# Differential Equations and Linear Algebra 3rd edition

Stephen Goode and Scott Annin
Publisher: Pearson Education

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• Chapter 1: First-Order Differential Equations
• 1.1: How Differential Equations Arise (6)
• 1.2: Basic Ideas and Terminology (3)
• 1.3: The Geometry of First-Order Differential Equations (6)
• 1.4: Separable Differential Equations (8)
• 1.5: Some Simple Population Models (5)
• 1.6: First-Order Linear Differential Equations (7)
• 1.7: Modeling Problems Using First-Order Linear Differential Equations (4)
• 1.8: Change of Variables (9)
• 1.9: Exact Differential Equations (9)
• 1.10: Numerical Solution to First-Order Differential Equations
• 1.11: Some Higher-Order Differential Equations (5)
• 1.12: Chapter Review (2)

• Chapter 2: Matrices and Systems of Linear Equations
• 2.1: Matrices: Definitions and Notation (3)
• 2.2: Matrix Algebra (10)
• 2.3: Terminology for Systems of Linear Equations (1)
• 2.4: Elementary Row Operations and Row-Echelon Matrices (11)
• 2.5: Gaussian Elimination (7)
• 2.6: The Inverse of a Square Matrix (8)
• 2.7: Elementary Matrices and the LU Factorization
• 2.8: The Invertible Matrix Theorem
• 2.9: Chapter Review

• Chapter 3: Determinants
• 3.1: The Definition of the Determinant
• 3.2: Properties of Determinants (11)
• 3.3: Cofactor Expansions (13)
• 3.4: Summary of Determinants
• 3.5: Chapter Review

• Chapter 4: Vector Spaces
• 4.1: Vectors in ℝn
• 4.2: Definition of a Vector Space (9)
• 4.3: Subspaces (11)
• 4.4: Spanning Sets (8)
• 4.5: Linear Dependence and Linear Independence (9)
• 4.6: Bases and Dimension (11)
• 4.7: Change of Basis
• 4.8: Row Space and Column Space (4)
• 4.9: The Rank-Nullity Theorem
• 4.10: The Invertible Matrix Theorem II
• 4.11: Inner Product Spaces
• 4.12: Orthogonal Sets of Vectors and the Gram-Schmidt Process
• 4.13: Chapter Review

• Chapter 5: Linear Transformations
• 5.1: Definition of a Linear Transformation (8)
• 5.2: Transformations of ℝ2
• 5.3: The Kernel and Range of a Linear Transformation (7)
• 5.4: Additional Properties of Linear Transformations
• 5.5: The Matrix of a Linear Transformation
• 5.6: The Eigenvalue/Eigenvector Problem (11)
• 5.7: General Results for Eigenvalues and Eigenvectors (14)
• 5.8: Diagonalization
• 5.9: An Introduction to the Matrix Exponential Function
• 5.10: Orthogonal Diagonalization and Quadratic Forms
• 5.11: Jordan Canonical Forms
• 5.12: Chapter Review

• Chapter 6: Linear Differential Equations of Order n
• 6.1: General Theory for Linear Differential Equations (9)
• 6.2: Constant-Coefficient Homogeneous Linear Differential Equations (9)
• 6.3: The Method of Undetermined Coefficients: Annihilators (12)
• 6.4: Complex-Valued Trial Solutions
• 6.5: Oscillations of a Mechanical System (10)
• 6.6: RLC Circuits
• 6.7: The Variation-of-Parameters Method (9)
• 6.8: A Differential Equation with Nonconstant Coefficients
• 6.9: Reduction of Order (5)
• 6.10: Chapter Review

• Chapter 7: Systems of Differential Equations
• 7.1: First-Order Linear Systems (6)
• 7.2: Vector Formulation (4)
• 7.3: General Results for First-Order Linear Differential Systems (3)
• 7.4: Vector Differential Equations: Nondefective Coefficient Matrix (7)
• 7.5: Vector Differential Equations: Defective Coefficient Matrix
• 7.6: Variation-of-Parameters for Linear Systems (5)
• 7.7: Some Applications of Linear Systems of Differential Equations
• 7.8: Matrix Exponential Function and Systems of Differential Equations
• 7.9: The Phase Plane for Linear Autonomous Systems
• 7.10: Nonlinear Systems
• 7.11: Chapter Review

• Chapter 8: The Laplace Transform and Some Elementary Applications
• 8.1: Definition of the Laplace Transform
• 8.2: The Existence of the Laplace Transform and the Inverse Transform
• 8.3: Periodic Functions and the Laplace Transform
• 8.4: The Transform of Derivatives and Solution of Initial-Value Problems
• 8.5: The First Shifting Theorem
• 8.6: The Unit Step Function
• 8.7: The Second Shifting Theorem
• 8.8: Impulsive Driving Terms: The Dirac Delta Function
• 8.9: The Convolution Integral
• 8.10: Chapter Review

• Chapter 9: Series Solutions to Linear Differential Equations
• 9.1: A Review of Power Series
• 9.2: Series Solutions about an Ordinary Point
• 9.3: The Legendre Equation
• 9.4: Series Solutions about a Regular Singular Point
• 9.5: Frobenius Theory
• 9.6: Bessel's Equation of Order p
• 9.7: Chapter Review

## Questions Available within WebAssign

Most questions from this textbook are available in WebAssign. The online questions are identical to the textbook questions except for minor wording changes necessary for Web use. Whenever possible, variables, numbers, or words have been randomized so that each student receives a unique version of the question. This list is updated nightly.

##### Question Group Key
TF - True/False Section Questions

##### Question Availability Color Key
BLACK questions are available now
GRAY questions are under development

Group Quantity Questions
Chapter 1: First-Order Differential Equations
1.1 6 TF.004 TF.005 TF.009 002 003 005
1.2 3 020 022 036
1.3 6 TF.001 TF.003 003 006 016 034
1.4 8 TF.003 TF.007 004 006 011 014 018 027
1.5 5 TF.003 TF.006 002 006 014
1.6 7 TF.002 TF.004 002 006 014 018 030
1.7 4 TF.005 TF.006 002 010
1.8 9 TF.003 TF.005 TF.007 012 018 026 030 038 050
1.9 9 TF.003 TF.006 TF.009 004 008 011 018 024 028
1.11 5 001 004 006 010 014
1.12 2 001 042
Chapter 2: Matrices and Systems of Linear Equations
2.1 3 008 011 022
2.2 10 TF.005 TF.007 TF.008 004 008 016 017 019 027 042
2.3 1 TF.004
2.4 11 TF.004 TF.005 TF.006 TF.008 TF.009 003 006 007 020 022 025
2.5 7 TF.002 TF.005 TF.006 002 010 018 022
2.6 8 TF.002 TF.005 TF.006 TF.007 TF.009 006 018 020
Chapter 3: Determinants
3.2 11 TF.001 TF.002 TF.003 TF.005 001 006 020 021 024 030 035
3.3 13 TF.004 TF.005 TF.006 TF.007 007 009 015 017 022 027 036 042 045
Chapter 4: Vector Spaces
4.2 9 TF.002 TF.003 TF.006 TF.007 001 002 003 005 012
4.3 11 TF.001 TF.002 TF.005 TF.007 TF.008 003 005 006 020 021 022
4.4 8 TF.001 TF.003 TF.008 TF.010 001 002 003 008
4.5 9 TF.001 TF.002 TF.003 TF.005 TF.008 007 008 014 030
4.6 11 TF.004 TF.006 TF.007 TF.011 003 004 008 012 019 023 028
4.8 4 TF.004 TF.005 008 010
Chapter 5: Linear Transformations
5.1 8 TF.002 TF.004 TF.005 001 004 011 014 023b
5.3 7 TF.001 TF.002 TF.003 001 002 003 017
5.6 11 TF.002 TF.003 TF.004 TF.005 TF.007 TF.009 005 007 009 015 028
5.7 14 TF.002 TF.004 TF.005 TF.006 001 001.alt 003 003.alt 005 005.alt 007 007.alt 019 019.alt
Chapter 6: Linear Differential Equations of Order n
6.1 9 TF.003 TF.007 001 003 005 006 009 013 031
6.2 9 TF.002 TF.003 TF.004 TF.005 TF.008 017 019 027 035
6.3 12 TF.001 TF.002 TF.003 TF.005 TF.008 001 003 004 017 019 021 026
6.5 10 TF.002 TF.004 TF.005 TF.008 TF.009 001 002 003 004 005
6.7 9 001 002 004 005 016 019 023 028 029
6.9 5 001 003 009b 014 015
Chapter 7: Systems of Differential Equations
7.1 6 TF.006 001 003 009 015 017
7.2 4 TF.002 TF.004 TF.005 012
7.3 3 001 003 004
7.4 7 TF.002 TF.003 TF.004 TF.005 001 003 017
7.6 5 TF.003 TF.004 001 003 008
Chapter 8: The Laplace Transform and Some Elementary Applications
8 0
Chapter 9: Series Solutions to Linear Differential Equations
9 0
Total 299