<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>
Understanding Multivariable Calculus: Problems, Solutions, and Tips
Overview
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.
