You CAN Ace Calculus

### Calculus Topics Listed Alphabetically

Single Variable Calculus

 Absolute Convergence Alternating Series Arc Length Area Under Curves Chain Rule Concavity Conics Conics in Polar Form Conditional Convergence Continuity & Discontinuities Convolution, Laplace Transforms Cosine/Sine Integration Critical Points Cylinder-Shell Method - Volume Integrals Definite Integrals Derivatives Differentials Direct Comparison Test Divergence (nth-Term) Test
 Ellipses (Rectangular Conics) Epsilon-Delta Limit Definition Exponential Derivatives Exponential Growth/Decay Finite Limits First Derivative First Derivative Test Formal Limit Definition Fourier Series Geometric Series Graphing Higher Order Derivatives Hyperbolas (Rectangular Conics) Hyperbolic Derivatives
 Implicit Differentiation Improper Integrals Indeterminate Forms Infinite Limits Infinite Series Infinite Series Table Infinite Series Study Techniques Infinite Series, Choosing a Test Infinite Series Exam Preparation Infinite Series Exam A Inflection Points Initial Value Problems, Laplace Transforms Integral Test Integrals Integration by Partial Fractions Integration By Parts Integration By Substitution Intermediate Value Theorem Interval of Convergence Inverse Function Derivatives Inverse Hyperbolic Derivatives Inverse Trig Derivatives
 Laplace Transforms L'Hôpital's Rule Limit Comparison Test Limits Linear Motion Logarithm Derivatives Logarithmic Differentiation Moments, Center of Mass Mean Value Theorem Normal Lines One-Sided Limits Optimization
 p-Series Parabolas (Rectangular Conics) Parabolas (Polar Conics) Parametric Equations Parametric Curves Parametric Surfaces Pinching Theorem Polar Coordinates Plane Regions, Describing Power Rule Power Series Product Rule
 Quotient Rule Radius of Convergence Ratio Test Related Rates Related Rates Areas Related Rates Distances Related Rates Volumes Remainder & Error Bounds Root Test Secant/Tangent Integration Second Derivative Second Derivative Test Shifting Theorems Sine/Cosine Integration Slope and Tangent Lines Square Wave Surface Area
 Tangent/Secant Integration Taylor/Maclaurin Series Telescoping Series Trig Derivatives Trig Integration Trig Limits Trig Substitution Unit Step Function Unit Impulse Function Volume Integrals Washer-Disc Method - Volume Integrals Work

Multi-Variable Calculus

 Acceleration Vector Arc Length (Vector Functions) Arc Length Function Arc Length Parameter Conservative Vector Fields Cross Product Curl Curvature Cylindrical Coordinates
 Directional Derivatives Divergence (Vector Fields) Divergence Theorem Dot Product Double Integrals - Area & Volume Double Integrals - Polar Coordinates Double Integrals - Rectangular Gradients Green's Theorem
 Lagrange Multipliers Line Integrals Partial Derivatives Partial Integrals Path Integrals Potential Functions Principal Unit Normal Vector
 Spherical Coordinates Stokes' Theorem Surface Integrals Tangent Planes Triple Integrals - Cylindrical Triple Integrals - Rectangular Triple Integrals - Spherical
 Unit Tangent Vector Unit Vectors Vector Fields Vectors Vector Functions Vector Functions Equations

Differential Equations

 Boundary Value Problems Bernoulli Equation Cauchy-Euler Equation Chebyshev's Equation Chemical Concentration Classify Differential Equations Differential Equations Euler's Method Exact Equations Existence and Uniqueness Exponential Growth/Decay
 First Order, Linear Fluids, Mixing Fourier Series Inhomogeneous ODE's Integrating Factors, Exact Integrating Factors, Linear Laplace Transforms, Solve Initial Value Problems Linear, First Order Linear, Second Order Linear Systems
 Partial Differential Equations Polynomial Coefficients Population Dynamics Projectile Motion Reduction of Order Resonance
 Second Order, Linear Separation of Variables Slope Fields Stability Substitution Undetermined Coefficients Variation of Parameters Vibration Wronskian

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17calculus > calculus notation

Using correct notation is extremely important in calculus. If you truly understand calculus, you will use correct notation. Take a few extra minutes to notice and understand notation whenever you run across a new concept. Start using correct notation from the very first.

You may not think this is important. However, if your teacher doesn't require correct notation now, you may (and probably will) get a calculus teacher in the future that WILL require correct notation. And it is easier to learn it correctly from the first than have to correct your notation later, after you have been doing it incorrectly for a while.

This brings up another point. Many teachers don't encourage you to learn math that you can use. It is easier as a teacher to get you to parrot back what they say than it is to teach you so that you learn. So, no matter what kind of teacher you get (good or bad), it is up to you to learn math. Take that responsibility yourself. If you do, you will be able to learn on your own. When you are in college, this is the time to start learning without needing a teacher to teach you. Doing so will free you to enjoy learning.

Simplifying

Every teacher has their own idea on what they think simplifying is and usually their idea is based on what they are teaching at the time. Sometimes, simplifying means multiplying out. Sometimes it means factoring. If your teacher asks you to simplify your answer, it is good to ask them to explain what they mean by simplifying. You will find in calculus, most teachers want you to simplify your answer by factoring and canceling common terms in fractions. That is the standard this site follows.

Use of The Greek Alphabet in Mathematics

The use of greek letters is widespread in calculus. You probably saw it a lot in trig to represent angles. Greek letters are also used in limits and all throughout calculus. When you see greek letters or any other kind of unusual use of notation, it is best not to change the variables to something you are familiar with. You are probably used to using $$x$$ as a variable from algebra. However, you need to get used to using greek letters. A good teacher will encourage this by taking off points if you change notation to something you are familiar with. You need to learn the new notation to succeed in calculus. And it's not that hard.

As you continue on in calculus and higher math, you will find that most mathematicians use the same or similar variables in similar contexts. This means variables are not just chosen randomly. They usually carry some meaning along with them. Here is a rundown on what some of them usually mean. However, this list is not cast in stone. You may occasionally find mathematicians or contexts that depart from this list.

Letter(s)[1]

Usual Meaning (depending on the context)

θ, α, γ

Angles

δ, ε

Very small (usually positive) numbers

Δ

Indicates change in a variable; often written as Δx; this is not Δ times x but is one variable and written this way to indicate a change in another variable x.

λ, μ

Parameters in parametric equations

[1] Hover your cursor over a letter in the first column to reveal it's name and case.