Prof. Arun Sharma‘s ****Course Notes:

MATH53_NOTE_MultivariableCalculus.pdf

Contents

10. Parametric Equations and Polar Coordinates

• 10.1 Curves Defined by Parametric Equations
• 10.2 Calculus with Parametric Curves
• 10.3 Polar Coordinates
• 10.4 Areas and Lengths in Polar Coordinates

12. Vectors and the Geometry of Space $\mathbb{R}→\mathbb{R}^n$

• 12.1 Three-Dimensional Coordinate Systems
• 12.2 Vectors
• 12.3 The Dot Product
• 12.4 The Cross Product
• 12.5 Equations of Lines and Planes

13. Vector Functions

• 13.1 Vector Functions and Space Curve
• 13.2 Derivatives and Integrals of Vector Functions
• 13.4 Motion in Space: Velocity and Acceleration

14. Partial Derivatives $\mathbb{R}^m→\mathbb{R}$