Chapter 1 First-Order Differential Equations
1.1 Four examples: linear and nonlinear
1.2 Basic Calculus Required
1.3 Exponential functions e^t and e^at
1.4 Four special solutions
1.5 Real sinusoids and complex sinusoids
1.6 Growth and Decline Model
1.7 Logistic Equation
1.8 Separable and Complete Equations


Chapter 2 Second-order differential equations
2.1 Second order derivatives in science and engineering
2.2 Key facts about complex numbers
2.3 Constant coefficients A, B, C
2.4 Forced vibration and exponential response
2.5 Electrical Circuits and Mechanical Systems
2.6 Solutions to second-order differential equations
2.7 Laplace transforms Y(s) and F(s)



Chapter 3: Diagrammatic and Numerical Calculations
3.1 Nonlinear equation y^'=f(t,y)
3.2 Source, suction, saddle, spiral
3.3 Linearization and stability in two and three dimensions
3.4 Basic Euler method
3.5 Higher accuracy using the Runge-Kutta method


Chapter 4 Linear Equations and Inverse Matrices
4.1 Two diagrams of linear equations
4.2 Solving linear equations by elimination
4.3 Matrix Multiplication
4.4 Inverse matrix
4.5 Symmetric and orthogonal matrices

Chapter 5 Vector Spaces and Subspaces
5.1 Column space of a matrix
5.2 Null space of A satisfying Av=0
5.3 Complete solution of Av=b
5.4 Linear independence, basis, and dimension
5.5 Four basic subspaces
5.6 Graphs and Networks

Chapter 6 Eigenvalues ​​and Eigenvectors
6.1 Introduction to Eigenvalues
6.2 Diagonalization of matrices
6.3 Linear system y^'=Ay
6.4 Matrix Exponents
6.5 Second-order systems and symmetric matrices

Chapter 7 Applied Mathematics and A^TA
7.1 Least Squares and Orthogonal Projection
7.2 Positive definite matrices and singular value decomposition
7.3 Boundary conditions replacing initial conditions
7.4 Laplace's Equation and A^TA
7.5 Networks and Graph Laplacians

Chapter 8 Fourier Transform and Laplace Transform
8.1 Fourier series
8.2 Fast Fourier Transform
8.3 Heat equation
8.4 Wave equation
8.5 Laplace Transform
8.6 Convolution (Fourier and Laplace)

supplement
A matrix decomposition
Properties of B determinant
C Linear Algebra Summary: A is an n×n matrix

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[characteristic]
① As the author's reputation suggests, the theory is explained easily and is developed with a focus on the core.
② Differential equations can be studied alone or together with linear algebra.
③ We have included plenty of practice problems for each chapter so that you can utilize the concepts you have learned in a variety of ways.
④ The main theory of the book is the author Gilbert Strang's lecture, and calculations can be learned using various tools.

Successfully understand differential equations by applying linear algebra.
Mathematics is not about formulas, calculations, or proofs, it's about ideas!
This book was written by Gilbert Strang, a professor of mathematics at MIT and an expert in applied mathematics, and is aimed at students in natural sciences or engineering fields that require mathematics as an applied discipline.
This is the only book in Korea that covers differential equations and linear algebra, which are required subjects in undergraduate courses, and explains differential equations by applying linear algebra concepts.
You can learn the fundamental concepts of the subject and apply key ideas to real-world cases in detail with Strang's characteristically friendly explanations.