tutorial.math.lamar.eduPauls Online Math Notes

-- Paul's Online Notes View Quick Nav Download This menu is only active after you have chosen one of the main topics (Algebra, Calculus or Differential Equations) from the Quick Nav menu to the right or Main Menu in the upper left corner. Classes Algebra Calculus I Calculus II Calculus III Differential Equations Extras Algebra & Trig Review Common Math Errors Complex Number Primer How To Study Math Cheat Sheets & Tables Misc Contact Me MathJax Help and Configuration My Students This menu is only active after you have chosen a topic from the Quick Nav menu to the left or Main Menu in the upper left corner. Print Page in Current Form (Default) Show all Solutions/Steps and Print Page Hide all Solutions/Steps and Print Page Home Classes Algebra Preliminaries Integer Exponents Rational Exponents Radicals Polynomials Factoring Polynomials Rational Expressions Complex Numbers Solving Equations and Inequalities Solutions and Solution Sets Linear Equations Applications of Linear Equations Equations With More Than One Variable Quadratic Equations - Part I Quadratic Equations - Part II Quadratic Equations : A Summary Applications of Quadratic Equations Equations Reducible to Quadratic in Form Equations with Radicals Linear Inequalities Polynomial Inequalities Rational Inequalities Absolute Value Equations Absolute Value Inequalities Graphing and Functions Graphing Lines Circles The Definition of a Function Graphing Functions Combining Functions Inverse Functions Common Graphs Lines, Circles and Piecewise Functions Parabolas Ellipses Hyperbolas Miscellaneous Functions Transformations Symmetry Rational Functions Polynomial Functions Dividing Polynomials Zeroes/Roots of Polynomials Graphing Polynomials Finding Zeroes of Polynomials Partial Fractions Exponential and Logarithm Functions Exponential Functions Logarithm Functions Solving Exponential Equations Solving Logarithm Equations Applications Systems of Equations Linear Systems with Two Variables Linear Systems with Three Variables Augmented Matrices More on the Augmented Matrix Nonlinear Systems Calculus I Review Functions Inverse Functions Trig Functions Solving Trig Equations Trig Equations with Calculators, Part I Trig Equations with Calculators, Part II Exponential Functions Logarithm Functions Exponential and Logarithm Equations Common Graphs Limits Tangent Lines and Rates of Change The Limit One-Sided Limits Limit Properties Computing Limits Infinite Limits Limits At Infinity, Part I Limits At Infinity, Part II Continuity The Definition of the Limit Derivatives The Definition of the Derivative Interpretation of the Derivative Differentiation Formulas Product and Quotient Rule Derivatives of Trig Functions Derivatives of Exponential and Logarithm Functions Derivatives of Inverse Trig Functions Derivatives of Hyperbolic Functions Chain Rule Implicit Differentiation Related Rates Higher Order Derivatives Logarithmic Differentiation Applications of Derivatives Rates of Change Critical Points Minimum and Maximum Values Finding Absolute Extrema The Shape of a Graph, Part I The Shape of a Graph, Part II The Mean Value Theorem Optimization More Optimization Problems L'Hospital's Rule and Indeterminate Forms Linear Approximations Differentials Newton's Method Business Applications Integrals Indefinite Integrals Computing Indefinite Integrals Substitution Rule for Indefinite Integrals More Substitution Rule Area Problem Definition of the Definite Integral Computing Definite Integrals Substitution Rule for Definite Integrals Applications of Integrals Average Function Value Area Between Curves Volumes of Solids of Revolution / Method of Rings Volumes of Solids of Revolution/Method of Cylinders More Volume Problems Work Extras Proof of Various Limit Properties Proof of Various Derivative Properties Proof of Trig Limits Proofs of Derivative Applications Facts Proof of Various Integral Properties Area and Volume Formulas Types of Infinity Summation Notation Constant of Integration Calculus II Integration Techniques Integration by Parts Integrals Involving Trig Functions Trig Substitutions Partial Fractions Integrals Involving Roots Integrals Involving Quadratics Integration Strategy Improper Integrals Comparison Test for Improper Integrals Approximating Definite Integrals Applications of Integrals Arc Length Surface Area Center of Mass Hydrostatic Pressure Probability Parametric Equations and Polar Coordinates Parametric Equations and Curves Tangents with Parametric Equations Area with Parametric Equations Arc Length with Parametric Equations Surface Area with Parametric Equations Polar Coordinates Tangents with Polar Coordinates Area with Polar Coordinates Arc Length with Polar Coordinates Surface Area with Polar Coordinates Arc Length and Surface Area Revisited Series & Sequences Sequences More on Sequences Series - The Basics Convergence/Divergence of Series Special Series Integral Test Comparison Test/Limit Comparison Test Alternating Series Test Absolute Convergence Ratio Test Root Test Strategy for Series Estimating the Value of a Series Power Series Power Series and Functions Taylor Series Applications of Series Binomial Series Vectors Vectors - The Basics Vector Arithmetic Dot Product Cross Product 3-Dimensional Space The 3-D Coordinate System Equations of Lines Equations of Planes Quadric Surfaces Functions of Several Variables Vector Functions Calculus with Vector Functions Tangent, Normal and Binormal Vectors Arc Length with Vector Functions Curvature Velocity and Acceleration Cylindrical Coordinates Spherical Coordinates Calculus III 3-Dimensional Space The 3-D Coordinate System Equations of Lines Equations of Planes Quadric Surfaces Functions of Several Variables Vector Functions Calculus with Vector Functions Tangent, Normal and Binormal Vectors Arc Length with Vector Functions Curvature Velocity and Acceleration Cylindrical Coordinates Spherical Coordinates Partial Derivatives Limits Partial Derivatives Interpretations of Partial Derivatives Higher Order Partial Derivatives Differentials Chain Rule Directional Derivatives Applications of Partial Derivatives Tangent Planes and Linear Approximations Gradient Vector, Tangent Planes and Normal Lines Relative Minimums and Maximums Absolute Minimums and Maximums Lagrange Multipliers Multiple Integrals Double Integrals Iterated Integrals Double Integrals over General Regions Double Integrals in Polar Coordinates Triple Integrals Triple Integrals in Cylindrical Coordinates Triple Integrals in Spherical Coordinates Change of Variables Surface Area Area and Volume Revisited Line Integrals Vector Fields Line Integrals - Part I Line Integrals - Part II Line Integrals of Vector Fields Fundamental Theorem for Line Integrals Conservative Vector Fields Green's Theorem Surface Integrals Curl and Divergence Parametric Surfaces Surface Integrals Surface Integrals of Vector Fields Stokes' Theorem Divergence Theorem Differential Equations Basic Concepts Definitions Direction Fields Final Thoughts First Order DE's Linear Equations Separable Equations Exact Equations Bernoulli Differential Equations Substitutions Intervals of Validity Modeling with First Order DE's Equilibrium Solutions Euler's Method Second Order DE's Basic Concepts Real & Distinct Roots Complex Roots Repeated Roots Reduction of Order Fundamental Sets of Solutions More on the Wronskian Nonhomogeneous Differential Equations Undetermined Coefficients Variation of Parameters Mechanical Vibrations Laplace Transforms The Definition Laplace Transforms Inverse Laplace Transforms Step Functions Solving IVP's with Laplace Transforms Nonconstant Coefficient IVP's IVP's With Step Functions Dirac Delta Function Convolution Integrals Table Of Laplace Transforms Systems of DE's Review : Systems of Equations Review : Matrices & Vectors Review : Eigenvalues & Eigenvectors Systems of Differential Equations Solutions to Systems Phase Plane Real Eigenvalues Complex Eigenvalues Repeated Eigenvalues Nonh...