Paul Dawkins
Paul's Online Notes: Algebra: Systems of Equations
Learners examine how to solve systems of equations. Topics investigated are linear systems with two variables, linear systems with three variables, augmented matrices, and nonlinear systems. Class notes, definitions, and examples with...
Paul Dawkins
Paul's Online Notes: Calculus I: Review
Learners review the algebra and trigonometric skills needed in a Calculus course. Topics investigated are solving trigonometric equations, logarithmic functions, exponential functions, functions, and common graphs. Class notes,...
Paul Dawkins
Paul's Online Notes: Calculus I: Limits
Learners explore limits. Topics investigated are continuity, limits at infinity, limit properties, tangent lines, and rates of change. Class notes, definitions, and examples with detailed solutions are included. The class notes are...
Paul Dawkins
Paul's Online Notes: Calculus I: Derivatives
Learners examine derivatives. Topics investigated are product rule, chain rule, derivatives of trigonometric functions, the definition of the derivative, and related rates. Class notes, definitions, and examples with detailed solutions...
Paul Dawkins
Paul's Online Notes: Calculus I: Applications of Derivatives
Learners examine applications of derivatives. Topics investigated are rates of change, the mean value theorem, optimization problems, critical points, linear approximations, and Newton?s method. Class notes, definitions, and examples...
Paul Dawkins
Paul's Online Notes: Calculus I: Integrals
The tutorial investigates integrals. Topics discussed are indefinite integrals, area problems, definite integrals, and the substitution rule. Class notes, definitions, and examples with detailed solutions are included. The class notes...
Paul Dawkins
Paul's Online Notes: Calculus I: Applications of Integrals
The tutorial investigates applications of integrals. Topics discussed are average function value, area between two curves, volumes of solids of revolution, and work. Class notes, definitions, and examples with detailed solutions are...
Paul Dawkins
Paul's Online Notes: Calculus I: Proof of Various Limit Properties
The tutorial proves some of the basic properties and facts about limits. Topics discussed are limit properties, triangle inequality, continuity, and limits at infinity. Class notes, definitions, and examples with detailed solutions are...
Paul Dawkins
Paul's Online Notes: Calculus I: Proof of Various Derivative Properties
The tutorial examines various derivative facts, formulas, and properties. Topics discussed are the definition of derivative, implicit differentiation, logarithmic differentiation, chain rule, and power rule. Class notes, proofs, and...
Paul Dawkins
Paul's Online Notes: Calculus I: Proof of Trig Limits
The tutorial investigates the squeeze theorem. Class notes, definitions, and examples with detailed solutions are included. The class notes are available in pdf format.
Paul Dawkins
Paul's Online Notes: Calculus I: Proofs of Derivative Applications Facts
The tutorial consists of proofs of derivative applications. Topics discussed are Fermat?s theorem, mean value theorem, and Rolle?s theorem. Class notes, definitions, and examples with detailed solutions are included. The class notes are...
Paul Dawkins
Paul's Online Notes: Calculus I: Proof of Various Integral Properties
The tutorial examines proofs of several properties of integrals. Topics discussed are the fundamental theorem of calculus, extreme value theorem, work, and mean value theorem. Class notes, proofs, and examples with detailed solutions are...
Paul Dawkins
Paul's Online Notes: Calculus I: Area and Volume Formulas
The tutorial examines the area between two curves and the volume of a solid of revolution. The class notes are available in pdf format.
Paul Dawkins
Paul's Online Notes: Calculus I: Types of Infinity
The tutorial examines types of infinity. Class notes, definitions, and an additional resource are included. The notes are available in pdf format.
Paul Dawkins
Paul's Online Notes: Calculus I: Summation Notation
The tutorial reviews summation notation. Topics discussed are the properties and formulas for summation notation. Class notes, definitions, and examples with detailed solutions are included. The notes are available in pdf format.
Paul Dawkins
Paul's Online Notes: Calculus I: Constants of Integration
The resource examines the constant of integration. Class notes, methods, and examples with detailed solutions are included. The notes are available in pdf format.
Paul Dawkins
Paul's Online Notes: Calculus Ii: Integration Techniques
The resource examines various integration techniques. Topics investigated are integration by parts, partial fractions, comparison test, and trigonometric substitutions. Class notes, definitions, and examples with detailed solutions are...
Paul Dawkins
Paul's Online Notes: Calculus Ii: Applications of Integrals
The resource examines applications of integration. Topics investigated are arc length, surface area, center of mass, hydrostatic pressure, and probability density functions. Class notes, definitions, and examples with detailed solutions...
Paul Dawkins
Paul's Online Notes: Calculus Ii: Parametric Equations and Polar Coordinates
The resource examines parametric equations and polar coordinates. Topics investigated are parametric curves, area with parametric equations, arc length with polar coordinates, and surface area with polar coordinates. Class notes,...
Paul Dawkins
Paul's Online Notes: Calculus Ii: Series and Sequences
The resource examines sequences and infinite series. Topics investigated are power series, convergence, comparison test, integral test, ratio test, and Taylor series. Class notes, definitions, and examples with detailed solutions are...
Paul Dawkins
Paul's Online Notes: Calculus Ii: Vectors
The resource examines vectors and their properties. Topics investigated are vector, vector arithmetic, dot product, and cross product. Class notes, definitions, and examples with detailed solutions are included. The notes are available...
Paul Dawkins
Paul's Online Notes: Calculus Iii: Partial Derivatives
The resource examines partial derivatives. Topics investigated are limits, higher order partial derivatives, chain rule, and directional derivatives. Class notes, definitions, and examples with detailed solutions are included. The notes...
Paul Dawkins
Paul's Online Notes: Calculus Iii: Applications of Partial Derivatives
The resource examines applications of partial derivatives. Topics investigated are tangent planes, linear approximation, gradient vector, and Lagrange multipliers. Class notes, definitions, and examples with detailed solutions are...
Paul Dawkins
Paul's Online Notes: Calculus Iii: Multiple Integrals
The resource examines applications of partial derivatives. Topics investigated are double integrals, triple integrals, surface area, and iterated integrals. Class notes, definitions, and examples with detailed solutions are included. The...