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Understanding Multivariable Calculus: Problems, Solutions, and Tips

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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