
MATH 231: Calculus IIIFall 2015, The Citadel  





Week  Date  Reading  Materials 
1  Wed 8/26  Ch. 3, 7  Lecture 1: Calculus Review
Course Outline: Math 231 Outline Paul's Notes: Differentiation Review Paul's Notes: Integration Review Patrick's Videos: usubstitution Examples Patrick's Videos: Integration by Parts Example 
Fri 8/28  Ch. 3, 7 
Lab 1: Calculus Basics,
Key
PreLab 1: Calculus Basics, Key 

2  Mon 8/31  Sec 12.1 
Lecture 2: 3D Coordinates
Paul's Notes: The 3D Coordinate System 
Tue 9/1  Sec 12.2 
Lecture 3: Vectors
Paul's Notes: Vectors  The Basics Paul's Notes: Vector Arithmetic Patrick's Videos: Introduction to Vectors Patrick's Vidoes: Drawing Vectors 

Wed 9/2  Sec 12.3 
Lecture 4: The Dot Product
Paul's Notes: Dot Product Patrick's Videos: Vectors  The Dot Product 

Fri 9/4  Sec 12.112.3 
Lab 2: Fun with Vectors,
Key
PreLab 2: Fun with Vectors, Key 

3  Mon 9/7  Sec 12.4 
Lecture 5: The Cross Product
Paul's Notes: Cross Product Patrick's Videos: The Cross Product Patrick's Videos: Application to Torque 
Tue 9/8  Sec 12.5 
Lecture 6: Lines & Planes
Paul's Notes: Equations of Lines Paul's Notes: Equations of Planes Patrick's Videos: Finding Equation of a Plane Patrick's Videos: Finding Intersection of Line & Plane Patrick's Videos: Vector Equation of a Line 

Wed 9/9  Sec 12.6 
Lecture 7: Quadric Surfaces
Paul's Notes: Quadric Surfaces Mathispower's Videos: Intro to Quadric Surfaces 

Fri 9/11  Sec 12.412.6 
Lab 3: Objects in 3D,
Key
PreLab 3: Objects in 3D, Key 

4  Mon 9/14  Sec 13.1 
Lecture 8: Vector Functions
Paul's Notes: Vector Functions 
Tue 9/15  Sec 13.2 
Lecture 9: Calculus of Vector Functions
Paul's Notes: Calculus of Vector Functions Patrick's Videos: Limit of a Vector Function 

Wed 9/16  Sec 13.3 
Lecture 10: Arc Length & Curvature
Paul's Notes: Tangent Normal & Binormal Vectors Paul's Notes: Arc Length with Vector Functions Paul's Notes: Curvature Patrick's Videos: Arc Length with Parametric Curves 

Fri 9/18  Sec 13.113.3 
Lab 4: Fun with Vector Functions,
Key
PreLab 4: Fun with Vector Functions, Key 

5  Mon 9/21  Sec 14.1 
Lecture 11: Multivariable Functions
Paul's Notes: Functions of Several Variables 
Tue 9/22  Sec 14.2 
Lecture 12: Limits & Continuity
Review: Exam 1 Outline of Topics Paul's Notes: Limits 

Wed 9/23  Exam 1: Sec 12.112.5, 13.113.3  
Fri 9/25  Sec 14.114.2 
Lab 5: Intro to Multivariable Functions,
Key
PreLab 5: Intro to Multivariable Functions, Key 

6  Mon 9/28  Sec 14.3 
Lecture 13: Partial Derivatives
Paul's Notes: Partial Derivatives Patrick's Videos: Partial Derivatives Patrick's Videos: Higher Order Partial Derivatives 
Tue 9/29  Sec 14.4 
Lecture 14: Tangent Planes & Differentials
Paul's Notes: Tangent Planes 

Wed 9/30  Sec 14.5 
Lecture 15: The Chain Rule
Paul's Notes: Chain Rule Patrick's Videos: Generalized Chain Rule I Patrick's Videos: Generalized Chain Rule II 

Fri 10/2  Sec 14.314.5 
NO CLASS  Citadel closed for weather
Lab 6: CANCELED PreLab 6: Partial Derivatives, Key 

7  Mon 10/5  Sec 14.6 
NO CLASS  Citadel closed for weather
Lecture 16: CANCELED 
Tue 10/6  Sec 14.7 
Lecture 17: Directional Derivatives & Gradients
Paul's Notes: Directional Derivatives Patrick's Videos: Finding the Directional Derivative 

Wed 10/7  Sec 14.7 
Lecture 18: Max & Min Values
Paul's Notes: Relative Max & Min Patrick's Videos: Local Max & Min with 2 Variables I Patrick's Videos: Local Max & Min with 2 Variables II Paul's Notes: Absolute Max & Min 

Fri 10/9  NO CLASS  PARENTS' DAY  
8  Mon 10/12  Sec 15.115.2 
Lecture 19: Double Integrals over Rectangles
Paul's Notes: Double Integrals Paul's Notes: Iterated Integrals Patrick's Videos: Double Integral Example 
Tue 10/13  Sec 15.3 
Lecture 20: Double Integrals over General Regions
Paul's Notes: Double Integrals over General Regions Patrick's Videos: Double Integrals over General Regions 

Wed 10/14  Sec 15.3 
Lecture 21: Double Integrals
Patrick's Videos: Changing Order of Integration 

Fri 10/16  Sec 15.115.3  Lab 7: Double Integrals  
9  Mon 10/19  Sec 15.4 
Lecture 22: Polar Coordinates
Paul's Notes: Double Integrals in Polar Coordinates 
Tue 10/20  Sec 15.4 
Lecture 23: Double Integrals in Polar Coordinates
Patrick's Videos: Double Integral in Polar Coordinates 

Wed 10/21  NO CLASS  Leadership Day  
Fri 10/23  Sec 15.315.4  Lab 8: Polar Coordinates  
10  Mon 10/26  Sec 15.4  Lecture 24: Applications of Double Integrals 
Tue 10/27  Sec 15.5  Lecture 25: Applications of Double Integrals II  
Wed 10/28  Sec 15.6 
Lecture 26: Surface Area
Paul's Notes: Surface Area 

Fri 10/30  Sec 15.515.6  Lab 9: Applications of Double Integrals  
11  Mon 11/2  Sec 15.7 
Lecture 27: Triple Integrals
Paul's Notes: Triple Integrals Patrick's Videos: Evaluating a Triple Integral 
Tue 11/3  Sec 15.7  Lecture 28: Triple Integrals II  
Wed 11/4  Exam 2: Sec 14.114.7, 15.115.6  
Fri 11/6  Sec 15.7  Lab 10: Triple Integrals  
12  Mon 11/9  Sec 15.8 
Lecture 29: Cylindrical Coordinates
Paul's Notes: Cylindrical Coordinates 
Tue 11/10  Sec 15.9 
Lecture 30: Spherical Coordinates
Paul's Notes: Spherical Coordinates Patrick's Videos: Triple Integral in Spherical Coordinates 

Wed 11/11  Sec 15.9 
Lecture 31: Coordinate Transformations
Paul's Notes: Change of Variables Patrick's Videos: Jacobian 

Fri 11/13  Sec 15.815.9  Lab 11: Coordinate Systems  
13  Mon 11/16  Sec 16.1 
Lecture 32: Vector Fields
Paul's Notes: Vector Fields Patrick's Videos: Sketching Vector Fields Java Applet: Vector Field Analyzer 
Tue 11/17  Sec 16.2 
Lecture 33: Line Integrals
Paul's Notes: Line Integrals, Part I Patrick's Videos: Line Integral Along a Straight Line Patrick's Videos: Evaluating a Line Integral 

Wed 11/18  Sec 16.2 
Lecture 34: Line Integrals over Vector Fields
Paul's Notes: Line Integrals, Part II Paul's Notes: Line Integrals of Vector Fields 

Fri 11/20  Sec 16.116.2  Lab 11: Line Integrals  
FB  Mon 11/23  Fri 11/27  NO CLASS  Fall Break  
14  Mon 11/30  Sec 16.3 
Lecture 35: Conservative Vector Fields
Paul's Notes: Conservative Vector Fields Patrick's Videos: Potential of a Conservative Field 1 Patrick's Videos: Potential of a Conservative Field 2 
Tue 12/1  Sec 16.3 
Lecture 36: Fundamental Theorem of Line Integrals
Paul's Notes: Fundamental Theorem for Line Integrals Patrick's Videos: Fundamental Theorem for Line Integrals Patrick's Videos: Proving a Field is Conservative 

Wed 12/2  Exam 3: Chapter 15.715.9, 16.116.3  
Fri 12/4  Sec 16.3  Lab 13: Conservative Fields  
15  Mon 12/7  Sec 16.4 
Lecture 37: Green's Theorem
Paul's Notes: Green's Theorem Patrick's Videos: Green's Theorem 
Tue 12/8  Sec 16.4  Lecture 38: Green's Theorem II  
Wed 12/9  Ch. 1216  Lab 14: Green's Theorem  
F  Final Exam
Sec 1 (9:00am lecture): Friday 12/11 8:0011:00am Sec 2 (1:00pm lecture): Wednesday 12/16 8:0011:00am 