented with other resources as needed.