Mathematics
Calculus I

Exploring Precalculus
Precalculus Textbook
Tangent Lines and Rates of Change
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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
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Basic Differentiation Formulas
Chain Rule
Chain Rule
Chain Rule
Definition of Derivative
Derivatives of Exponential and Logarithmic 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
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Applications of Maximum and Minimum Values
Business Applications
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
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Bernoulli Differential Equations
Definitions
Differentials
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
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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
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Linear Approximations and Differentials
Mechanical Vibrations
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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
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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 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
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