PHY205 Ch0: Math & Physics preliminaries

1. PHY205 Ch0: Math & Physics preliminaries Consider a function of time: Plot it: Define rate of change as: Rate of change=rise over run = slope of secant! When , secant becomes tangent and rate of change becomes derivative. Math: Derivatives Rate of change of a function.

2. PHY205 Ch0: Math & Physics preliminaries So the derivative Let’s compute the derivative in our example: 1st the rate of change : Then the limit as: Final result is: Derivatives of common functions: Product and composition rule: Math: Derivatives Derivative

3. PHY205 Ch0: Math & Physics preliminaries Consider a function of time: Plot it: For Phun, let’s compute the area under plot from, say, t=1s to t=3s But g(t) is also the derivative of Let’s compute Miracle? Consider Math: Integrals Integral area under curve:

4. PHY205 Ch0: Math & Physics preliminaries Why useful? Consider that we know the acceleration a of an object. Since the goal of the game is to find velocity and position and since a=dv/dtand v=dx/dt we need integrals! Math: Integrals Integral area under curve:

5. PHY205 Ch0: Math & Physics preliminaries Physics: What is is? Scientific Paradigm Abstract Realm: Theories, Models,… Theoretical Prediction Experimental Test Reality: all phenomena in the Universe Physics: the science of fundamental processes Empirical Science (Based on observation) Fundamental Science Complex systems: Large number of processes involved. Fundamental Systems: Only a few processes at play

6. PHY205 Ch0: Math & Physics preliminaries Physics: What is is? The tools of Physics: • Theoretical Physics: • Mathematical structures (models, laws, theories) represent the workings of the universe • Reductionism • Experimental Physics: • Measurements: Theoretical predictions are tested • Standards: Material representation of physical concept. Example: the standard meter which is a bar with 2 scratches; the scratches represent what is a distance. Units are the number associated with the standard. • Error analysis

7. PHY205 Ch0: Math & Physics preliminaries Clickers D. examples • Law 1: y = 9.81t^2 for position vs time • Law 2: v = GmM/R^2 t • Empirical • Fundamental • Astrology not a science because its models: • Offer no prediction • Are not falsifiable • Do not use numbers • Are not tested / revised • Intelligent design is not a science because the theory: • offers no testable prediction and thus is not falsifiable • does not use numbers • Is not tested / revised