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Volume 1: Deterministic Modeling, Methods and Analysis
For more than half a century, stochastic calculus and stochastic differential equations have played a major role in analyzing the dynamic phenomena in the biological and physical sciences, as well as engineering. The advancement of knowledge in stochastic differential equations is spreading rapidly across the graduate and postgraduate programs in universities around the globe. This will be the first available book that can be used in any undergraduate/graduate stochastic modeling/applied mathematics courses and that can be used by an interdisciplinary researcher with a minimal academic background.
An Introduction to Differential Equations: Volume 2 is a stochastic version of Volume 1 (“An Introduction to Differential Equations: Deterministic Modeling, Methods and Analysis”). Both books have a similar design, but naturally, differ by calculi. Again, both volumes use an innovative style in the presentation of the topics, methods and concepts with adequate preparation in deterministic Calculus.
Errata
Errata (32 KB)
Sample Chapter(s)
Chapter-1:
1.0 Introduction (37 KB)
1.3 Ito-Doob Stochastic Calculus (203 KB)
1.5 Method of Integration by Parts (109 KB)
Chapter-2:
2.0 Introduction (61 KB)
2.1 Mathematical Modeling (288 KB)
2.3 Linear homogeneous Equations (480 KB)
2.4 Linear Nonhomogeneous Equations (474 KB)
2.5 Fundamental Conceptual Algorithm and Analysis (245 KB)
Chapter-3:
3.0 Introduction (96 KB)
3.2. Energy Function Method (205 KB)
3.5 Variable Separable Equations (463 KB)
3.7 Bernoulli Equations (352 KB)
Chapter-4:
4.0 Introduction (81 KB)
Chapter-5:
5.0 Introduction (40 KB)
Chapter-6:
6.0 Introduction (82 KB)
Contents:
- Elements of Stochastic Processes and Itô–Doob Stochastic Calculus
- First-Order Differential Equations
- First-Order Nonlinear Differential Equations
- First-Order Systems of Linear Differential Equations
- Higher-Order Differential Equations
- Topics in Differential Equations
Readership: Advanced undergraduate students, interdisciplinary researchers; researchers in the mathematical sciences.
