
MATH 234: Applied Engineering Math ISpring 2016, The Citadel  





Week  Date  Reading  Materials 
1  Wed 1/13  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 1/14  1.11.3, 2.1  Lecture 2: Introduction to ODEs
Paul's Notes: Definitions Paul's Notes: Direction Fields 

Fri 1/15  1.11.3  Lab 1: Introduction to ODEs,
Key
PreLab 1: Introduction to ODEs, Key 

2  Mon 1/18  NO CLASS  MLK Day  
Wed 1/20  2.2  Lecture 3: Separation of Variables
Paul's Notes: Separable Equations Patrick's Videos: Separable Differential Equations 

Thur 1/21  2.3  Lecture 4:
The Integrating Factor Method
Paul's Notes: Linear Equations Patrick's Videos: First Order Linear DEs 

Fri 1/22  2.22.3  Lab 2: First Order ODEs,
Key
PreLab 2: First Order ODEs, Key 

3  Mon 1/25  2.5  Lecture 5: Solutions by Substitutions
Paul's Notes: Substitutions 
Wed 1/27  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 1/29  2.52.8  Lab 3: Modeling with ODEs,
Key
PreLab 3: Modeling with ODEs, Key 

4  Mon 2/1  3.13.2  Lecture 8: Higher Order ODEs
Paul's Notes: Reduction of Order 
Wed 2/3  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 2/4  3.4  Lecture 10: Undetermined Coefficients
Paul's Notes: Undetermined Coefficients 

Fri 2/5  3.13.4  Lab 4: 2nd Order ODEs,
Key
PreLab 4: 2nd Order ODEs, Key 

5  Mon 2/8  3.5  Lecture 11: Variation of Parameters
Paul's Notes: Variation of Parameters 
Wed 2/10  3.6  Lecture 12: The CauchyEuler Equation  
Thur 2/11  3.8  Lecture 13: Initial Value Problems
Paul's Notes: Mechanical Vibrations 

Fri 2/12  3.53.8  Lab 5: Homogeneous + Particular Solutions,
Key
PreLab 5: Homogeneous + Particular Solutions, Key 

6  Mon 2/15  4.1  Lecture 14: The Laplace Transform
Paul's Notes: Definition of Laplace Transform Patrick's Videos: Calculating a Laplace Transform 
Wed 2/17  Exam 1: Chapter 13  
Thur 2/18  4.1  Lecture 15: The Laplace Transform, Part 2
Handout: Table of Laplace Transforms Paul's Notes: Laplace Transforms 

Fri 2/19  4.1  Lab 6: Laplace Transforms,
Key
PreLab 6: Laplace Transforms, Key 

7  Mon 2/22  4.2  Lecture 16: Partial Fractions Review
Paul's Notes: Partial Fractions 
Wed 2/24  4.2  Lecture 17: The Inverse Laplace Transform
Paul's Notes: Inverse Laplace Transforms Paul's Notes: Solving IVPs with Laplace Transforms 

Thur 2/25  4.4  Lecture 18: Properties of Laplace Transforms
Paul's Notes: Convolution Integrals 

Fri 2/26  4.2, 4.4  Lab 7: Inverse Laplace Tranforms,
Key
PreLab 7: Inverse Laplace Tranforms, Key 

8  Mon 2/29  4.3  Lecture 19: The Unit Step Function
Paul's Notes: Step Functions Paul's Notes: IVPs with Step Functions 
Wed 3/2  4.5  Lecture 20: The Unit Impulse Function
Paul's Notes: Dirac Delta Function 

Thur 3/3  4.5  Lecture 21: Solving IVPs with Laplace Transforms
Handout: Unit Step & Unit Impulse Functions 

Fri 3/4  4.3, 4.5  Lab 8: Initial Value Problems,
Key
PreLab 8: Initial Value Problems, Key 

9  Mon 3/7  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 3/9  Exam 2: Chapter 4  
Thur 3/10  7.37.4  Lecture 23: Vector Operations
Paul's Notes: Dot Product Paul's Notes: Cross Product Patrick's Videos: The Cross Product 

Fri 3/11  7.17.4  Lab 9: Fun with Vectors,
Key
PreLab 9: Fun with Vectors, Key 

10  Mon 3/14  8.1  Lecture 24: Matrix Arithmetic
Patrick's Videos: Basic Matrix Operations Patrick's Videos: Multiplying Matrices Mathmeeting's Videos: Matrix Multiplication 
Wed 3/16  8.1  Lecture 25: Matrix Arithmetic, Part 2
Handout: Computational Linear Algebra Last day to withdraw with "W" 

Thur 3/17  8.48.5  Lecture 26: GaussJordan Elimination
Paul's Notes: Augmented Matrices Paul's Notes: More on the Augmented Matrix Paul's Notes: Review  Systems of Equations 

Fri 3/18  NO CLASS  Leadership Day  
11  Mon 3/21  8.28.3  Lecture 27: Systems of Linear Equations
Patrick's Videos: GaussJordan Elimination 
Wed 3/23  8.28.3  Lecture 28: Determinants
Paul's Notes: Review  Matrices and Vectors Patrick's Videos: Finding Determinant of 3x3 Matrix 

Thur 3/24  8.6  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 3/25  8.28.3, 8.6  Lab 11: Solving Systems of Equations,
Key
PreLab 11: Solving Systems of Equations, Key 

SB  3/284/1  NO CLASS  Spring Break  
12  Mon 4/4  8.7  Lecture 30: Cramer's Rule
Patrick's Videos: Cramer's Rule to Solve a 3x3 System Patrick's Videos: Proof of Cramer's Rule for 2x2 Systems 
Wed 4/6  8.8  Lecture 31: Eigenvalues & Eigenvectors
Paul's Notes: Review  Eigenvalues & Eigenvectors Patrick's Videos: Finding Eigenvalues & Eigenvectors 

Thur 4/7  8.8  Lecture 32: Complex Eigenvalues  
Fri 4/8  8.78.8  Lab 12: Fun with Eigenvalues,
Key
PreLab 12: Fun with Eigenvalues, Key 

13  Mon 4/11  10.2  Lecture 33: DE Systems with Real Eigenvalues
Paul's Notes: Phase Plane Paul's Notes: Real Eigenvalues 
Wed 4/13  10.2  Lecture 34: DE Systems with Complex Eigenvalues
Paul's Notes: Complex Eigenvalues Paul's Notes: Repeated Eigenvalues 

Thur 4/14  10.4  Lecture 35: Nonhomogeneous DE Systems
Paul's Notes: Nonhomogeneous Systems 

Fri 4/15  10.2, 10.4  Lab 13: Solving Systems of ODEs,
Key
PreLab 13: Solving Systems of ODEs, Key 

14  Mon 4/18  10.4  Lecture 36: Applications of Systems of Equations 
Wed 4/20  Exam 3: Chapter 78, 10  
Thur 4/21  10.4  Lecture 37: Applications of DE Systems
Paul's Notes: Modeling with Systems 

Fri 4/22  10.4  Lab 14: ODE Systems,
Key
PreLab 14: ODE Systems, Key 

15  Mon 4/25  Review: Gym Battle  
F  Final Exam Sec 3 (1:00pm lecture): Friday 4/29 1:004:00pm Sec 4 (9:00am lecture): Thursday 4/28 1:004:00pm 