Difference Equations to Differential Equations
This book covers the following topics: Sequences, limits, and difference equations; functions and their properties; best affine approximations; integration; polynomial approximations and Taylor series; transcendental functions; the complex plane; differential equations.
Written with the advanced undergraduate or graduate student in mind, Electromagnetic Field Theory is a textbook on the theory of electrodynamics, at roughly the same level as the well-known textbooks by Jackson and Panofsky&Phillips. The book is written mainly from a classical field theoretical point of view, emphasising fundamental and subtle properties of the EM field and includes a comprehensive appendix on the mathematical methods used.
Basics of Fluid Mechanics
This book describes the fundamentals fluid mechanics phenomena for engineers and others. This book is designed to replace all introductory textbook(s) or instructor's notes for the fluid mechanics in undergraduate classes for engineering/science students but also for technical peoples. It is hoped that the book could be used as a reference book for people who have at least some basics knowledge of science areas such as calculus, physics, etc.
This is an on-line resource on topics of Applied Calculus, including on-line tutorial sessions.
Some of the topics that this book addresses are: Vector spaces; finite-dimensional vector spaces; differential calculus; compactness and completeness; scalar product space; differential equations; multilenear functionals; integration; differentiable manifolds; integral calculus on manifolds; exterior calculus. Note: this is a 57 MB PDF Document.
A Problem Course in Mathematical Logic
A Problem Course in Mathematical Logic is intended to serve as the text for an introduction to mathematical logic for undergraduates with some mathematical sophistication. It supplies definitions, statements of results, and problems, along with some explanations, examples, and hints. The idea is for the students, individually or in groups, to learn the material by solving the problems and proving the results for themselves. The book should do as the text for a course taught using the modified Mo
A First Course in Linear Algebra
A First Course in Linear Algebra is an introductory textbook aimed at college-level sophomores and juniors. Typically such a student will have taken calculus, but this is not a prerequisite. The book begins with systems of linear equations, then covers matrix algebra, before taking up finite-dimensional vector spaces in full generality. The final chapter covers matrix representations of linear transformations, through diagonalization, change of basis and Jordan canonical form. Along the way, det
A Computational Introduction to Number Theory and Algebra
A book introducing basic concepts from computational number theory and algebra, including all the necessary mathematical background.
Atoms to X-rays: How Do Proteins Fold? Theory Meets Experiments
The machinery of life depends on proteins--large organic molecules composed of tens, hundreds or even thousands of amino acids bound together and folded into specifically shaped structures. How they fold into these three-dimensional structures is known as the second genetic code and is one of great challenges in science today. Join UCSD biophysicist Jose Onuchic, as he explores how physics, chemistry, biology and mathematics are all being applied to crack the protein folding mystery. Series: Ato
Geometry - from MathWorld
Another extensive reference site from MathWorld, this index offers pages on advanced and basic skills alike, though the information is presented with the very advanced student in mind. Very good notes and diagrams accompany reference material for plane geometry, non-Euclidean geometry, and general geometry, among many others. This resource is part of the Teaching Quantitative Skills in the Geosciences collection. http://serc.carleton.edu/quantskills/
Geometry Formulas and Facts
This excerpt from the CRC Standard Mathematical Tables and Formulas covers geometry, excluding differential geometry. It is a reference for advanced students, and covers the material in quick, condensed sections of notes. Notes and diagrams are organized into sections and subsections, starting with coordinate systems, plane transformations, lines, and polygons in two-dimensional geometry. The section on three-dimensional geometry covers coordinate systems in space, space symmetries, directions,
GeoMaths - Revision Topics
This site, part of the University College London's GeoMath site, provides a review of basic math skills, including basic equations and functions, areas and volumes, and coordinates and graphs. The notation is linked throughout to a glossary of terms, and several examples are geologically based and have realistic scenarios. This resource is part of the Teaching Quantitative Skills in the Geosciences collection. http://serc.carleton.edu/quantskills/
GeoMaths MathHelp Material
This site provides students with mathematics self-study material which is embedded within the context of the geosciences. The material consists of many MathHelp "notebooks" covering specific mathematical topics related to a relevant geological context, such as plate velocity or cliff erosion. The notebooks contain explanations, illustrations, and examples. A mathematical glossary is also constantly available, providing a brief explanation of mathematical keywords and links to the relevant notebo
GeoMaths - 2nd Level Modules
The highest level of math on the University College London's GeoMath site, this covers skills such as complex numbers, partial differentiation, matrices, advanced vectors, and probability. Each section features a menu of topics and links to a glossary. Many have geology-based examples, using the mathematical skill within a realistic scenario. This resource is part of the Teaching Quantitative Skills in the Geosciences collection. http://serc.carleton.edu/quantskills/
GeoMaths - 1st Level Modules
University of College London hosts a site of notation and reference material on math skills in the context of geoscience. These exercises provide realistic geologic scenarios and work through examples, with notation on the math used to solve them. Examples include using trigonometry to find the true width of strata, logarithms to understand the Richter scale, and vectors to find plate velocities at a triple junction. Relevant vocabulary is linked to a glossary of mathematical terms. Many of the
Functions of 2 Variables: Partial Derivatives
Brandeis hosts several pages demonstrating the involvement of calculus in biology. This site gives a short explanation of the partial derivative of two variables, using illustrations and various levels of magnification to demonstrate. This resource is part of the Teaching Quantitative Skills in the Geosciences collection. http://serc.carleton.edu/quantskills/
Calculus - from MathWorld
MathWorld again provides a broad range of topics, this time under its calculus index, with subjects ranging from limits to differential equations. General calculus, continuity, maxima and minima, and integrals are all covered, with lots of notes, diagrams, and examples. Many cross-references and lists of relevant texts provide a well-rounded and thorough reference for the curious and demanding student. This resource is part of the Teaching Quantitative Skills in the Geosciences collection. http:
Algebra.help - Simplifying expressions/equations with exponents
Follow this lesson to review basic exponent manipulation. Worksheets, further lessons, and lists of resources are also available. This resource is part of the Teaching Quantitative Skills in the Geosciences collection. http://serc.carleton.edu/quantskills/
Algebra - from MathWorld
Definition of the term “algebra” and examples of various “algebras”.
Hip Math and Shape Art
This lesson builds upon student knowledge of basic geometric shapes by studying the art in the illustrations shown in the video. Students draw and name organic, non-geometric shapes.