Stewart 5^th Edition

MATH-263

Calculus 4

Section Topic Days

Vector Functions

14.1 Vector functions and space curves 3

(with dot and cross products of vectors)

14.2 Derivatives and Integrals of Vector Functions 1

14.3 Arclength and curvature 1

14.4 Motion in space: Velocity and Acceleration 1

Partial Derivatives

15.1 Functions of several variables 1

15.3 Partial derivatives 1.5

15.4 Tangent planes and Linear Approximation 1.5

15.5 The chain rule 1

15.6 Directional derivatives and gradient 1.5

15.7 Maximum and minimum values 1.5

15.8 Lagrange multipliers (optional) 1

Multiple Integrals

16.1 Double integrals over rectangles 0.5

16.2 Iterated integrals 1.5

16.3 Double integrals over general regions 1

16.4 Double integrals in polar coordinates 1

16.7 Triple integrals 1

16.8 Triple integrals in cylindrical and spherical 1

coordinates

16.9 Change of variable in multiple integrals (optional) 1

Vector Calculus

17.1 Vector fields 1

17.2 Line integrals 1.5

17.3 The Fundamental Theorem for line integrals 1.5

17.4 Green’s Theorem 2

17.5 Curl and Divergence 2

17.6 Parametric surfaces (to be merged in 17.7)

17.7 Surface integrals 2

17.8 Stokes’ Theorem 1.5

17.9 The Divergence Theorem 1.5

About 35 hours. About 5 hours for examinations and review.

Notes.

This course is aimed towards the Green, Stokes and Divergence theorems and should be organized correspondingly. The students have to be advised that the course is fast paced, and requires intensive work and full cooperation.

The instructor should focus on the main topics and avoid small details, deviations and time consuming computations.

Maple V can be used for graphing vector functions, surfaces and for the illustration of max/min points and tangent planes.

The main theorems should be accompanied by short proofs, avoiding long formal details and using more geometrical intuition.