Free Download Master Calculus with Ease Volume 3Published 1/2026
Created by Ethan Tsai (Ming-Yao Tsai)
MP4 |
Video: h264, 1920x1080 |
Audio: AAC, 44.1 KHz, 2 Ch
Level: Intermediate |
Genre: eLearning |
Language: English |
Duration: 50 Lectures ( 21h 38m ) |
Size: 39 GB
✓ Understand limits, continuity, and differentiability of multivariable functions with clear geometric intuition.
✓ Compute partial derivatives, directional derivatives, and tangent/normal equations for surfaces in space.
✓ Analyze and solve optimization problems of multivariable functions, including constrained extrema using rigorous methods.
✓ Master multiple integrals (double and triple integrals), including changing the order of integration and using polar, cylindrical, and spherical coordinates.
✓ Develop a solid understanding of line integrals, surface integrals, and their physical interpretations.
✓ Apply Green's Theorem, Stokes' Theorem, and Gauss' Theorem to convert between integrals and solve complex vector calculus problems.
Requirements● A solid understanding of single-variable calculus, including limits, derivatives, and basic integrals.
● Familiarity with fundamental concepts from Calculus I and II, such as the chain rule and definite integrals.
● Basic comfort with algebra and functions, including manipulating equations and interpreting graphs.
● No prior experience with multivariable calculus or vector calculus is required - all new concepts are developed carefully and step by step.
DescriptionThis course is designed to help you truly master Multivariable Calculus, not just memorize complex formulas. If you've ever felt that moving from 2D to 3D calculus feels "overwhelming" or that you struggle to visualize spatial problems, this course is for you. The key to mastering multivariable calculus is not spatial talent - it's a clear geometric method and a strong conceptual foundation. And that is exactly what we focus on here.
Rather than rushing through long computations and abstract theorems, you'll learn why the ideas in multivariable calculus work, how geometry translates into algebra, and how to apply these concepts to real-world dimensions. We move systematically through Vectors and 3D Space, Partial Derivatives, Multiple Integrals, and Vector Calculus (including Green's, Stokes', and Divergence Theorems), so every topic builds naturally on the previous one.
What makes this course different
• We focus on geometric intuition: We translate abstract algebraic rules into clear pictures you can visualize.
• We prioritize logic over rote memorization: You will understand the origin of formulas like the Gradient or Lagrange Multipliers, not just how to calculate them.
• We solve problems using structured thinking: You will learn a consistent step-by-step approach to handle complex 3D constraints.
• You'll develop the ability to reason, explain, and apply calculus confidently in higher dimensions.
This teaching framework has helped students from various backgrounds - including those who previously struggled with math - gain confidence and excel in their university mathematics studies.
By the end of this course, you will
• Master 3D Geometry: confidently handle Vectors, Lines, Planes, and Surfaces in space.
• Understand Partial Differentiation: including the Chain Rule, Gradient Vectors, and Optimization (Lagrange Multipliers).
• Conquer Multiple Integrals: skillfully set up and solve Double and Triple Integrals in Cartesian, Polar, Cylindrical, and Spherical coordinates.
• Grasp the Core of Vector Calculus: truly understand the physical meaning behind Vector Fields, Line Integrals, and Surface Integrals.
• Build a solid foundation for Engineering, Physics, and Data Science: ready for advanced fields that rely on multivariable analysis.
Whether you are a university student, preparing for STEM fields, or simply want to build real mathematical understanding, this course will help you learn multivariable calculus in a way that is clear, logical, and lasting.
Who this course is forâ University and college students taking their first calculus course.
â High school students preparing for AP Calculus or university-level math.
â Adults or professionals who want to rebuild a solid understanding of calculus.
â Anyone who struggled with calculus before and wants to finally understand it clearly.
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