Rabu, 11 Juli 2012

Prominent Mathematical Physicists

The seventeenth century English physicist and mathematicianIsaac Newton [1642–1727], developed a wealth of new mathematics (for example, calculus and several numerical methods [e.g. Newton's method ]) to solve problems inphysics. Other important mathematical physicists of the seventeenth century included the Dutchman Christiaan Huygens [1629–1695] (famous for suggesting the wave theory of light), and the German Johannes Kepler [1571–1630] (Tycho Brahe's assistant, and discoverer of the equations for planetary motion/orbit).
In the eighteenth century, two of the innovators of mathematical physics were Swiss: Daniel Bernoulli [1700–1782] (for contributions to fluid dynamics, and vibrating strings), and, more especially, Leonhard Euler [1707–1783], (for his work in variational calculus, dynamics, fluid dynamics, and many other things). Another notable contributor was the Italian-born Frenchman, Joseph-Louis Lagrange [1736–1813] (for his work in mechanics and variational methods).
In the late eighteenth and early nineteenth centuries, important French figures were Pierre-Simon Laplace [1749–1827] (in mathematical astronomypotential theory, and mechanics) and Siméon Denis Poisson [1781–1840] (who also worked in mechanics and potential theory). In Germany, both Carl Friedrich Gauss [1777–1855] (in magnetism) and Carl Gustav Jacobi [1804–1851] (in the areas of dynamics and canonical transformations) made key contributions to the theoretical foundations of electricity, magnetism, mechanics, and fluid dynamics.
Gauss's contributions to non-Euclidean geometry laid the groundwork for the subsequent development of Riemannian geometry by Bernhard Riemann [1826–1866]. As we shall see later, this work is at the heart of general relativity.
The nineteenth century also saw the Scot, James Clerk Maxwell [1831–1879], win renown for his four equations of electromagnetism, and his countryman, Lord Kelvin [1824–1907] make substantial discoveries in thermodynamics. Among the English physics community, Lord Rayleigh [1842–1919] worked on sound; and George Gabriel Stokes [1819–1903] was a leader in optics and fluid dynamics; while the Irishman William Rowan Hamilton [1805–1865] was noted for his work in dynamics. 

The German Hermann von Helmholtz [1821–1894] is best remembered for his work in the areas of electromagnetismwavesfluids, and sound. In the U.S.A., the pioneering work of Josiah Willard Gibbs[1839–1903] became the basis for statistical mechanics. Together, these men laid the foundations of electromagnetic theory, fluid dynamics and statistical mechanics.
The late nineteenth and the early twentieth centuries saw the birth of special relativity. This had been anticipated in the works of the Dutchman, Hendrik Lorentz [1853–1928], with important insights from Jules-Henri Poincaré [1854–1912], but which were brought to full clarity by Albert Einstein [1879–1955]. Einstein then developed the invariant approach further to arrive at the remarkable geometrical approach to gravitational physics embodied in general relativity. This was based on the non-Euclidean geometry created by Gauss and Riemann in the previous century.
Einstein's special relativity replaced the Galilean transformations of space and time with Lorentz transformations in four dimensional Minkowski space-time. His general theory of relativity replaced the flat Euclidean geometry with that of a Riemannian manifold, whose curvature is determined by the distribution of gravitational matter. This replaced Newton's vector gravitational force by the Riemann curvature tensor.
Another revolutionary development of the twentieth century has been quantum theory, which emerged from the seminal contributions of Max Planck [1856–1947] (on black body radiation) and Einstein's work on the photoelectric effect

This was, at first, followed by a heuristic framework devised by Arnold Sommerfeld [1868–1951] and Niels Bohr [1885–1962], but this was soon replaced by the quantum mechanics developed by Max Born [1882–1970], Werner Heisenberg [1901–1976], Paul Dirac [1902–1984], Erwin Schrödinger [1887–1961], and Wolfgang Pauli [1900–1958]. This revolutionary theoretical framework is based on a probabilistic interpretation of states, and evolution and measurements in terms of self-adjoint operators on an infinite dimensional vector space (Hilbert space, introduced by David Hilbert [1862–1943]). 

Paul Dirac, for example, used algebraic constructions to produce a relativistic model for the electron, predicting its magnetic moment and the existence of its antiparticle, the positron.
Later important contributors to twentieth century mathematical physics include Satyendra Nath Bose [1894–1974], Julian Schwinger [1918–1994], Sin-Itiro Tomonaga [1906–1979], Richard Feynman [1918–1988], Freeman Dyson [1923– ], Hideki Yukawa [1907–1981], Roger Penrose [1931– ], Stephen Hawking [1942– ], Edward Witten [1951– ] and Rudolf Haag [1922– ]

Senin, 11 Juni 2012

Theoretical Physics

Theoretical physics is a branch of physics which employs mathematical models and abstractions of physics to rationalize, explain and predict natural phenomena. This is in contrast toexperimental physics, which uses experimental tools to probe these phenomena.
The advancement of science depends in general on the interplay between experimental studies and theory. In some cases, theoretical physics adheres to standards of mathematical rigor while giving little weight to experiments and observations. For example, while developing special relativityAlbert Einstein was concerned with the Lorentz transformation which left Maxwell's equations invariant, but was apparently uninterested in the Michelson-Morley experiment on Earth's drift through a luminiferous ether. On the other hand, Einstein was awarded the Nobel Prizefor explaining the photoelectric effect, previously an experimental result lacking a theoretical formulation.

Jumat, 18 Mei 2012


Calculus (Latincalculus, a small stone used for counting) is a branch of mathematics focused on limitsfunctionsderivativesintegrals, and infinite series. This subject constitutes a major part of modern mathematics education. It has two major branches, differential calculus and integral calculus, which are related by the fundamental theorem of calculus. Calculus is the study of change, in the same way that geometry is the study of shape and algebra is the study of operations and their application to solving equations. A course in calculus is a gateway to other, more advanced courses in mathematics devoted to the study of functions and limits, broadly called mathematical analysis. Calculus has widespread applications in science,economics, and engineering and can solve many problems for which algebra alone is insufficient.
Calculus has historically been called "the calculus of infinitesimals", or "infinitesimal calculus". More generally, calculus (plural calculi) refers to any method or system of calculation guided by the symbolic manipulation of expressions. Some examples of other well-known calculi are propositional calculusvariational calculuslambda calculuspi calculus, and join calculus.

Topics in calculus
Fundamental theorem
Limits of functions
Vector calculus
Matrix calculus
Mean value theorem
Product rule
Quotient rule
Chain rule
Change of variables
Implicit differentiation
Taylor's theorem
Related rates
List of differentiation identities
Lists of integrals
Improper integrals
Integration by:
trigonometric substitution,
partial fractionschanging order

Rabu, 18 April 2012

Mainstream theories

Mainstream theories (sometimes referred to as central theories) are the body of knowledge of both factual and scientific views and possess a usual scientific quality of the tests of repeatability, consistency with existing well-established science and experimentation. There do exist mainstream theories that are generally accepted theories based solely upon their effects explaining a wide variety of data, although the detection, explanation and possible composition are subjects of debate.


Minggu, 11 Maret 2012




  Beberapa Sifat Aljabar Bilangan Kompleks  4 
  Perkalian dan Pemangkatan, Rumus de Moivre dan Euler 10 
  Rumus Binomium Newton  14 
  Penerapan Bilangan Kompleks  22 
   Mekanika  22 
   Osilator Selaras Teredam  23 
   Masalah Kelistrikan  26 
   Optika  28 
  Sifat-Sifat Skalar dan Vektor  32 
  Besar Vektor  33 
  Sifat-Sifat Ruang Vektor  33 
  Penjumlahan Vektor  34 
  Perkalian Antara Vektor  36 
  Perkalian Skalar  36 
  Perkalian Vektor/Silang  40 
  Delta dan Epsilon Kronecker  42 
  Garis dan Bidang  48 
  Bebas dan Gayut Linear  54 
  Operasi Matriks  60  
  Rotasi Sumbu-sumbu Koordinat  63 
  Determinan  65 
  Rumus Cramer  70 
  Fungsi  81   
  Macam−macam Fungsi Kontinu  84  
  Limit Fungsi  92  
  Sifat−sifat Limit Fungsi  92 
  Turunan Fungsi  94  
  Deret Taylor dan Deret MacLaurin  98  
  Penerapan Turunan  101 
  Integral sebagai Inversi Penurunan (Anti Derivatif)  106 
  Rumus-Rumus Integral Dasar dan Metode Pengintegralan 106 iv
  Pengintegralan Parsial  108 
  Substitusi Variabel  108 
  Metode Pecahan Parsial  109 
  Integral Tertentu (Integral Riemann  113 
  Penerapan Integral Tertentu   116 
   Mencari Luas di bawah Benda Putar  116 
   Volume Benda Putar  117 
   Menentukan Panjang Busur Kurva  118 
  Fungsi Gamma  120 
  Fungsi Beta  125 
  Turunan Parsial  132 
  Diferensial Total  134 
  Dalil Rantai  138 
  Diferensial Implisit  139  
  Pengubahan Variabel  144 
  Transformasi Legendre    147 
  Ekstremum Fungsi Dua Variabel  150 

Rabu, 01 Februari 2012

Materi Kuliah Pengantar Matematika

Pengantar Matematika termasuk Mata Kuliah Dasar di Departemen Matematika UI. Pengantar Matematika memperkenalkan kepada mahasiswa bagaimana membuktikan suatu proporsi dengan memakai logika matematika. Bahasa matematika dan logika matematika sangatlah berbeda dengan pengertian logika pada umumnya. Dalam logika matematika banyak digunakan lambang-lambang tertentu. Sebagai referensi, Anda bisa mengunduh file-file berikut.
  1. b_induk.pdf
  2. Bab2_fol.pdf
  3. Bab3_teori_bil_1.pdf
  4. Bab4_teori_bil_2.pdf
  5. Func_Series.pdf
  6. Inference_Rule.pdf
  7. Logika_Proporsi.pdf
  8. LogPuzzles.pdf
  9. Pembuktian.pdf
  10. Pohon_Semantik.pdf
  11. Set.pdf
  12. Set_12.rtf

File-file tersebut merupakan salah satu referensi bagi mahasiswa yang ingin memahami logika matematika.


Minggu, 01 Januari 2012

Mathematical Methods in the Physical Sciences

Mathematical Methods in the Physical Sciences is a 1966 textbook by mathematician Mary L. Boas intended to develop skills in mathematical problem solving needed for junior to senior-graduate courses in engineeringphysics, and chemistry. The book provides a comprehensive survey of analytic techniques and provides careful statements of important theorems while omitting most detailed proofs. Each section contains a large number of problems, with selected answers. Numerical computational approaches using computers are outside the scope of the book.
The book, now in its third edition, is still widely used in university classrooms[1] and is frequently cited in other textbooks and scientific papers.


  1. Infinite seriespower series
  2. Complex numbers
  3. Linear algebra
  4. Partial differentiation
  5. Multiple integrals
  6. Vector analysis
  7. Fourier series and transforms
  8. Ordinary differential equations
  9. Calculus of variations
  10. Tensor analysis
  11. Special functions
  12. Series solution of differential equationsLegendreBesselHermite, and Laguerre functions
  13. Partial differential equations
  14. Functions of a complex variable
  15. Integral transforms
  16. Probability and statistics
Jika anda mahasiswa, dosen, guru fisika, atau siapapun yang ingin memahami lebih mendalam konsep fisika-matematik, e-book ini sangat tepat menjadi referens. Jika tertarik, anda bisa men-download-nya dengan klik disini.



Ucapan Terima Kasih:

Ibunda Dra. Roswati Mudjiarto, M.Pd.
Pendidikan Fisika Universitas Pendidikan Indonesia