﻿ MAT2705 syllabus

## MAT2705 Differential Equations with Linear Algebra

Elementary use of MAPLE is a required supporting tool in the entire MAT1500-1505-2500-2705 sequence of Calculus and Differential Equations with Linear Algebra for Science and Engineering majors. For use in this course, see below.

Equations and Linear Algebra [first 7 chapters]
Edwards, Penney, Calvis (Pearson) current edition e-text with MyLab Math:
Textbook web page (click here)

Access to the e-textbook with MyLab Math portal for enhanced textbook features,  online homework and interactive student help can be purchased directly from the publisher (\$69.99) or through the Villanova University Shop, with a 2 week grace period following registration.

Textbook coverage: Chapters 1-7.
The following core sections are recommended; optional sections are indicated with the square bracket notation [...],
omitted sections with double square bracket notation [[..]] :

1. First-Order Differential Equations.
1.1: Differential Equations and Mathematical Models.
1.2: Integrals as General and Particular Solutions.
1.3: Slope Fields and Solution Curves.
1.4: Separable Equations and Applications.
1.5: Linear First-Order Equations.
1.6: [[Substitution Methods and Exact Equations.]]

2. Mathematical Models and Numerical Methods.
2.1: Population Models.
2.2: [[Equilibrium Solutions and Stability.]]
2.3: [Acceleration-Velocity Models.]
2.4: [Numerical Approximation: Euler's Method.]
2.5: [[A Closer Look at the Euler Method.]]
2.6: [[The Runge-Kutta Method.]]

3. Linear Systems and Matrices.
3.1: Introduction to Linear Systems.
3.2: Matrices and Gaussian Elimination.
3.3: Reduced Row-Echelon Matrices.
3.4: Matrix Operations.
3.5: Inverses of Matrices.
3.6: Determinants. (emphasis on row operation evaluation;
Cramer's rule and adjoint formula for inverse can be omitted after mentioning)
3.7: [Linear Equations and Curve Fitting.]

4. Vector Spaces.
4.1: The Vector Space R^3.
4.2: The Vector Space R^n and Subspaces.
4.3: Linear Combinations and Independence of Vectors.
4.4: Bases and Dimension for Vector Spaces.
4.5: [[Row and Column Spaces]]
4.6: [[Orthogonal Vectors in R^n.]]
4.7: [General Vector Spaces.]

5. Linear Equations of Higher Order.
5.1: Introduction: Second-Order Linear Equations.
5.2: General Solutions of Linear Equations. (de-emphasize n>2)
5.3: Homogeneous Equations with Constant Coefficients.
5.4: Mechanical Vibrations.
5.5: Nonhomogeneous Equations and Undetermined Coefficients.
(de-emphasize most general case) [[omit variation of parameters]]
5.6: Forced Oscillations and Resonance. (pick carefully from too much material here)

6. Eigenvalues and Eigenvectors.
6.1: Introduction to Eigenvalues.
6.2: Diagonalization of Matrices.
6.3: [Applications Involving Powers of Matrices.]

7. Linear Systems of Differential Equations.
7.1: First-Order Systems and Applications.
7.2: Matrices and Linear Systems.
7.3: The Eigenvalue Method for Linear Systems.
7.4 A Gallery of Solution Curves of Linear Systems
7.5: Second-Order Systems and Mechanical Applications.
7.6: Multiple Eigenvalue Solutions. (non-defective matrices only)
7.6: [[Numerical Methods for Systems.]]

Exercise problem numbering is the same for editions 2-4. Edition text differences are not very significant.