MTHS 211: Advance Calculus I (English)

Categories: MTHS 211

About Course

Master the key concepts of multivariable calculus with clear, structured explanations and step-by-step problem-solving.

This course is designed for students who want to build a strong understanding of MTHS 211 / Analysis III, especially the topics that often feel abstract or difficult when first encountered.

Throughout the course, we work carefully through the main ideas of advanced calculus, including functions of several variables, limits and continuity, partial derivatives, tangent planes, linear approximations, directional derivatives, optimization, Lagrange multipliers, double integrals, polar coordinates, triple integrals, and coordinate transformations.

The goal is not only to help you get answers, but to help you understand why each method works and when to use it.

In this course, you will get access to:

✅ Clear video explanations
✅ Step-by-step examples
✅ Guidance on common test and exam-style questions
✅ Conceptual explanations to strengthen understanding
✅ Revision support for difficult topics
✅ Access to recordings that you can watch in your own time

This course is ideal for students who are currently taking MTHS 211 and want extra support, clearer explanations, and structured revision to prepare for tests and exams.

By the end of the course, you should feel more confident in approaching multivariable calculus problems and selecting the correct method for different types of questions.

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What Will You Learn?

  • Understand vectors and the geometry of space
  • Work with vector functions and space curves
  • Calculate and interpret partial derivatives
  • Use directional derivatives and the gradient vector
  • Find maximum and minimum values of functions of several variables
  • Apply Lagrange multipliers to constrained optimization problems
  • Evaluate double integrals over rectangular and general regions
  • Use polar coordinates in double integrals
  • Evaluate triple integrals
  • Use cylindrical and spherical coordinates
  • Approach test and exam-style problems with more confidence

Course Content

Chapter 12: Vectors and the Geometry of Space

  • 12.5: Equations of Lines and Planes
    01:17:20
  • 12.6: Cylinders and Quadratic Surfaces
    01:04:18
  • 12.5: Equations of Lines and Planes; 12.6: Cylinders and Quadratic Surfaces
    04:56:53

Chapter 13: Vector Functions

Chapter 14: Partial Derivatives

Chapter 15: Multiple Integrals

Semester Tests and Exam Preparation

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