Francis' Elementary Differential Equations with Applications: Part 1

A highly comprehensive gold standard textbook on elementary differential equations. Perfect for engineering students, BS Physics, BS Mathematics, etc. Includes a wide range of actual applications in the real world. Features highly technological advancements in the field of engineering design, population collapse, energy developments, etc. Topics: Introduction to Differential Equations, Free-fall in the y direction, Basic List of Differential Equations, Basic Terminology and Nomenclature for Differential Equations, Definition of an ODE, PDE, Derivative Notations, Order and Degree of a Differential Equation, Linearity, Families of Solutions, Explicit and Implicit Solutions, General and Particular Solutions, Variable Separable Differential Equations, Brachistochrone Problem, Exponential Increase with Limit M, Rain Precipitation and Agricultural Produce Time Variations, Epidemics, Logistic Function, Torricelli’s Law, Chemical Decomposition, Belt Tension, Machine Pistons, Ideal Gas, Real Gas, Reaction Equilibrium Constant, Clausius-Clapeyron Equation, Barometric Equation, Gibbs- Helmholtz Equation, Food Supply, Verhulstic Population Growth, Beam Deformation, Brachistochrone Problem, Revisited; Francis’ Astronomical Equations, Debye Formula for Isochoric Molal Heat Capacity, Planck Distribution of Energies, Maxwell-Boltzmann Distribution of Molecular Speeds, Most Probable Speed, Average Speed, Root-Mean-Square Speed, Homogeneous Differential Equations, Definition of Homogeneity, Method of Solving, Pitfalls, Safest Slide Model, A Model for Restoring Force in Oscillatory Systems, Series Expansions, General Forms of Homogeneous Differential Equations, Homogeneity of m (d^2 x)/(dt^2 )+b dx/dt+kx(t)=0, The Solar Collector Array Problem, Exact Differential Equations, Condition of Exactness, Maxwell Relations, Forcefields, Thermodynamic Optimization, Additional Applications of Variable Separable Differential Equations, Radioactive Decay, Radiaoctive Elements, Half-Life, Radioisotope Lifetime, Hydrogen-7 Isotope, Carbon-11, Nuclear Battery, Uranium-235, Radiocarbon Dating, Shroud of Turin Verifications, Artefact Age, Advanced Archeological Dating Methods, Population Growth Models, Unlimited Growth Model, Bacterial Growth, Limited Growth Model, Rainfall Time, Agricultural Models (Mitscherlich), Logistic Growth Model,World Population and its Catastrophic Point, City Demography, Gompertz Model, Surface Tissue Growth, Run-away Growth of Pests, Wildlife Conversation (Allee Model), Newton’s Law of Cooling, Boiling Water, Boiling Time Determination without Measuring Ambient Temperature, Cooling Water to Ice, Determination of Ambient Temperature (Psychrometry), Melting Ice, Forensics – Time of Death, Compound Interest, Duration of Financial Deposit to Achieve 10% Gain, Trajetories of Curves, Global Meridians and Parallels, Terrain of Safest Civilization, Curves of Greatest Fish Catch, Illumination Arrangement, Orthogonal Trajectories of Parabolas and Hyperbolas, Typhoon Path, Streamlines, Defensive Fortress, Pursuit Curves, Linear Differential Equation of Order 1, LDE Form, Falling Body Dynamics with Velocity-Proportional Air Resistance, Parachutist’ Equation, Coefficient of Friction Between S, Concentration Changes in a Constantly Stirred Tank ,Chemical Reaction A -> B -> C, Hormone Levels, Atomic Waste Disposal, Elementary Circuits, Introduction; Ordinary emf-R Circuit, RL Circuit, RC Circuit, LC Circuit, RLC Circuit, Higher-Ordered Linear Differential Equations of Homogeneous Type, Mass-Spring Dashpot Systems, Underdamped Spring Motion, General Form of a Higher-Ordered Linear Differential Equation,Application of A (d^2 x)/(dt^2 )+B dx/dt+Cx(t)=0, Vibrations, Springs, Overdamping, Critical Damping, Underdamping, Parallel and Series Springs, Determination of Spring Constant, Equation for a Vibrating Mass-Spring-Dashpot System, Gas Piston Springs, Design of an Analytical Balance, Asymptotes of Underdamped Spring Motion, Peaks, and so on....