Module Handbook

Concise Syllabus

Series, complex numbers, linear algebra, partial differentiation, multiple integrals, vector analysis, Fourier series and transforms, ordinary differential equations

 

Complete Syllabus

Series: convergence, test of convergence, power series, expanding function in power series (Taylor and Maclaurin series) Complex Numbers: complex algebra (addition, complex conjugate, multiplication, power, roots, logarithms), hyperbolic functions, application of complex numbers Linear Algebra: matrices, row reduction, vectors, lines and planes, matrix operations, linear vector spaces, eigen value problems, diagonalization, applications of diagonalization Partial Differentiation: power series in two variables, total differentials, approximations, chain rule and implicit differentiation, maximum and minimum problems, Lagrange multipliers, differentiation of integrals Multiple Integrals: double and triple integrals, applications of multiple integrals, change of variables in integrals (Jacobian), surface integrals Vector Analysis: vector multiplication, triple product, differentiation of vectors, gradient, divergence, curl, line integrals, Green's theorem, divergence theorem, Stoke's theorem Fourier series and transforms: periodic functions, Fourier coefficients, odd and even functions, complex Fourier series, Parseval's theorem, Fourier transforms Ordinary Differential Equations: methods for solving first and second order ODE with contants coefficients, Laplace transforms, solution of ODE by Laplace transform, convolution, Green function

 

Outcomes

1. demonstrate knowledge of various mathematical devices, their uses in physics and their properties, including series, complex numbers, matrices, partial derivatives, multiple integrals, vector analysis, Fourier series and transformations, ordinary differential equations


2. apply mathematical tools to solve basic and simple problems.


3. apply mathematical tools to solve problems using many concepts (not complex problems and not open problems)


4. identify and/or formulate suitable mathematical models for physical problems in mechanics, magnetism, thermodynamics, quantum mechanics, relativity


5. apply mathematical tools to solve various physical problems in mechanics, magnetism, thermodynamics, quantum mechanics, relativity

 

Related Courses

1. MA1101 Mathematics IA


2. MA1201 Mathematics IIA


3. Elementary Physics IA


4. FI1201 Elementary Physics IIA

 

References

1. M. L. Boas, Mathematical Methods in The Physical Sciences, 3rd, John Wiley & Sons, 2006


2. K. F. Riley, M. P. Hobson, S. J. Bence, Mathematical Methods for Physics and Engineering, , Cambridge University Press, 2006

 

Rating Guide

Quiz, homework, assignments, UTS and UAS

Concise Syllabus

Kinematics of Particle, Dinamics of Particle, Central Force, Dynamics of System of Particles, Noninertial Reference System, Lagrangian and Hamiltonian Dynamics

 

Complete Syllabus

Kinematics of Particles; Dynamics of Particles: Newton’s Laws, work‐energy theorem, conservative and nonconservative forces, functional forces; Central Force: characteristics force, Kepler’s laws, planetary orbits; Dynamics of System of Particles: center of mass, collision, scattering; Noninertial References System: translating coordinate system, rotating coordinate system; Lagrangian and Hamiltonian Dynamics: Lagrange’s equation, Hamilton’s equation

 

Outcomes

1. recognize and formulate the motion of one-particle systems and many-particle systems with Newtonian mechanics


2. analyzing the motion of a system of particles with Newtonian mechanics


3. solve standard problems concerning the motion of a single particle to an oscillating system coupled with Newtonian mechanics


4. formulate and solve problems of motion of particle systems in non-inertial frames with Newtonian mechanics


5. formulate and solve simple physics problems using the Lagrange formulation


6. formulate and solve simple physics problems using Hamiltons formulations

 

Related Courses

1. MA1101 Mathematics IA (Prerequisite)


2. MA1201 Mathematics IIA (Prerequisite)


3. FI1101 Elementary Physics IA (Prerequisite)


4. FI1201 Elementary Physics IIA (Prerequisite)

 

References

1. Arya, A. P, An Introduction to Classical Mechanics, , Prentice Hall, 1990


2. Symon, K. R, Mechanics, , Addison Wesley, 1980


3. Fowles, G. R, Analytical Mechanics, , Harcourt College Publishing, 1999

 

Rating Guide

The final score is weighted based on the scores of the exam (1 and 2), quiz, and assignments.

Concise Syllabus

This subject should enable the students to get foundations of measurement data processing and presentation in accordance with statistical rules, understand and able to apply the foundation of data processing and analysis in physics and others; probability, probability distribution, presentation of data, central tendency and dispersion in data description; uncertainty and errors and their propagation; confidence interval, statistical hyphotesis testing; curve fitting and modelling; multivariate analysis; overview of big data.

 

Complete Syllabus

Understand about the needs of data processing and analysis in physical sciences and others; basic theories of probability (bayesian and frequentist) and probability density functions; using graphs in presenting data, central tendency and dispersion of data and presenting results of measurements; expectation value of probability density function, binomial distribution, normal distribution and chi squares distribution and their applications; uncertainty and error in measurements and its propagation, systematic and biased errors; confidence interval, single and 2-tails intervals, upper and lower limits of measurements in various probability distributions; statistical hypothesis testing, test if the data agrees with the hypothesis, test if the data does not agree with the hypothesis, test of comparison hypothesis, curve fitting and modelling, least squares or chi-squares criteria, fitting using least squares and maximum likelihood; introduction to multivariate analysis for multivariable models; overview of big data

 

Outcomes

1. Know and understand the basics of presenting measurement data (PLO5,8)


2. Know and understand how to apply data concentration and dispersion measures in data presentation. (PLO5)


3. Know and understand the basics of probability theory and probability density functions.(PLO5)


4. Understand and be able to take into account the sources of error and uncertainty and calculate their propagation. (PLO5)


5. Understand and be able to apply probability distributions in estimating confidence intervals in data presentation (PLO5,8)


6. Understand and be able to compile statistical hypotheses and perform statistical tests in drawing conclusions. (PLO5,8)


7. Understand and be able to apply optimization in fitting curves to measurement data. (PLO5,8)


8. Understand and be able to perform multivariate analysis involving many variables in the sample classification. (PLO5,8)

 

Related Courses

1. FI1101 Elementary Physics IA (Prerequisite)


2. FI1201 Elementary Physics IIA (Prerequisite)

 

Support Activities

Using spreadsheets programs and computer software in statistical analysis. Research Based Learning projects at the end of the semester.

 

References

1. Adrian Bevan, Statistical Data Analysis for Physical Sciences, , Cambridge University Press., 2013


2. Nathan Marz & James Warren, Big Data: Principles and best practices of scalable realtime data systems, 1st, Manning Pub.Co, 2015

 

Rating Guide

Component of evaluations: Quizzes, Homeworks, RBL, Midterm Exam, Final Exam Final score is : Final Score = 10%Homework + 10%Quiz+ 10% RBL + 30% Midterm + 40%Final Exam Index is defined as the followings A : 100>NA≥75 AB : 75>NA≥68 B : 68>NA≥60 BC : 60>NA≥55 C : 55>NA≥50 D : 50>NA≥45 E : NA<45