Dr. Larry K. NorrisMA 242.003

www.math.ncsu.edu/~lkn

Spring Semester, 2013North Carolina State University

Grading

• 4 semester tests @ 15% = 60%• Maple Homework @ 10% = 10%• Final Exam @ 30%+ = 30%+

where + means that I will replace the lowest of the 4 tests with the final exam grade if it is higher.

Daily Schedule

1. Answer questions and work example problems from suggested homework (0-15 minutes)

2. Daily topics (35-50 minutes) --including example problems (you should study

to prepare for tests).

4 parts to the semester

Chapters:• 9 and 10: Review and curve analysis (Test #1)• 11: Differential multivariable calculus (Test #2)• 12: Integral multivariable calculus (Test #3)• 13: Vector calculus (Test #4)• Final Exam

Chapters 9: Review 3-D geometry

• Cartesian coordinates in 3 space

Chapters 9: Review 3-D geometry

• Vectors in 3 space

• The dot and cross products

Chapters 9: Review 3-D geometry

• Equations of lines and planes in space

Chapters 10: Curve analysis

• Vector-valued functions and parametric curves in 3-space

Chapters 10: Curve analysis

• Derivatives and integrals of vector-valued functions

Chapters 10: Curve analysis

• Curve analysis: curvature, unit tangent and unit normal, Theorem: the acceleration vector always lies in the osculating plane

Chapter 11: Differential multivariable calculus

Chapter 11

Chapter 11

Chapter 11: Partial Derivatives

Application of partial derivatives

OptimizationFind the local and global maxima and minima of

functions f(x,y) of 2 variables

Chapter 12:Integral Multivariable Calculus

Chapter 12:Integral Multivariable Calculus

Double Integrals in Cartesian coordinates

Double Integrals in Polar coordinates

Chapter 12:Integral Multivariable Calculus

Double Integrals in Polar coordinates

Chapter 12:Integral Multivariable Calculus

Triple Integrals in Cartesian coordinates

Chapter 12:Integral Multivariable Calculus

Triple Integrals in Cylindrical coordinates

Triple Integrals in Spherical coordinates

Chapter 13:Vector Calculus

Vector fields in space

Chapter 13:Vector Calculus

Chapter 13: Vector Calculus

Curl and Divergence

Chapter 13:Vector Calculus

• Stokes’ Theorem

• The Divergence Theorem of Gauss