UCSB Mathematics Online Math Lab

Online Math Lab

Here are a list of web resources that we hope you will find helpful. The sublinks point to areas of particular interest.

List of General Online Resources

Text
University Lectures
Video
Fun

Text

Calculus.org
Sample problems and exams, calculus applets and animations, and a comprehensive list of calculus resources on the web.

Paul's Notes
Thorough text-based lessons on algebra, calculus, linear algebra, and differential equations. Lots of examples. (sublinks)

College Algebra - Polynomials, graphs, equations, functions, exponents/logarithms. Math 34A spends some time reviewing these topics, but Math 3A will assume students are familiar with this material.

Algebra/Trig Review - Rather than presenting lessons like the previous link, this review consists of practice problems and detailed solutions. Math 34A spends the first few weeks on this (minus the trig), while Math 3A students should consider this material as prerequisite.

Calculus I - Provides some review, then covers limits, derivatives, and integrals. 34 students should note that the 34 curriculum does not cover all of the topics shown here.

Calculus II - 3B/6A/6B: Integration techniques, polar coordinates, parametric equations, sequences and series.

Calculus III - 6A: Partial derivatives, multiple integrals, vector fields, line integrals, curl/divergence, Green's Theorem, and surface integrals.

Linear Algebra - 4A: Matrices, determinants, vectors, linear transformations, vector spaces (basis/dimension), and eigenvalues/eigenvectors.

Differential Equations - 4B/6B: First order differential equations, second order differential equations, Laplace transforms, systems of differential equations, higher order differential equations, fourier series, and partial differential equations.

Complex number primer - Brief introduction to complex numbers.

Cheat sheets - Cheat sheets for algebra, trig, calculus (limits, derivatives, integrals), Laplace transforms. Note that these cheat sheets may not completely align with the curriculum of any one UCSB math course.

How to study math - Tips on how to improve math study habits.

Purplemath
Text lessons largely focusing on algebra. This includes graphing, polynomials, lines, equations, exponents/logarithms, intro trig, and matrix operations. 34A students may find the section on solving word problems to be particularly useful.

Mathisfun
Aimed at a younger age group, but provides a number of useful visual aides in its explanations of pre-calculus topics including geometry and algebra. (sublinks)

Trigonometry - Triangles, trig functions, identities

Geometry - Triangles, polygons, perimeter, area, circles, angles, parallel/perpendicular, symmetry, Cartesian coordinates, conic sections, Pythagorean Theorem

Algebra - Exponents, simplifying, factoring, logarithms, polynomials, linear equations, quadratic equations, sequences/series

Algebra II - Sets, complex numbers, inequalities, exponents, polynomials, equations, graphs, linear equations, functions, quadratic equations, exponents/logarithms, probability, sequences, series

One Mathematical Cat
Text lessons and practice modules on algebra, geometry, pre-calculus (in progress), and calculus (in progress). (sublinks)

Algebra - Fractions, unit conversion, exponents, foil, linear equations/inequalities, absolute value, quadratic equations, percent increase, lines, functions.

Geometry - Angles, polygons, congruence, area, perimeter, and introduction to proofs.

Algebra II - Recursion, sequences, functions, probability, systems of equations, matrices, graphical transformations, quadratic functions, exponential and logarithmic functions, polynomials.

Applied Calculus 5e
Online calculus textbook with interactive tutorials (best for those taking the 3 series). (sublinks)

Finite Mathematics - Some sections relevant for Math 8 (Ch.6: Sets and Counting) and Math 4 (Ch. 3: Matrix Algebra)

Introduction to Logic - Logic, truth tables, proofs.

Visual Calculus
Employs java applets, flash, and other interactive applications to provide tutorials on pre-calculus, limits, derivatives, integration, sequences, and series. (sublinks)

Pre-calculus - Functions, polynomials, functions, trig, exponential functions, function inverses, logarithms, parametric equations, polar coordinates, curve fitting, conic sections.

Limits and Continuity - Limits, continuous functions, horizontal asymptotes, vertical asymptotes

Derivatives - Tangent lines, lienar approximations, derivatives, derivative rules, chain rule

Applications of Differentiation - Derivatives and graphing, tangent lines and parametric curves, implicit differentiation, derivatives of inverse functions, maxima/minima, optimization, Newton's Method.

Integration - Antiderivatives/indefinite integrals, areas, Riemann sums, definite integrals, Fundamental Theorem of Calculus, techniques of integration (substitution, integration by parts, reduction formulas), trapezoidal rule, improper integrals.

Applications of Integration - Area between two curves, volumes, arc length, average value of a function, work, moments and center of mass.

Sequences and Series - Sequences, series, power series.

WolframAlpha
Do-it-all calculator / encyclopedia.

University Lectures

UC Berkeley
Lecture videos/audio (material available varies depending on class). (sublinks)

Analytic Geometry and Calculus (Fall 2011) - Class lectures that cover derivatives, definite integrals, maxima and minima, and exponential and logarithmic functions.

Analytic Geometry and Calculus II (Fall 2011) - Class lectures that cover integrals, differential equations, multivariable functions, partial derivatives, and optimization.

Multivariable Calculus (Fall 2009) - Class lectures on multivariable calculus.

MIT Online Courses
Lecture videos and course materials from MIT math classes (material available varies depending on class). Best for people in the 3 series or above. (sublinks)

Calculus applets - Applets demonstrating various concepts from pre-calculus through multivariable calculus.

Video

Khan Academy
Videos and practice problems covering topics from pre-algebra through linear algebra and differential equations. (sublinks)

Arithmetic and Pre-Algebra - Order of Operations, fractions, decimals, percents, ratios, exponents

Algebra - Linear functions, systems of equations, exponents, logarithms, polynomials, quadratic functions

Geometry - Angles, triangles, polygons, circles

Trigonometry and Precalculus - Radians/degrees, graph of trig functions, trig identities, polar coordinates, limits, sequences, functions

Differential Calculus - 34A/3A (many topics are 3A only): Derivatives, product/quotient/chain rule, implicit derivatives, L'Hopital's Rule, Mean Value Theorem

Integral Calculus - 34B/3B (many topics are 3B only): Indefinite integrals, definite integrals, trig substitution, solid of revolution, Taylor series

Linear Algebra - 4A: Matrices, vectors, linear independence, dot/cross product, linear transformations, determinants, basis, eigenvectors/eigenspaces

Differential Equations - 4B: Separable differential equations, integrating factors, homogenous equations, undetermined coefficients, Laplace transforms

Multivariable Calculus - 6A: Partial derivatives, divergence, curl, double integrals, line integrals, surface integrals, Green Theorem

PatrickJMT
This site has a large number of videos spanning many mathematical topics (pre-algebra, algebra, trig, calculus, linear algebra, differential equations, and even some Math 8 material). If you are looking for an alternative video library to Khan Academy, this is a good place to check.

Mathispower4u
Over 2,000 videos covering arithmetic, algebra, geometry, trig, calculus (single and multivariable), linear algebra, and differential equations. (sublinks)

Arithmetic - Fractions, decimals, proportions, percentages, exponents, measurements/data, geometry

Algebra - Variables, linear equations, functions, inequalities, polynomials, factoring, quadratic functions, polynomial functions, radicals, rational expressions, exponents, logarithms, graphing, function transformations, sequences, series, matrices, counting, probability, conic sections

Geometry - Angles, Pythagorean theorem, polygons, parallel/perpendicular lines, triangles, similarity, right angle trigonometry, circles

Trigonometry - Trig functions, radians, graphing trig functions, trig identities, inverse trig functions, trig equations, law of sines, polar equations, complex numbers

Calculus - 34A/34B/3A/3B/6A/6B: Limits, differentiation, maxima/minima, integration, differential equations, volume of revolution, surface area of revolution, improper integrals, infinite series, parametric equations, polar equations, vectors, cylindrical/spherical coordinates, vector valued functions, functions of several variables, multiple integration, vector calculus

LInear Algebra - 4A: Systems of linear equations, matrices, determinants, vectors

Differential Equations - 4B: First order differential equations, exponential growth, Newton's Law of Cooling

YourMathGal
Youtube videos on a variety of topics, including pre-algebra, geometry, trig, graphing, and sets. However, the most developed section (so far) is algebra. (sublinks)

Algebra - Equations, functions, polynomials, graphing, word problems

Simply Math
Youtube videos covering a range of classes, including pre-calculus, trig/geometry, calculus, differential equations, linear algebra, and Math 8 material.

Fun

Khan Academy: Brain Teasers
Logic puzzles and brain teasers.

Mathematical Moments
Series of posters in PDF form depicting the role of mathematics in the real world.

The Math and Magic of Origami
TED talk (15:53) on how math and engineering, combined with origami, has yielded not only magnificent art but has real world applications.

Vi Hart Videos
Fun videos connecting math to music, doodles, and more. You can fine more content on her blog.