This book covers essential Microsoft EXCEL®'s computational skills while analyzing introductory physics projects.
Topics of numerical analysis include; multiple graphs on the same sheet, calculation of descriptive statistical parameters, a 3-point interpolation, the Euler and the Runge-Kutter methods to solve equations of motion, the Fourier transform to calculate the normal modes of a double pendulum, matrix calculations to solve coupled linear equations of a DC circuit, animation of waves and Lissajous figures, electric and magnetic field calculations from the Poisson equation and its 3D surface graphs, variational calculus such as Fermat's least traveling time principle and the least action principle. Nelson's stochastic quantum dynamics is also introduced to draw quantum particle trajectories.
Author(s): Shinil Cho
Series: IOP Concise Physics
Publisher: IOP Publishing
Year: 2019
Language: English
Pages: 162
City: Bristol
PRELIMS.pdf
Preface
Acknowledgements
Author biography
Shinil Cho
Book description
CH001.pdf
Chapter 1 Response time of the nervous system
1.1 Objectives
EXCEL note
1.2 Theory and procedure
1.3 Data analysis
1.3.1 Histogram
1.3.2 Another histogram available in EXCEL
1.3.3 Statistical variables
1.3.4 Numerical calculation of statistical variables
1.4 Central limit theorem
1.4.1 Gaussian curve fitting to raw data
1.4.2 Uniform distribution and the central limit theorem
References
CH002.pdf
Chapter 2 Constant acceleration motion
2.1 Objectives
EXCEL note
2.2 Theory and procedure
2.3 Data analysis
2.3.1 Displacement vrs time graph
2.3.2 Displacement vrs (time)2 graph
2.3.3 Velocity vrs time graph
CH003.pdf
Chapter 3 Equation of motion
3.1 Objectives
EXCEL note
3.2 Theory and procedure
3.2.1 Projectile motion
3.3 Data analysis
3.4 Solving equation of motion using the Euler method
3.4.1 The Euler method for projectile motion
3.4.2 A falling object with air resistance using the Euler method
3.5 Runge–Kutta method
3.5.1 Limitation of the Euler method
3.5.2 Algorithm of the Runge–Kutta method
3.5.3 Harmonic oscillator
3.5.4 Van der Pool equation
3.6 Runge–Kutta method for simultaneous ordinary differential equations
3.6.1 Algorithm
3.6.2 Planetary motion
References
CH004.pdf
Chapter 4 Periodic motions
4.1 Objectives
EXCEL note
4.2 Theory and procedure
4.3 Data analysis
4.4 Further investigation—minimum period of a physical pendulum
4.5 More periodic motions
4.5.1 Double pendulum
4.5.2 Fourier transform
4.5.3 Coupled oscillators
References
CH005.pdf
Chapter 5 Lissajous figures
5.1 Objectives
EXCEL note
5.2 Theory and procedure
5.3 Lissajous figures using EXCEL
5.4 Animation of graphs
5.4.1 The idea of animating EXCEL chart
5.4.2 A propagating sine-wave
5.4.3 Rotating Lissajous figures
References
CH006.pdf
Chapter 6 Kirchhoff’s law
6.1 Objectives
EXCEL note
6.2 Theory and procedure
6.3 Circuit under measurement
6.3.1 Matrix calculation using EXCEL
6.4 Data analysis
CH007.pdf
Chapter 7 Equipotential surface
7.1 Objectives
EXCEL note
7.2 Measurement procedure
7.3 Data analysis
7.3.1 3D Surface graph
7.3.2 Calculation of the 3D equipotential surface of an electric dipole
7.4 Further investigation
7.4.1 Two-dimensional electric potential from Poisson’s equation
7.4.2 Two-dimensional electric field from electric potential
7.4.3 Spreadsheet for calculating electric dipole field
7.4.4 Graphical representation of the electric field
References
CH008.pdf
Chapter 8 Magnetic field profile
8.1 Objectives
EXCEL note
8.2 Theory and procedure
8.3 Measurement
8.4 Additional study
8.4.1 Magnetic field calculated from vector potential
8.4.2 Vector potential and magnetic field due to a pair of current wire
8.4.3 Graphical representation of the magnetic field from a pair of current wires
References
CH009.pdf
Chapter 9 Law of refraction
9.1 Objective
EXCEL note
9.2 Theory and procedure
9.3 Data analysis
9.3.1 Angle measurement
9.3.2 Fermat’s least traveling principle using EXCEL’s Solver
9.4 Projectile motion based on the least action principle
9.4.1 Lagrangian approach
9.4.2 Projectile motion
9.5 Eigen value problems using Solver
9.5.1 Eigenvalues of Strum–Liouville equation
9.5.2 Example
References
CH010.pdf
Chapter 10 Quantum particle trajectories
10.1 Objectives
EXCEL notes
10.2 Theory—Nelson’s approach
10.3 Analysis of quantum particle trajectories
10.3.1 One-dimensional free particle
10.3.2 One-dimensional potential barrier
10.3.3 Harmonic oscillator
10.3.4 Hydrogen atom
References
APP1.pdf
Chapter
A.1 EXCEL options
A.1.1 Autofill
A.1.2 Adding ‘data analysis’
A.1.3 Enabling VBA macro
A.1.4 Recording macro code
A.1.5 Enabling iterative calculation
A.1.6 Generating Gaussian random numbers
A.2 Calculation of firing speed of a rolling ball
A.3 RLC oscillator circuit
A.4 Another circuit for exercising Kirchoff’s law
A.5 Macro codes for quantum particles
References
