Functions

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1

What Are Functions in Math?

2

Why Are Functions Important in Real Life?

3

What Is the Definition of a Function?

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What Is a Coordinate System?

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What Are Function Tables?

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How to Find x and y Values of a Function

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How to Calculate Domain and Range in Math

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How to Calculate and Interpret Intersection Points

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How to Calculate Zeros or Roots of a Function

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What Are Linear Functions?

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How Are Linear Functions Used in Real Life?

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What Makes a Function Proportional?

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What Are Quadratic Functions?

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What Are Polynomial Functions?

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What Are Exponential Functions?

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Exponential Functions with Euler's Number

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What Does Inversely Proportional Mean in Math?

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What Are Power and Root Functions?

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What Are Logarithmic Functions?

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What Are Rational Functions?

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Calculate and Interpret Average Rate of Change in Math

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What Is the Point-Slope Equation?

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Interpret and Find Instantaneous Rate of Change in Math

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How to Approximate Instantaneous Rate of Change in Math

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How to Interpret and Calculate Limits of a Function

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How Do You Determine Continuity of a Function?

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How to Interpret and Calculate Asymptotes of a Function

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What Does the Definition of the Derivative Mean?

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How Do You Determine if a Function Is Differentiable?

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Rules of Differentiation for Finding Derivatives

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How Does the Chain Rule for Differentiation Work?

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How to Find Derivatives using the Product Rule

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How to Differentiate Functions Using the Quotient Rule

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Make Sign Charts of the Derivatives of a Function

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Derivation of Distance to Get Velocity and Acceleration

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What Are Stationary Points of a Function?

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How to Calculate the Curvature of a Function

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What Are Inflection Points of a Function?

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How to Analyze Polynomial Functions

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How to Analyze Logarithmic Functions

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How to Analyze Power Functions

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How to Analyze the Cosine Function

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Analyzing Exponential Functions

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What Are Riemann Sums Used for?

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What Are the Important Integration Rules?

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Which Basic Relations in Integration Should You Know?

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How to Interpret and Calculate the Definite Integral

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How to Interpret and Calculate the Indefinite Integral

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How to Use the Formula for Integration by Parts

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How to Do Integration by Substitution

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Use Partial Fraction Decomposition for Integration

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How to Find the Area Between Two Graphs by Integration

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How to Use Solids of Revolution to Find Volumes

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What Is a Differential Equation?

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What Are Integral Curves and Direction Fields Used for?

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What Can Differential Equations Be Used for?

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What Are First Order Differential Equations?

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First Order Differential Equations with Constant Coefficients

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First Order Differential Equations with Initial Conditions

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How to Solve Exact First Order Differential Equations

A differential equation is exact if you can integrate the right-hand side and the left-hand side directly. This is the simplest type of differential equations.

Rule

Exact Differential Equations

y^{'} = f (x) \Rightarrow y = \int f (x) d x + C

Example 1

Solve the differential equation $y^{'} = \frac{1}{x} + 2 x$

\begin{array}{l} y & = \int y^{'} d x \\ = \int \frac{1}{x} + 2 x d x \\ = \ln | x | + x^{2} + C \end{array}

\begin{array}{l} y = \int y^{'} d x = \int \frac{1}{x} + 2 x d x = \ln | x | + x^{2} + C \end{array}

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61

How to Write and Solve Separable Differential Equations

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Integrating Factor Method for Differential Equations

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Logistic Growth and Carrying Capacity of a Population

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What Are Second Order Differential Equations?

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How to Solve Exact Second Order Differential Equations

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Homogeneous Second Order Differential Equations with Constant Coefficients

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Second Order Differential Equations with Initial Conditions

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Verify Solutions to Second Order Differential Equations

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Find the Equation of a Tangent Line of a Function

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The Differential Equation for Harmonic Oscillators

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Reduction of Order Method for Differential Equations

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What Does Mathematical Modeling Mean?

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What Is Mathematical Regression?

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The Difference Between Interpolation and Extrapolation

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What Are Linear Models?

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What Are Quadratic Models?

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What Are Exponential Models?

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What Are Power Models in Math?

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What Are Logistic Models Used For?

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What Are Cubic Models in Math?

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What Are Trigonometric Models?

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What Does the Feasible Region in Optimization Mean?

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How to Use the Graphical Method for Linear Optimization

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How to Use the Ruler Method for Linear Optimization