Catalog Description:
Multivariable calculus treated in depth.

Prerequisite:
C or better in 1181H or 4181H.

Exclusions:
Not open to students with credit for both 162.01H and 263.01H

Text:
Calculus with Analytic Geometry, 2nd Edition, by George F. Simmons, published by McGraw-
Hill, ISBN: 0070576424


Topics List:

15.1; 15.2 Conic sections: Ellipse, Parabola, Hyperbola
15.3; 15.4 Conic sections: Ellipse, Parabola, Hyperbola

16.1 Polar coordinate system
16.2 Graphs of polar equations
16.3 Polar Equations of conics and spirals
16.3; 16.4 Polar Equations of conics and spirals; Arc length and tangent lines
16.5 Areas in polar coordinates

17.1 Parametric Equations of Curves
17.2 Cycloids and other similar Figures
17.3 Vector Algebra, the Unit Vectors i and j;
17.4 Derivatives of Vector Functions, Velocity and Acceleration
17.5 Curvature and the Unit Normal Vector
17.6 Tangential and Normal Components of Acceleration
17.7 Kepler's Laws and Newton's Law of Universal Gravitation

18.1 Coordinates and Vectors in 3-D Space
18.2 The Cross Product of Two Vectors
18.3 The Dot Product of Two Vectors
18.4 Lines and Planes
18.5 Cylinders and Surfaces of Revolution
18.6 Quadratic Surfaces;
18.7 Cylindrical and Spherical Coordinates

19.1 Function of Several Variables
19.2 Partial Derivatives
19.3 The Plane Tangent to a Surface
19.4 Increments and Differentials, the Fundamental Lemma
19.5 Directional Derivatives and the Gradient
19.6 The Chain Rule for Partial Derivatives
19.7; 19.8 Maximum and Minimum Problems
19.10 Implicit Functions

20.1 Volumes as Iterated Integrals
20.2 Double Integrals and Iterated Integrals
20.3 Physical Applications of Double Integrals
20.4 Double Integrals in Polar Coordinates
20.5 Triple Integrals
20.6 Cylindrical Coordinates
20.7 Spherical Coordinates, Gravitational Attraction
20.8 Area of Curved Surfaces

21.1 Line Integrals in the Plane
21.2 Independence of Path, Conservative Fields
21.3 Green's Theorem
21.4 Surface Integrals and Gauss' Theorem
21.5 Stokes' Theorem