
MATH 234: Applied Engineering Math ISpring 2015, The Citadel  





Week  Date  Reading  Materials 
1  Wed 1/14  Review  Lecture 1: Calculus Review
Slides: Course Outline Paul's Notes: Differentiation Review Paul's Notes: Integration Review Patrick's Videos: usubstitution Examples Patrick's Videos: Integration by Parts Example 
Thur 1/15  1.11.3, 2.1  Lecture 2: Introduction to ODEs
Paul's Notes: Definitions Paul's Notes: Direction Fields 

Fri 1/16  1.11.3, 2.1  Lab 1: Introduction
to ODEs, Key
Prelab 1: Introduction to ODEs, Key 

2  Mon 1/19  NO CLASS  MLK Day  
Wed 1/21  2.2  Lecture 3: Separation of Variables
Paul's Notes: Separable Equations Patrick's Videos: Separable Differential Equations 

Thur 1/22  2.3  Lecture 4: The Integrating Factor Method
Paul's Notes: Linear Equations Patrick's Videos: First Order Linear DEs 

Fri 1/23  2.22.3  Lab 2: First Order ODEs,
Key
PreLab 2: First Order ODEs, Key 

3  Mon 1/26  2.5  Lecture 5: Solutions by Substitutions
Paul's Notes: Substitutions 
Wed 1/28  2.7  Lecture 6: Linear Models
Paul's Notes: Modeling with 1st Order DEs 

Thur 1/28  2.8  Lecture 7: Nonlinear Models
Paul's Notes: Equilibrium Solutions Patrick's Videos: The Logistic Equation Patrick's Videos: Logistic Population Growth Example 

Fri 1/30  2.52.8  Lab 3: Modeling with ODEs  
4  Mon 2/2  3.13.2  Lecture 8: Higher Order ODEs
Paul's Notes: Reduction of Order 
Wed 2/4  3.3  Lecture 9: Homogeneous Linear ODEs with Constant Coefficients
Paul's Notes: Basic Concepts Paul's Notes: Real & Distinct Roots Paul's Notes: Complex Roots Paul's Notes: Repeated Roots Patrick's Videos: 2nd Order Linear DEs 

Thur 2/5  3.4  Lecture 10: Undetermined Coefficients
Paul's Notes: Undetermined Coefficients 

Fri 2/6  3.13.4  Lab 4: 2nd Order ODEs  
5  Mon 2/9  3.5  Lecture 11: Variation of Parameters
Paul's Notes: Variation of Parameters 
Wed 2/11  3.6  Lecture 12: The CauchyEuler Equation  
Thur 2/12  3.8  Lecture 13: Initial Value Problems
Paul's Notes: Mechanical Vibrations 

Fri 2/13  3.53.8  Lab 5: Homogeneous + Particular Solutions  
6  Mon 2/16  4.1  Lecture 14: The Laplace Transform
Paul's Notes: Definition of Laplace Transform Patrick's Videos: Calculating a Laplace Transform 
Wed 2/18  4.1  Lecture 15: The Laplace Transform, Part 2
Paul's Notes: Laplace Transforms 

Thur 2/19  Exam 1: Chapter 13  
Fri 2/20  4.1  Lab 6: Forward Laplace Transforms  
7  Mon 2/23  4.2  Lecture 16: Partial Fractions Review
Paul's Notes: Partial Fractions 
Wed 2/25  4.2  Lecture 17: The Inverse Laplace Transform
Paul's Notes: Inverse Laplace Transforms Paul's Notes: Solving IVPs with Laplace Transforms 

Thur 2/26  4.4  Lecture 18: Convolutions & Translation Theorems
Paul's Notes: Convolution Integrals 

Fri 2/27  4.2, 4.4  Lab 7: Inverse Laplace Tranforms  
8  Mon 3/2  4.3  Lecture 19: The Unit Step Function
Paul's Notes: Step Functions Paul's Notes: IVPs with Step Functions 
Wed 3/4  4.5  Lecture 20: The Delta Function
Paul's Notes: Dirac Delta Function 

Thur 3/5  4.5  Lecture 21: Solving IVPs with Laplace Transforms  
Fri 3/6  4.3, 4.5  Lab 8: Initial Value Problems  
9  Mon 3/9  7.17.2  Lecture 22: Vectors
Paul's Notes: The 3D Coordinate System Paul's Notes: Vectors  The Basics Paul's Notes: Vector Arithmetic Patrick's Videos: Introduction to Vectors Patrick's Vidoes: Drawing Vectors 
Wed 3/11  7.37.4, 7.6  Lecture 23: Vector Operations
Paul's Notes: Dot Product Paul's Notes: Cross Product Patrick's Videos: The Cross Product 

Thur 3/12  Exam 2: Chapter 4  
Fri 3/13  7.17.4, 7.6  Lab 9: Fun with Vectors  
10  Mon 3/16  8.1  Lecture 24: Matrix Algebra
Patrick's Videos: Basic Matrix Operations Patrick's Videos: Multiplying Matrices Mathmeeting's Videos: Matrix Multiplication 
Wed 3/18  8.1  Lecture 25: Matrix Algebra, Part 2
Handout: Computational Linear Algebra Last day to withdraw with "W" 

Thur 3/19  8.6  Lecture 26: Determinants
Paul's Notes: Review  Matrices and Vectors Patrick's Videos: Finding Determinant of 3x3 Matrix 

Fri 3/20  8.18.3  Lab 10: Fun with Matrices  
SB  3/233/27  NO CLASS  Spring Break  
11  Mon 3/30  8.28.3  Lecture 27: GaussJordan Elimination
Paul's Notes: Augmented Matrices Paul's Notes: More on the Augmented Matrix Paul's Notes: Review  Systems of Equations 
Wed 4/1  8.28.3  Lecture 28: Systems of Linear Equations
Patrick's Videos: GaussJordan Elimination 

Thur 4/2  8.8  Lecture 29: The Inverse of a Matrix
Patrick's Videos: Finding Inverse of a 2x2 Matrix Patrick's Videos: Finding Inverse of a 3x3 Matrix 

Fri 4/3  8.6, 8.8  Lab 11: Solving Systems of Equations  
12  Mon 4/6  8.8  Lecture 30: Eigenvalues & Eigenvectors
Paul's Notes: Review  Eigenvalues & Eigenvectors 
Wed 4/8  8.8  Lecture 31: Complex Eigenvalues  
Thur 4/9  10.1  Lecture 32: Introduction to Systems of DEs  
Fri 4/10  8.8, 10.1  Lab 12: Fun with Eigenvalues  
13  Mon 4/13  10.2  Lecture 33: Systems with Real Eigenvalues
Paul's Notes: Phase Plane Paul's Notes: Repeated Eigenvalues 
Wed 4/15  10.2  Lecture 34: Systems with Complex Eigenvalues
Paul's Notes: Complex Eigenvalues 

Thur 4/16  10.4  Lecture 35: Nonhomogeneous Systems
Paul's Notes: Nonhomogeneous Systems 

Fri 4/17  10.2, 10.4  Lab 13: Solving Systems of ODEs  
14  Mon 4/20  10.4  Lecture 36: Applications of Systems 
Wed 4/22  10.4  Lecture 37: Applications of Systems, Part 2  
Thur 4/23  Exam 3: Chapter 78, 10  
Fri 4/24  10.4  Lab 14: Fun with Systems  
15  Mon 4/27  Review: Gym Battle  
F  Final Exam Friday 5/1, 1:004:00pm 