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Understanding Multivariable Calculus: Problems, Solutions, and Tips

via The Great Courses Plus

Overview

<p>Gain a profound understanding of multivariable calculus with this excellent and clear guide that is useful for students, professionals, and lovers of mathematics.</p>

Syllabus

  • By This Professor
  • 01: A Visual Introduction to 3-D Calculus
  • 02: Functions of Several Variables
  • 03: Limits, Continuity, and Partial Derivatives
  • 04: Partial Derivatives-One Variable at a Time
  • 05: Total Differentials and Chain Rules
  • 06: Extrema of Functions of Two Variables
  • 07: Applications to Optimization Problems
  • 08: Linear Models and Least Squares Regression
  • 09: Vectors and the Dot Product in Space
  • 10: The Cross Product of Two Vectors in Space
  • 11: Lines and Planes in Space
  • 12: Curved Surfaces in Space
  • 13: Vector-Valued Functions in Space
  • 14: Kepler's Laws-The Calculus of Orbits
  • 15: Directional Derivatives and Gradients
  • 16: Tangent Planes and Normal Vectors to a Surface
  • 17: Lagrange Multipliers-Constrained Optimization
  • 18: Applications of Lagrange Multipliers
  • 19: Iterated integrals and Area in the Plane
  • 20: Double Integrals and Volume
  • 21: Double Integrals in Polar Coordinates
  • 22: Centers of Mass for Variable Density
  • 23: Surface Area of a Solid
  • 24: Triple Integrals and Applications
  • 25: Triple Integrals in Cylindrical Coordinates
  • 26: Triple Integrals in Spherical Coordinates
  • 27: Vector Fields-Velocity, Gravity, Electricity
  • 28: Curl, Divergence, Line Integrals
  • 29: More Line Integrals and Work by a Force Field
  • 30: Fundamental Theorem of Line Integrals
  • 31: Green's Theorem-Boundaries and Regions
  • 32: Applications of Green's Theorem
  • 33: Parametric Surfaces in Space
  • 34: Surface Integrals and Flux Integrals
  • 35: Divergence Theorem-Boundaries and Solids
  • 36: Stokes's Theorem and Maxwell's Equations

Taught by

Bruce H. Edwards, Ph.D.

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4.9 rating at The Great Courses Plus based on 59 ratings

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