MATH 234: Applied Engineering Math I

Spring 2016, The Citadel

SYLLABUS
SCHEDULE
HOMEWORK
EXAMS
GRADES

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: u-substitution Examples
Patrick's Videos: Integration by Parts Example
Thur 1/14 1.1-1.3, 2.1 Lecture 2: Introduction to ODEs
Paul's Notes: Definitions
Paul's Notes: Direction Fields
Fri 1/15 1.1-1.3 Lab 1: Introduction to ODEs, Key
Pre-Lab 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 2.2-2.3 Lab 2: First Order ODEs, Key
Pre-Lab 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 2.5-2.8 Lab 3: Modeling with ODEs, Key
Pre-Lab 3: Modeling with ODEs, Key
4 Mon 2/1 3.1-3.2 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 3.1-3.4 Lab 4: 2nd Order ODEs, Key
Pre-Lab 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 Cauchy-Euler Equation
Thur 2/11 3.8 Lecture 13: Initial Value Problems
Paul's Notes: Mechanical Vibrations
Fri 2/12 3.5-3.8 Lab 5: Homogeneous + Particular Solutions, Key
Pre-Lab 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 1-3
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
Pre-Lab 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
Pre-Lab 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
Pre-Lab 8: Initial Value Problems, Key
9 Mon 3/7 7.1-7.2 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 7.3-7.4 Lecture 23: Vector Operations
Paul's Notes: Dot Product
Paul's Notes: Cross Product
Patrick's Videos: The Cross Product
Fri 3/11 7.1-7.4 Lab 9: Fun with Vectors, Key
Pre-Lab 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 8.4-8.5 Lecture 26: Gauss-Jordan 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 8.2-8.3 Lecture 27: Systems of Linear Equations
Patrick's Videos: Gauss-Jordan Elimination
Wed 3/23 8.2-8.3 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 8.2-8.3, 8.6 Lab 11: Solving Systems of Equations, Key
Pre-Lab 11: Solving Systems of Equations, Key
SB 3/28-4/1 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 8.7-8.8 Lab 12: Fun with Eigenvalues, Key
Pre-Lab 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
Pre-Lab 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 7-8, 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
Pre-Lab 14: ODE Systems, Key
15 Mon 4/25 Review: Gym Battle
F Final Exam
Sec 3 (1:00pm lecture): Friday 4/29 1:00-4:00pm
Sec 4 (9:00am lecture): Thursday 4/28 1:00-4:00pm