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.