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Pauls Online Math Notes
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Welcome to my math notes site. Contained in this site are the notes (free and downloadable) that I use to teach Algebra, Calculus (I, II and III) as well as Differential Equations at Lamar University. The notes contain the usual topics that are taught in those courses as well as a few extra topics that I decided to include just because I wanted to. There are also a set of practice problems, with full solutions, to all of the classes except Differential Equations. In addition there is also a selection of cheat sheets available for download.
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descriptionWelcome to my math notes site. Contained in this site are the notes (free and downloadable) that I use to teach Algebra, Calculus (I, II and III) as well as Differential Equations at Lamar University. The notes contain the usual topics that are taught in those courses as well as a few extra topics that I decided to include just because I wanted to. There are also a set of practice problems, with full solutions, to all of the classes except Differential Equations. In addition there is also a selection of cheat sheets available for download.
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descriptionWelcome to my math notes site. Contained in this site are the notes (free and downloadable) that I use to teach Algebra, Calculus (I, II and III) as well as Differential Equations at Lamar University. The notes contain the usual topics that are taught in those courses as well as a few extra topics that I decided to include just because I wanted to. There are also a set of practice problems, with full solutions, to all of the classes except Differential Equations. In addition there is also a selection of cheat sheets available for download.
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Found links on this page

LinkAttributesAnchor text
https://tutorial.math.lamar.edu/Anchor No Text
https://tutorial.math.lamar.edu/Paul's Online Notes
/Classes/Alg/Alg.aspxAlgebra
A-TITLE Go To Algebra Notes
/Classes/CalcI/CalcI.aspxCalculus I
A-TITLE Go To Calculus I Notes
/Classes/CalcII/CalcII.aspxCalculus II
A-TITLE Go To Calculus II Notes
/Classes/CalcIII/CalcIII.aspxCalculus III
A-TITLE Go To Calculus III Notes
/Classes/DE/DE.aspxDifferential Equations
A-TITLE Go To Differential Equations Notes
/Extras/AlgebraTrigReview/Alge...Algebra & Trig Review
A-TITLE Go To Algebra & Trig Review
/Extras/CommonErrors/CommonMat...Common Math Errors
A-TITLE Go To Common Math Errors
/Extras/ComplexPrimer/ComplexN...Complex Number Primer
A-TITLE Go To Complex Numbers Primer
/Extras/StudyMath/HowToStudyMa...How To Study Math
A-TITLE Go To How To Study Math
/Extras/CheatSheets_Tables.aspxCheat Sheets & Tables
A-TITLE Go To List of Cheat Sheets and Tables
/contact.aspxContact Me
A-TITLE Contact Me!
/mathjax.aspxMathJax Help and Configuration
A-TITLE Info on MathJax and MathJax Configuration Menu
https://tutorial.math.lamar.edu/Home
/Classes/Alg/Alg.aspxText duplicate Algebra
/Classes/Alg/Preliminaries.aspx1. Preliminaries
/Classes/Alg/IntegerExponents....1.1 Integer Exponents
/Classes/Alg/RationalExponents...1.2 Rational Exponents
/Classes/Alg/Radicals.aspx1.3 Radicals
/Classes/Alg/Polynomials.aspx1.4 Polynomials
/Classes/Alg/Factoring.aspx1.5 Factoring Polynomials
/Classes/Alg/RationalExpressio...1.6 Rational Expressions
/Classes/Alg/ComplexNumbers.aspx1.7 Complex Numbers
/Classes/Alg/Solving.aspx2. Solving Equations and Inequalities
/Classes/Alg/SolutionSets.aspx2.1 Solutions and Solution Sets
/Classes/Alg/SolveLinearEqns.aspx2.2 Linear Equations
/Classes/Alg/LinearApps.aspx2.3 Applications of Linear Equations
/Classes/Alg/SolveMultiVariabl...2.4 Equations With More Than One Variable
/Classes/Alg/SolveQuadraticEqn...2.5 Quadratic Equations - Part I
/Classes/Alg/SolveQuadraticEqn...2.6 Quadratic Equations - Part II
/Classes/Alg/SolveQuadraticEqn...2.7 Quadratic Equations : A Summary
/Classes/Alg/QuadraticApps.aspx2.8 Applications of Quadratic Equations
/Classes/Alg/ReducibleToQuadra...2.9 Equations Reducible to Quadratic in Form
/Classes/Alg/SolveRadicalEqns....2.10 Equations with Radicals
/Classes/Alg/SolveLinearInequa...2.11 Linear Inequalities
/Classes/Alg/SolvePolyInequali...2.12 Polynomial Inequalities
/Classes/Alg/SolveRationalIneq...2.13 Rational Inequalities
/Classes/Alg/SolveAbsValueEqns...2.14 Absolute Value Equations
/Classes/Alg/SolveAbsValueIneq...2.15 Absolute Value Inequalities
/Classes/Alg/Graphing_Function...3. Graphing and Functions
/Classes/Alg/Graphing.aspx3.1 Graphing
/Classes/Alg/Lines.aspx3.2 Lines
/Classes/Alg/Circles.aspx3.3 Circles
/Classes/Alg/FunctionDefn.aspx3.4 The Definition of a Function
/Classes/Alg/GraphFunctions.aspx3.5 Graphing Functions
/Classes/Alg/CombineFunctions....3.6 Combining Functions
/Classes/Alg/InverseFunctions....3.7 Inverse Functions
/Classes/Alg/CommonGraphs.aspx4. Common Graphs
/Classes/Alg/Lines_Circles_PWF...4.1 Lines, Circles and Piecewise Functions
/Classes/Alg/Parabolas.aspx4.2 Parabolas
/Classes/Alg/Ellipses.aspx4.3 Ellipses
/Classes/Alg/Hyperbolas.aspx4.4 Hyperbolas
/Classes/Alg/MiscFunctions.aspx4.5 Miscellaneous Functions
/Classes/Alg/Transformations.aspx4.6 Transformations
/Classes/Alg/Symmetry.aspx4.7 Symmetry
/Classes/Alg/GraphRationalFcns...4.8 Rational Functions
/Classes/Alg/PolynomialFunctio...5. Polynomial Functions
/Classes/Alg/DividingPolynomia...5.1 Dividing Polynomials
/Classes/Alg/ZeroesOfPolynomia...5.2 Zeroes/Roots of Polynomials
/Classes/Alg/GraphingPolynomia...5.3 Graphing Polynomials
/Classes/Alg/FindingZeroesOfPo...5.4 Finding Zeroes of Polynomials
/Classes/Alg/PartialFractions....5.5 Partial Fractions
/Classes/Alg/ExpAndLog.aspx6. Exponential and Logarithm Functions
/Classes/Alg/ExpFunctions.aspx6.1 Exponential Functions
/Classes/Alg/LogFunctions.aspx6.2 Logarithm Functions
/Classes/Alg/SolveExpEqns.aspx6.3 Solving Exponential Equations
/Classes/Alg/SolveLogEqns.aspx6.4 Solving Logarithm Equations
/Classes/Alg/ExpLogApplication...6.5 Applications
/Classes/Alg/Systems.aspx7. Systems of Equations
/Classes/Alg/SystemsTwoVrble.aspx7.1 Linear Systems with Two Variables
/Classes/Alg/SystemsThreeVrble...7.2 Linear Systems with Three Variables
/Classes/Alg/AugmentedMatrix.aspx7.3 Augmented Matrices
/Classes/Alg/AugmentedMatrixII...7.4 More on the Augmented Matrix
/Classes/Alg/NonlinearSystems....7.5 Nonlinear Systems
/Classes/CalcI/CalcI.aspxText duplicate Calculus I
/Classes/CalcI/ReviewIntro.aspx1. Review
/Classes/CalcI/Functions.aspx1.1 Functions
/Classes/CalcI/InverseFunction...1.2 Inverse Functions
/Classes/CalcI/TrigFcns.aspx1.3 Trig Functions
/Classes/CalcI/TrigEquations.aspx1.4 Solving Trig Equations
/Classes/CalcI/TrigEquations_C...1.5 Trig Equations with Calculators, Part I
/Classes/CalcI/TrigEquations_C...1.6 Trig Equations with Calculators, Part II
/Classes/CalcI/ExpFunctions.aspx1.7 Exponential Functions
/Classes/CalcI/LogFcns.aspx1.8 Logarithm Functions
/Classes/CalcI/ExpLogEqns.aspx1.9 Exponential and Logarithm Equations
/Classes/CalcI/CommonGraphs.aspx1.10 Common Graphs
/Classes/CalcI/limitsIntro.aspx2. Limits
/Classes/CalcI/Tangents_Rates....2.1 Tangent Lines and Rates of Change
/Classes/CalcI/TheLimit.aspx2.2 The Limit
/Classes/CalcI/OneSidedLimits....2.3 One-Sided Limits
/Classes/CalcI/LimitsPropertie...2.4 Limit Properties
/Classes/CalcI/ComputingLimits...2.5 Computing Limits
/Classes/CalcI/InfiniteLimits....2.6 Infinite Limits
/Classes/CalcI/LimitsAtInfinit...2.7 Limits At Infinity, Part I
/Classes/CalcI/LimitsAtInfinit...2.8 Limits At Infinity, Part II
/Classes/CalcI/Continuity.aspx2.9 Continuity
/Classes/CalcI/DefnOfLimit.aspx2.10 The Definition of the Limit
/Classes/CalcI/DerivativeIntro...3. Derivatives
/Classes/CalcI/DefnOfDerivativ...3.1 The Definition of the Derivative
/Classes/CalcI/DerivativeInter...3.2 Interpretation of the Derivative
/Classes/CalcI/DiffFormulas.aspx3.3 Differentiation Formulas
/Classes/CalcI/ProductQuotient...3.4 Product and Quotient Rule
/Classes/CalcI/DiffTrigFcns.aspx3.5 Derivatives of Trig Functions
/Classes/CalcI/DiffExpLogFcns....3.6 Derivatives of Exponential and Logarithm Functions
/Classes/CalcI/DiffInvTrigFcns...3.7 Derivatives of Inverse Trig Functions
/Classes/CalcI/DiffHyperFcns.aspx3.8 Derivatives of Hyperbolic Functions
/Classes/CalcI/ChainRule.aspx3.9 Chain Rule
/Classes/CalcI/ImplicitDIff.aspx3.10 Implicit Differentiation
/Classes/CalcI/RelatedRates.aspx3.11 Related Rates
/Classes/CalcI/HigherOrderDeri...3.12 Higher Order Derivatives
/Classes/CalcI/LogDiff.aspx3.13 Logarithmic Differentiation
/Classes/CalcI/DerivAppsIntro....4. Applications of Derivatives
/Classes/CalcI/RateOfChange.aspx4.1 Rates of Change
/Classes/CalcI/CriticalPoints....4.2 Critical Points
/Classes/CalcI/MinMaxValues.aspx4.3 Minimum and Maximum Values
/Classes/CalcI/AbsExtrema.aspx4.4 Finding Absolute Extrema
/Classes/CalcI/ShapeofGraphPtI...4.5 The Shape of a Graph, Part I
/Classes/CalcI/ShapeofGraphPtI...4.6 The Shape of a Graph, Part II
/Classes/CalcI/MeanValueTheore...4.7 The Mean Value Theorem
/Classes/CalcI/Optimization.aspx4.8 Optimization
/Classes/CalcI/MoreOptimizatio...4.9 More Optimization Problems
/Classes/CalcI/LHospitalsRule....4.10 L'Hospital's Rule and Indeterminate Forms
/Classes/CalcI/LinearApproxima...4.11 Linear Approximations
/Classes/CalcI/Differentials.aspx4.12 Differentials
/Classes/CalcI/NewtonsMethod.aspx4.13 Newton's Method
/Classes/CalcI/BusinessApps.aspx4.14 Business Applications
/Classes/CalcI/IntegralsIntro....5. Integrals
/Classes/CalcI/IndefiniteInteg...5.1 Indefinite Integrals
/Classes/CalcI/ComputingIndefi...5.2 Computing Indefinite Integrals
/Classes/CalcI/SubstitutionRul...5.3 Substitution Rule for Indefinite Integrals
/Classes/CalcI/SubstitutionRul...5.4 More Substitution Rule
/Classes/CalcI/AreaProblem.aspx5.5 Area Problem
/Classes/CalcI/DefnOfDefiniteI...5.6 Definition of the Definite Integral
/Classes/CalcI/ComputingDefini...5.7 Computing Definite Integrals
/Classes/CalcI/SubstitutionRul...5.8 Substitution Rule for Definite Integrals
/Classes/CalcI/IntAppsIntro.aspx6. Applications of Integrals
/Classes/CalcI/AvgFcnValue.aspx6.1 Average Function Value
/Classes/CalcI/AreaBetweenCurv...6.2 Area Between Curves
/Classes/CalcI/VolumeWithRings...6.3 Volumes of Solids of Revolution / Method of Rings
/Classes/CalcI/VolumeWithCylin...6.4 Volumes of Solids of Revolution/Method of Cylinders
/Classes/CalcI/MoreVolume.aspx6.5 More Volume Problems
/Classes/CalcI/Work.aspx6.6 Work
/Classes/CalcI/ExtrasIntro.aspxAppendix A. Extras
/Classes/CalcI/LimitProofs.aspxA.1 Proof of Various Limit Properties
/Classes/CalcI/DerivativeProof...A.2 Proof of Various Derivative Properties
/Classes/CalcI/ProofTrigDeriv....A.3 Proof of Trig Limits
/Classes/CalcI/DerivativeAppsP...A.4 Proofs of Derivative Applications Facts
/Classes/CalcI/ProofIntProp.aspxA.5 Proof of Various Integral Properties
/Classes/CalcI/Area_Volume_For...A.6 Area and Volume Formulas
/Classes/CalcI/TypesOfInfinity...A.7 Types of Infinity
/Classes/CalcI/SummationNotati...A.8 Summation Notation
/Classes/CalcI/ConstantofInteg...A.9 Constant of Integration
/Classes/CalcII/CalcII.aspxText duplicate Calculus II
/Classes/CalcII/IntTechIntro.aspx7. Integration Techniques
/Classes/CalcII/IntegrationByP...7.1 Integration by Parts
/Classes/CalcII/IntegralsWithT...7.2 Integrals Involving Trig Functions
/Classes/CalcII/TrigSubstituti...7.3 Trig Substitutions
/Classes/CalcII/PartialFractio...7.4 Partial Fractions
/Classes/CalcII/IntegralsWithR...7.5 Integrals Involving Roots
/Classes/CalcII/IntegralsWithQ...7.6 Integrals Involving Quadratics
/Classes/CalcII/IntegrationStr...7.7 Integration Strategy
/Classes/CalcII/ImproperIntegr...7.8 Improper Integrals
/Classes/CalcII/ImproperIntegr...7.9 Comparison Test for Improper Integrals
/Classes/CalcII/ApproximatingD...7.10 Approximating Definite Integrals
/Classes/CalcII/IntAppsIntro.aspx8. Applications of Integrals
/Classes/CalcII/ArcLength.aspx8.1 Arc Length
/Classes/CalcII/SurfaceArea.aspx8.2 Surface Area
/Classes/CalcII/CenterOfMass.aspx8.3 Center of Mass
/Classes/CalcII/HydrostaticPre...8.4 Hydrostatic Pressure
/Classes/CalcII/Probability.aspx8.5 Probability
/Classes/CalcII/ParametricIntr...9. Parametric Equations and Polar Coordinates
/Classes/CalcII/ParametricEqn....9.1 Parametric Equations and Curves
/Classes/CalcII/ParaTangent.aspx9.2 Tangents with Parametric Equations
/Classes/CalcII/ParaArea.aspx9.3 Area with Parametric Equations
/Classes/CalcII/ParaArcLength....9.4 Arc Length with Parametric Equations
/Classes/CalcII/ParaSurfaceAre...9.5 Surface Area with Parametric Equations
/Classes/CalcII/PolarCoordinat...9.6 Polar Coordinates
/Classes/CalcII/PolarTangents....9.7 Tangents with Polar Coordinates
/Classes/CalcII/PolarArea.aspx9.8 Area with Polar Coordinates
/Classes/CalcII/PolarArcLength...9.9 Arc Length with Polar Coordinates
/Classes/CalcII/PolarSurfaceAr...9.10 Surface Area with Polar Coordinates
/Classes/CalcII/ArcLength_Surf...9.11 Arc Length and Surface Area Revisited
/Classes/CalcII/SeriesIntro.aspx10. Series & Sequences
/Classes/CalcII/Sequences.aspx10.1 Sequences
/Classes/CalcII/MoreSequences....10.2 More on Sequences
/Classes/CalcII/Series_Basics....10.3 Series - The Basics
/Classes/CalcII/ConvergenceOfS...10.4 Convergence/Divergence of Series
/Classes/CalcII/Series_Special...10.5 Special Series
/Classes/CalcII/IntegralTest.aspx10.6 Integral Test
/Classes/CalcII/SeriesCompTest...10.7 Comparison Test/Limit Comparison Test
/Classes/CalcII/AlternatingSer...10.8 Alternating Series Test
/Classes/CalcII/AbsoluteConver...10.9 Absolute Convergence
/Classes/CalcII/RatioTest.aspx10.10 Ratio Test
/Classes/CalcII/RootTest.aspx10.11 Root Test
/Classes/CalcII/SeriesStrategy...10.12 Strategy for Series
/Classes/CalcII/EstimatingSeri...10.13 Estimating the Value of a Series
/Classes/CalcII/PowerSeries.aspx10.14 Power Series
/Classes/CalcII/PowerSeriesand...10.15 Power Series and Functions
/Classes/CalcII/TaylorSeries.aspx10.16 Taylor Series
/Classes/CalcII/TaylorSeriesAp...10.17 Applications of Series
/Classes/CalcII/BinomialSeries...10.18 Binomial Series
/Classes/CalcII/VectorsIntro.aspx11. Vectors
/Classes/CalcII/Vectors_Basics...11.1 Vectors - The Basics
/Classes/CalcII/VectorArithmet...11.2 Vector Arithmetic
/Classes/CalcII/DotProduct.aspx11.3 Dot Product
/Classes/CalcII/CrossProduct.aspx11.4 Cross Product
/Classes/CalcII/3DSpace.aspx12. 3-Dimensional Space
/Classes/CalcII/3DCoords.aspx12.1 The 3-D Coordinate System
/Classes/CalcII/EqnsOfLines.aspx12.2 Equations of Lines
/Classes/CalcII/EqnsOfPlanes.aspx12.3 Equations of Planes
/Classes/CalcII/QuadricSurface...12.4 Quadric Surfaces
/Classes/CalcII/MultiVrbleFcns...12.5 Functions of Several Variables
/Classes/CalcII/VectorFunction...12.6 Vector Functions
/Classes/CalcII/VectorFcnsCalc...12.7 Calculus with Vector Functions
/Classes/CalcII/TangentNormalV...12.8 Tangent, Normal and Binormal Vectors
/Classes/CalcII/VectorArcLengt...12.9 Arc Length with Vector Functions
/Classes/CalcII/Curvature.aspx12.10 Curvature
/Classes/CalcII/Velocity_Accel...12.11 Velocity and Acceleration
/Classes/CalcII/CylindricalCoo...12.12 Cylindrical Coordinates
/Classes/CalcII/SphericalCoord...12.13 Spherical Coordinates
/Classes/CalcIII/CalcIII.aspxText duplicate Calculus III
/Classes/CalcIII/3DSpace.aspxText duplicate 12. 3-Dimensional Space
/Classes/CalcIII/3DCoords.aspxText duplicate 12.1 The 3-D Coordinate System
/Classes/CalcIII/EqnsOfLines.aspxText duplicate 12.2 Equations of Lines
/Classes/CalcIII/EqnsOfPlanes....Text duplicate 12.3 Equations of Planes
/Classes/CalcIII/QuadricSurfac...Text duplicate 12.4 Quadric Surfaces
/Classes/CalcIII/MultiVrbleFcn...Text duplicate 12.5 Functions of Several Variables
/Classes/CalcIII/VectorFunctio...Text duplicate 12.6 Vector Functions
/Classes/CalcIII/VectorFcnsCal...Text duplicate 12.7 Calculus with Vector Functions
/Classes/CalcIII/TangentNormal...Text duplicate 12.8 Tangent, Normal and Binormal Vectors
/Classes/CalcIII/VectorArcLeng...Text duplicate 12.9 Arc Length with Vector Functions
/Classes/CalcIII/Curvature.aspxText duplicate 12.10 Curvature
/Classes/CalcIII/Velocity_Acce...Text duplicate 12.11 Velocity and Acceleration
/Classes/CalcIII/CylindricalCo...Text duplicate 12.12 Cylindrical Coordinates
/Classes/CalcIII/SphericalCoor...Text duplicate 12.13 Spherical Coordinates
/Classes/CalcIII/PartialDerivs...13. Partial Derivatives
/Classes/CalcIII/Limits.aspx13.1 Limits
/Classes/CalcIII/PartialDeriva...13.2 Partial Derivatives
/Classes/CalcIII/PartialDerivI...13.3 Interpretations of Partial Derivatives
/Classes/CalcIII/HighOrderPart...13.4 Higher Order Partial Derivatives
/Classes/CalcIII/Differentials...13.5 Differentials
/Classes/CalcIII/ChainRule.aspx13.6 Chain Rule
/Classes/CalcIII/DirectionalDe...13.7 Directional Derivatives
/Classes/CalcIII/PartialDerivA...14. Applications of Partial Derivatives
/Classes/CalcIII/TangentPlanes...14.1 Tangent Planes and Linear Approximations
/Classes/CalcIII/GradientVecto...14.2 Gradient Vector, Tangent Planes and Normal Lines
/Classes/CalcIII/RelativeExtre...14.3 Relative Minimums and Maximums
/Classes/CalcIII/AbsoluteExtre...14.4 Absolute Minimums and Maximums
/Classes/CalcIII/LagrangeMulti...14.5 Lagrange Multipliers
/Classes/CalcIII/MultipleInteg...15. Multiple Integrals
/Classes/CalcIII/DoubleIntegra...15.1 Double Integrals
/Classes/CalcIII/IteratedInteg...15.2 Iterated Integrals
/Classes/CalcIII/DIGeneralRegi...15.3 Double Integrals over General Regions
/Classes/CalcIII/DIPolarCoords...15.4 Double Integrals in Polar Coordinates
/Classes/CalcIII/TripleIntegra...15.5 Triple Integrals
/Classes/CalcIII/TICylindrical...15.6 Triple Integrals in Cylindrical Coordinates
/Classes/CalcIII/TISphericalCo...15.7 Triple Integrals in Spherical Coordinates
/Classes/CalcIII/ChangeOfVaria...15.8 Change of Variables
/Classes/CalcIII/SurfaceArea.aspx15.9 Surface Area
/Classes/CalcIII/Area_Volume.aspx15.10 Area and Volume Revisited
/Classes/CalcIII/LineIntegrals...16. Line Integrals
/Classes/CalcIII/VectorFields....16.1 Vector Fields
/Classes/CalcIII/LineIntegrals...16.2 Line Integrals - Part I
/Classes/CalcIII/LineIntegrals...16.3 Line Integrals - Part II
/Classes/CalcIII/LineIntegrals...16.4 Line Integrals of Vector Fields
/Classes/CalcIII/FundThmLineIn...16.5 Fundamental Theorem for Line Integrals
/Classes/CalcIII/ConservativeV...16.6 Conservative Vector Fields
/Classes/CalcIII/GreensTheorem...16.7 Green's Theorem
/Classes/CalcIII/SurfaceIntegr...17.Surface Integrals
/Classes/CalcIII/CurlDivergenc...17.1 Curl and Divergence
/Classes/CalcIII/ParametricSur...17.2 Parametric Surfaces
/Classes/CalcIII/SurfaceIntegr...17.3 Surface Integrals
/Classes/CalcIII/SurfIntVector...17.4 Surface Integrals of Vector Fields
/Classes/CalcIII/StokesTheorem...17.5 Stokes' Theorem
/Classes/CalcIII/DivergenceThe...17.6 Divergence Theorem
/Classes/DE/DE.aspxText duplicate Differential Equations
/Classes/DE/IntroBasic.aspx1. Basic Concepts
/Classes/DE/Definitions.aspx1.1 Definitions
/Classes/DE/DirectionFields.aspx1.2 Direction Fields
/Classes/DE/FinalThoughts.aspx1.3 Final Thoughts
/Classes/DE/IntroFirstOrder.aspx2. First Order DE's
/Classes/DE/Linear.aspx2.1 Linear Equations
/Classes/DE/Separable.aspx2.2 Separable Equations
/Classes/DE/Exact.aspx2.3 Exact Equations
/Classes/DE/Bernoulli.aspx2.4 Bernoulli Differential Equations
/Classes/DE/Substitutions.aspx2.5 Substitutions
/Classes/DE/IoV.aspx2.6 Intervals of Validity
/Classes/DE/Modeling.aspx2.7 Modeling with First Order DE's
/Classes/DE/EquilibriumSolutio...2.8 Equilibrium Solutions
/Classes/DE/EulersMethod.aspx2.9 Euler's Method
/Classes/DE/IntroSecondOrder.aspx3. Second Order DE's
/Classes/DE/SecondOrderConcept...3.1 Basic Concepts
/Classes/DE/RealRoots.aspx3.2 Real & Distinct Roots
/Classes/DE/ComplexRoots.aspx3.3 Complex Roots
/Classes/DE/RepeatedRoots.aspx3.4 Repeated Roots
/Classes/DE/ReductionofOrder.aspx3.5 Reduction of Order
/Classes/DE/FundamentalSetsofS...3.6 Fundamental Sets of Solutions
/Classes/DE/Wronskian.aspx3.7 More on the Wronskian
/Classes/DE/NonhomogeneousDE.aspx3.8 Nonhomogeneous Differential Equations
/Classes/DE/UndeterminedCoeffi...3.9 Undetermined Coefficients
/Classes/DE/VariationofParamet...3.10 Variation of Parameters
/Classes/DE/Vibrations.aspx3.11 Mechanical Vibrations
/Classes/DE/LaplaceIntro.aspx4. Laplace Transforms
/Classes/DE/LaplaceDefinition....4.1 The Definition
/Classes/DE/LaplaceTransforms....4.2 Laplace Transforms
/Classes/DE/InverseTransforms....4.3 Inverse Laplace Transforms
/Classes/DE/StepFunctions.aspx4.4 Step Functions
/Classes/DE/IVPWithLaplace.aspx4.5 Solving IVP's with Laplace Transforms
/Classes/DE/IVPWithNonConstant...4.6 Nonconstant Coefficient IVP's
/Classes/DE/IVPWithStepFunctio...4.7 IVP's With Step Functions
/Classes/DE/DiracDeltaFunction...4.8 Dirac Delta Function
/Classes/DE/ConvolutionIntegra...4.9 Convolution Integrals
/Classes/DE/Laplace_Table.aspx4.10 Table Of Laplace Transforms
/Classes/DE/SystemsIntro.aspx5. Systems of DE's
/Classes/DE/LA_Systems.aspx5.1 Review : Systems of Equations
/Classes/DE/LA_Matrix.aspx5.2 Review : Matrices & Vectors
/Classes/DE/LA_Eigen.aspx5.3 Review : Eigenvalues & Eigenvectors
/Classes/DE/SystemsDE.aspx5.4 Systems of Differential Equations
/Classes/DE/SolutionsToSystems...5.5 Solutions to Systems
/Classes/DE/PhasePlane.aspx5.6 Phase Plane
/Classes/DE/RealEigenvalues.aspx5.7 Real Eigenvalues
/Classes/DE/ComplexEigenvalues...5.8 Complex Eigenvalues
/Classes/DE/RepeatedEigenvalue...5.9 Repeated Eigenvalues
/Classes/DE/NonhomogeneousSyst...5.10 Nonhomogeneous Systems
/Classes/DE/SystemsLaplace.aspx5.11 Laplace Transforms
/Classes/DE/SystemsModeling.aspx5.12 Modeling
/Classes/DE/SeriesIntro.aspx6. Series Solutions to DE's
/Classes/DE/PowerSeries.aspx6.1 Review : Power Series
/Classes/DE/TaylorSeries.aspx6.2 Review : Taylor Series
/Classes/DE/SeriesSolutions.aspx6.3 Series Solutions
/Classes/DE/EulerEquations.aspx6.4 Euler Equations
/Classes/DE/IntroHigherOrder.aspx7. Higher Order Differential Equations
/Classes/DE/HOBasicConcepts.aspx7.1 Basic Concepts for nth Order Linear Equations
/Classes/DE/HOHomogeneousDE.aspx7.2 Linear Homogeneous Differential Equations
/Classes/DE/HOUndeterminedCoef...7.3 Undetermined Coefficients
/Classes/DE/HOVariationOfParam...7.4 Variation of Parameters
/Classes/DE/HOLaplaceTransform...7.5 Laplace Transforms
/Classes/DE/HOSystems.aspx7.6 Systems of Differential Equations
/Classes/DE/HOSeries.aspx7.7 Series Solutions
/Classes/DE/IntroBVP.aspx8. Boundary Value Problems & Fourier Series
/Classes/DE/BoundaryValueProbl...8.1 Boundary Value Problems
/Classes/DE/BVPEvals.aspx8.2 Eigenvalues and Eigenfunctions
/Classes/DE/PeriodicOrthogonal...8.3 Periodic Functions & Orthogonal Functions
/Classes/DE/FourierSineSeries....8.4 Fourier Sine Series
/Classes/DE/FourierCosineSerie...8.5 Fourier Cosine Series
/Classes/DE/FourierSeries.aspx8.6 Fourier Series
/Classes/DE/ConvergenceFourier...8.7 Convergence of Fourier Series
/Classes/DE/IntroPDE.aspx9. Partial Differential Equations
/Classes/DE/TheHeatEquation.aspx9.1 The Heat Equation
/Classes/DE/TheWaveEquation.aspx9.2 The Wave Equation
/Classes/DE/PDETerminology.aspx9.3 Terminology
/Classes/DE/SeparationofVariab...9.4 Separation of Variables
/Classes/DE/SolvingHeatEquatio...9.5 Solving the Heat Equation
/Classes/DE/HeatEqnNonZero.aspx9.6 Heat Equation with Non-Zero Temperature Boundaries
/Classes/DE/LaplacesEqn.aspx9.7 Laplace's Equation
/Classes/DE/VibratingString.aspx9.8 Vibrating String
/Classes/DE/PDESummary.aspx9.9 Summary of Separation of Variables
/Extras/AlgebraTrigReview/Alge...Text duplicate Algebra & Trig Review
/Extras/AlgebraTrigReview/Alge...1. Algebra
/Extras/AlgebraTrigReview/Expo...1.1 Exponents
/Extras/AlgebraTrigReview/Abso...1.2 Absolute Value
/Extras/AlgebraTrigReview/Radi...Text duplicate 1.3 Radicals
/Extras/AlgebraTrigReview/Rati...1.4 Rationalizing
/Extras/AlgebraTrigReview/Func...1.5 Functions
/Extras/AlgebraTrigReview/Mult...1.6 Multiplying Polynomials
/Extras/AlgebraTrigReview/Fact...1.7 Factoring
/Extras/AlgebraTrigReview/Simp...1.8 Simplifying Rational Expressions
/Extras/AlgebraTrigReview/Grap...1.9 Graphing and Common Graphs
/Extras/AlgebraTrigReview/Solv...1.10 Solving Equations, Part I
/Extras/AlgebraTrigReview/Solv...1.11 Solving Equations, Part II
/Extras/AlgebraTrigReview/Solv...1.12 Solving Systems of Equations
/Extras/AlgebraTrigReview/Solv...1.13 Solving Inequalities
/Extras/AlgebraTrigReview/Solv...1.14 Absolute Value Equations and Inequalities
/Extras/AlgebraTrigReview/Trig...2. Trigonometry
/Extras/AlgebraTrigReview/Trig...2.1 Trig Function Evaluation
/Extras/AlgebraTrigReview/Trig...2.2 Graphs of Trig Functions
/Extras/AlgebraTrigReview/Trig...2.3 Trig Formulas
/Extras/AlgebraTrigReview/Solv...2.4 Solving Trig Equations
/Extras/AlgebraTrigReview/Inve...2.5 Inverse Trig Functions
/Extras/AlgebraTrigReview/ExpL...3. Exponentials & Logarithms
/Extras/AlgebraTrigReview/Expo...3.1 Basic Exponential Functions
/Extras/AlgebraTrigReview/Loga...3.2 Basic Logarithm Functions
/Extras/AlgebraTrigReview/LogP...3.3 Logarithm Properties
/Extras/AlgebraTrigReview/Simp...3.4 Simplifying Logarithms
/Extras/AlgebraTrigReview/Solv...3.5 Solving Exponential Equations
/Extras/AlgebraTrigReview/Solv...3.6 Solving Logarithm Equations
/Extras/CommonErrors/CommonMat...Text duplicate Common Math Errors
/Extras/CommonErrors/GeneralEr...1. General Errors
/Extras/CommonErrors/AlgebraEr...2. Algebra Errors
/Extras/CommonErrors/TrigError...3. Trig Errors
/Extras/CommonErrors/CommonErr...4. Common Errors
/Extras/CommonErrors/CalculusE...5. Calculus Errors
/Extras/ComplexPrimer/ComplexN...Text duplicate Complex Number Primer
/Extras/ComplexPrimer/Definiti...1. The Definition
/Extras/ComplexPrimer/Arithmet...2. Arithmetic
/Extras/ComplexPrimer/Conjugat...3. Conjugate and Modulus
/Extras/ComplexPrimer/Forms.aspx4. Polar and Exponential Forms
/Extras/ComplexPrimer/Roots.aspx5. Powers and Roots
/Extras/StudyMath/HowToStudyMa...Text duplicate How To Study Math
/Extras/StudyMath/GeneralTips....1. General Tips
/Extras/StudyMath/TakingNotes....2. Taking Notes
/Extras/StudyMath/GettingHelp....3. Getting Help
/Extras/StudyMath/Homework.aspx4. Doing Homework
/Extras/StudyMath/ProblemSolvi...5. Problem Solving
/Extras/StudyMath/StudyForExam...6. Studying For an Exam
/Extras/StudyMath/TakingExam.aspx7. Taking an Exam
/Extras/StudyMath/Errors.aspx8. Learn From Your Errors
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tutorial.math.lamar.edu
Pauls Online Math Notes
Welcome to my math notes site. Contained in this site are the notes (free and downloadable) that I use to teach Algebra, Calculus (I, II and III) as well as Differential Equations at Lamar University. The notes contain the usual topics that are taught in those courses as well as a few extra topics that I decided to include just because I wanted to. There are also a set of practice problems, with full solutions, to all of the classes except Differential Equations. In addition there is also a selection of cheat sheets available for download.

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