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

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Topics List:

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