Mathematics
• Exploring Precalculus
• Precalculus Bookshelf
• Precalculus Textbook
• Tangent Lines and Rates of Change
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• Analysis Bookshelf
• Calculating Limits
• Computing Limits
• Continuity
• Continuity
• Continuity of Functions of One Variable
• Definition of the Limit
• Determining Limits Using L'Hopital's Rule
• Indeterminate Forms and L'Hopital's Rule
• Infinite Limits
• Limits
• Limit Definition of a Definite Integral
• Limits of Exponential Functions
• Limit of a Function
• Limits of a Function as x Approaches a Constant
• Limits of a Function as x Approaches Plus or Minus Infinity
• Limits at Infinity, Part I
• Limits at Infinity, Part II
• Limits Involving Infinity
• Limit Properties
• One-Sided Limits
• Precises Limits of a Function as x Approaches a Constant
• Proof of Trig Limits
• Proof of Various Limit Properties
• Squeeze Principle
• Types of Infinity
• Top of Page
• Basic Differentiation Formulas
• Chain Rule
• Chain Rule
• Chain Rule
• Definition of Derivative
• Derivative Calculator
• Derivatives of Exponential and Logarithmic Functions
• Derivatives of Inverse Functions
• Derivatives of Exponential and Logarithmic Functions Proofs
• Derivative as a Function
• Derivatives of Hyperbolic Functions
• Derivatives of Logarithmic and Exponential Functions
• Derivatives of Inverse Trig Functions
• Derivatives of Inverse Trig Functions Proofs
• Derivatives and Rates of Change
• Derivatives Rules Proofs
• Derivatives of Trig Functions
• Derivatives of Trig Functions Proofs
• Derivatives Using the Limit Definition
• Differentiation Formulas
• Differentiation of Inverse Trigonometric Functions
• Differentiation of Trigonometric Functions
• Differentiation Using the Chain Rule
• Differentiation Using the Product Rule
• Differentiation Using the Quotient Rule
• Graphing Functions Using First and Second Derivatives
• Higher Order Derivatives
• Implicit Differentiation
• Implicit Differentiation
• Interpretation of Derivative
• Logarithmic Differentiation
• Logarithmic Differentiation
• Maximum and Minimum Values
• Maximum and Minimum Values Using Derivatives
• Product and Quotient Rules
• Product and Quotient Rules
• Quotient Rule
• Proof of Various Derivative Properties
• Related Rates
• Top of Page
• Applications of Maximum and Minimum Values
• Critical Points
• Curve Sketching
• Derivatives and the Shapes of Graphs
• Finding Absolute Extrema
• Implicit Differentiation Problems
• Instantaneous Velocity and Related Rates
• L'Hospital's Rule and Indeterminant Forms
• Linear Approximations
• Logistic Functions
• Logistic Functions Examples
• Maximum and Minimum Problems
• Minimum and Maximum Values
• Mean Value Theorem
• Mean Value Theorem
• Newton's Method
• Optimization Problems
• Optimization Problems, Part I
• Optimization Problems, Part II
• Proofs of Derivative Applications
• Rates of Change
• Shape of a Graph, Part I
• Shape of a Graph, Part II
• Top of Page
• Bernoulli Differential Equations
• Definitions
• Differentials
• Differential Equations Bookshelf
• Differential Equations Notes
• Direction Fields
• Equilibrium Solutions
• Euler's Method
• Exact Equations
• Intervals of Validity
• Linear First Order Differential Equations
• Modeling with First Order Differential Equations
• Separable Equations
• Substitutions
• Top of Page
• Basic Concepts
• Complex Roots
• Euler Equations
• Fundamental Sets of Solutions
• Non-Homogeneous
• Variation of Parameters
• Undetermined Coefficients
• Wronskian
• Real Roots
• Repeated Roots
• Reduction of Order
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• Homogeneous Linear Higher Order Differential Equations
• Undetermined Coefficients
• Variation of Parameters
• Top of Page
• Linear Approximations and Differentials
• Mechanical Vibrations
• Top of Page
• Complex Eigenvalues
• Differential Equations
• Eigenvalues and Eigenvectors
• Modeling with DEs
• Non-homogeneous Systems
• Phase Plane
• Real Eigenvalues
• Repeated Eigenvalues
• Solutions to Systems
• Systems of Differential Equations
• Top of Page
• Heat Equation
• Heat Equation with Non-zero Temperature Boundaries
• Laplace's Equation
• Separation of Variables
• Solving the Heat Equation
• Terminology for Separation of Variables
• Vibrating String
• Wave Equation
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• Convolution Integral
• Dirac Delta Function
• Inverse Laplace Transforms
• IVPs with Step Functions
• Laplace Transforms
• Laplace Transform Definition
• Non-constant Coefficient IVPs
• Solving IVPs
• Step Functions
• Table of Laplace Transforms
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• Boundary Value Problems
• Convergence of Fourier Series
• Fourier Series
• Fourier Cosine Serices
• Fourier Sine Series
• Periodic Functions and Orthogonal Functions
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• Calculus Bookshelf
• Calculus I Review and Practice Problems
• Calculus II Review and Practice Problems
• Calculus III Review and Practice Problems
• Common Calculus Errors
• eCalculus Resources for the Calculus Student
• Fundamental Theorem of Calculus
• MIT Open Courseware Calculus Textbook
• Top of Page