Introduction to Mathematical Modeling and Computer Simulations [Hardcover]

I. General Principles and Methods. 1. Principles of Mathematical Modeling. 1.1. How to develop a mathematical model. 1.2. Types of models. 1.3. Stability of models. 1.4. Dimension, units, and scaling. 2. Numerical and symbolic computations. 2.1. Numerical and symbolic computations of derivatives and integrals. 2.2. Iterative methods. 2.3. Newtons method. 2.4. Method of successive approximations. 2.5. Banach Fixed Point Theorem. 2.6. Why is it difficult to numerically solve some equations? Exercises and mini-projects. II. Basic Applications. 3. Application of calculus to classic mechanics. 3.1. Mechanical meaning of the derivative. 3.2. Integral and energy. 3.3. Potential energy. 3.4. Interpolation. 3.5. Integration of discrete functions. Exercises and mini-projects. 4. Ordinary differential equations and their applications. 4.1. Principle of transition for ODE. 4.2. Radioactive decay. 4.3. Logistic differential equation and its modifications. 4.4. Time delay. 4.5. Approximate solution to differential equations. 4.6. Harmonic oscillation. 4.7. Lotka-Volterra model. 4.8. Linearization. Exercises and mini-projects. 5. Stochastic models. 5.1. Method of least squares. 5.2. Fitting. 5.3. Method of Monte Carlo. 5.4. Random walk. Exercises and mini-projects. 6. One-dimensional stationary problems. 6.1. 1D geometry. 6.2. Second order equations. 6.3. 1D Greens function. 6.4. Greens function as a source. 6.5. The ?function. III. Advanced Applications. 7. Vector analysis. 7.1. Euclidean space R3. 7.2. Scalar, vector and mixed products. 7.3. Rotation of bodies. 7.4. Scalar, vector, and mixed product in Mathematica. 7.5. Tensors. 7.6. Scalar and vector fields. 7.7. Integral theorems. Exercises and mini-projects. 8. Heat equations. 8.1. Heat conduction equations. 8.2. Initial and bl#-