Math& 254 ~ Calculus IV  
 
 
 

Course Description
Topics include: Infinite series, sequences, convergent-divergent series, convergent tests, power series, Maclaurin and Taylor polynomials, vector calculus, Green's theorem, Stokes' theorem.

Pre-requisite
Math 153 with a grade of C or higher.

Mode of Delivery (Modes)
Lecture

Offered
Fall

Required for:


Course Content

Text: Calculus: Early Transcendentals, 5th Ed., Stewart, Cengage

13. Vector Functions
13.1 Vector Functions and Space Curves
13.2 Derivatives and Integrals of Vector Functions
13.3 Arc Length and Curvature

14. Partial Derivatives Functions of Several Variables
14.1 Limits and Continuity
14.2 Partial Derivatives
14.3 Tangent Planes and Differentials
14.4 The Chain Rule
14.5 Directional Derivatives and the Gradient Vector
14.6 Maximum and Minimum Values
14.7 Lagrange Multipliers

15. Multiple Integrals
15.1 Double Integrals Over Rectangles
15.2 Iterated Integrals
15.3 Double Integrals over General Regions
15.4 Double Integrals in Polar Coordinates
15.5 Surface Area
15.6 Triple Integrals
15.7 Triple Integrals in Cylindrical and Spherical Coordinates
15.8 Change of Variables in Multiple Integrals

16. Vector Calculus
16.1 Vector Fields
16.2 Line Integrals
16.3 The Fundamental Theorem for Line Integrals
16.4 Greens Theorem
16.5 Curl and Divergence
16.6 Parametric Surfaces and Their Areas
16.7 Surface Integrals
16.8 The Divergence Theorem