《微分方程及其套用（第4版英文版）》是2015年7月1日世界圖書出版公司出版的圖書，作者是Martin、Braun。
基本介紹
- 中文名：微分方程及其套用（第4版英文版）
- 作者：Martin、Braun
- 出版社：世界圖書出版公司
- ISBN：9787510098864
內容簡介,圖書目錄,
內容簡介
《微分方程及其套用（第4版 英文版）》書寫清晰，全面地介紹了微分方程及其套用。《微分方程及其套用（第4版 英文版）》適合於一個或者二個學期的課程，以具有已經學過大學基礎微積分的學生為對象。《微分方程及其套用（第4版 英文版）》區別於其他微積分教材的顯著特點是，將微積分套用於吸引人的項目或者將其併入到該領域相對新的進展。
圖書目錄
Chapter 1 First-order differential equations
1．1 Introduction
1．2 First-orderlinear differential equations
1．3 The Van Meegeren art forgeries
1．4 Separableequations
1．5 Populationmodels
1．6 The spread of technological innovations
1．7 An atomic waste disposal problem
1．8 The dynamics of tumor growth， nuxing problems， and orthogonal trajectories
1．9 Exact equations， and why we cannot solve very many differential equations
1．10 The existence-uniqueness theorem； Picard iteration
1．11 Finding roots of equations by iteration
1．11．1 Newton's method
1．12 Difference equations， and how to compute the interest due on your student loans
1．13 Numerical approximations； Euler's method
1．13．1 Error analysis for Euler's method
1．14 The three term Taylor series method
1．15 An improved Euler method
1．16 The Runge-Kutta method
1．17 What to do in practice
Chapter 2 Second-order linear differential equations
2．1 Algebraic properties of solutions
2．2 Linear equations with constant coefficients
2．2．1 Complexroots
2．2．2 Equal roots； reduction of order
2．3 The nonhomogeneous equation
2．4 The method of variation of parameters
2．5 The method ofjudicious guessing
2．6 Mecharucalvibrations
2．6．1 The Tacoma Bridge disaster
2．6．2 Electricalnetworks
2．7 A model for the detection of diabetes
2．8 Series solutions
2．8．1 Singular points， Euler equations
2．8．2 Regular singular points， the method of Frobenius
2．8．3 Equal roots， and roots differing by an integer
2．9 The method of Laplace transforms
2．10 Some useful properties of Laplace transforms
2．11 Differential equations with discontinuous right-hand sides
2．12 The Dirac delta function
2．13 The convolution integral
2．14 The method of elimination for systems
2．15 Higher-order equations
Chapter 3 Systems of differential equations
3．1 Algebraic properties of solutions of linear systems
3．2 Vectorspaces
3．3 Dimension of a vector space
3．4 Applications of linear algebra to differential equations
3．5 The theory of determinants
3．6 Solutions of simultaneous linear equations
3．7 Linear transformations
3．8 The eigenvalue-eigenvector method of finding solutions
3．9 Complexroots
3．10 Equalroots
3．11 Fundamental matrix solutions； eAt
3．12 The nonhomogcneous equation； variation of parameters
3．13 Solving systems by Laplace transforms
Chapter 4 Qualitative theory of differential equations
4．1 Introduction
4．2 Stability oflinear systems
4．3 Stability of equilibrium solutions
4．4 Thephase-plane
4．5 Mathematical theories of war
4．5．1 L．F．Richardson's theory of conflict
4．5．2 Lanchester's combat models and the battle of Iwo Jima
4．6 Qualitative properties of orbits
4．7 Phase portraits of linear systems
4．8 Long time behavior of solutions； the Poincare～Bendixson Theorem
4．9 Introduction to bifurcation theory
4．10 Predator-prey problems； or why the percentage of sharks caught in the Mediterranean Sea rose dramatically during World War I
4．11 The principle of competitive exclusion in population biology
4．12 The Threshold Theorem of epidemiology
4．13 A model for the spread of gonorrhea
Chapter 5 Separation of variables and Fourier series
5．1 Two point boundary-value problems
5．2 Introduction to partialdifferentialequations
5．3 The heat equation； separation of variables
5．4 Fourierseries
5．5 Even and odd functions
5．6 Retum to the heat equation
5．7 The wave equation
5．8 Laplace'sequation
Chapter 6 Sturm-Liouville boundary value problems
6．1 Introduction
6．2 Inner product spaces
6．3 Orthogonalbases， Hermitian operators
6．4 Sturm-'Liouvilletheory
Appendix A
Some simple facts concerning functions of several variables
Appendix B
Sequences and series
Appendix C
C Programs
Answers to odd-numbered exercises
Index
