Calculus
Calculus is concerned with change and motion; it deals with the quantities that approach other quantities.
Sir Isaac Newton invented his version of calculus in order to explain the motion of planets around the sun. Today, calculus is used in calculating the orbits of satellites and spacecrafts, in predicting population sizes, in estimating how fast prices rise, in forecasting weather, in calculating life insurance premiums, and in many other areas.
Differential Calculus
The study of differential calculus is concerned with how one quantity changes in relation to another quantity. The central concept of differential calculus is the derivative .
Introduction to Calculus The Limits of a Function – Definition and Techniques to find Limits
Derivatives – Definition and Slope of Tangent
Power Rule – Constant Multiple Rule, Sum Rule, Difference RuleProduct Rule – Find the derivative of the product of two functionsQuotient Rule - Find the derivative of the quotient of two functions
Chain Rule - Find the derivative of composite functions More Chain Rule Examples
Derivative Rules - Product Rule, Quotient Rule, Chain Rule, Power Rule, Exponential and Logarithmic Functions, Trigonometric Functions, Inverse Trigonometric Functions, Hyperbolic Functions and Inverse Hyperbolic Functions
Examples using the Derivative Rules More Examples using the Derivative Rules
Trigonometrc Derivatives - Derivatives of sin, cos, tan, scs, sec, cot More Derivatives Involving Trigonometric Functions
Inverse Trigonometric Derivatives - Derivatives of the inverse of sin, cos, tan, scs, sec, cot
Trigonometric Substitution Videos Deriving the Derivative Formulas for Tan, Cot, Sec, Cosecant, Arctan
Derivatives of Exponential Functions - Derivatives of ex ax , a g (x )
Derivative of the Natural Log - Derivatives of ln(x ), ln[g(x )]Examples of Logarithmic Differentiation
Implicit Differentiation - Find the derivatives of non-functions Examples using Implicit Differentiation
Second Derivative and Higher Derivatives - Find the derivatives of derivatives and their applications
Maxima and Minima - Maximum amd Minimum Values, Fermat's Theorem, Critical Number, Extreme Value Theorem, Closed Interval Method Maximum and Minimum Videos
Finding Critical Numbers
Derivative Test - First Derivative Test, Second Derivative Test, Minima, Maxima, Increasing/Decreasing Test
Concavity Problems I - Analyze functions through increasing, decreasing, concavity, inflection points, critical points, and extremum Concavity Problems II - Analyze functions through increasing, decreasing, concavity, inflection points, critical points, and extremum
Curve Sketching using Calculus
Mean Value Theorem - What is Mean Value Theorem?
Asymptotes - Vertical Asymptote, Horizontal Asymptote, Oblique Asymptote
Hyperbolic Functions - Hyperbolic Identities, Derivatives of Hyperbolic Functions and Derivatives of Inverse Hyperbolic Functions
L'Hopitals Rule - Indeterminate Quotients, Product, Differences, and Power
Optimization Problems using Derivatives More Optimization Problems using Derivatives
Related Rates using Derivatives More Related Rates using Derivatives
Newton's Method - Used to approximate a root
Integral Calculus
Antiderivative - Formulas for powers of x , trigonometric functions, exponential functions
Definite Integral - Area, Riemann Sum, Properties of Definte Integral Approximating Integrals - using Rectangles, Trapezoid Rule, Simpsons RuleCalculating a Definite Integral Using Riemann Sums
The Fundamental Theorem of Calculus - What is the Fundamental Theorem of Calculus?
Indefinite Integrals - Integral Notation, Integral Formulas Improper Integrals
Integration by Parts - Formula and Examples Integration by Parts Examples
Integration using U-Substitution
Integration using Partial Fractions Long Partial Fractions Problem - Repeated Irreducible Quadratic Factors
Integrating Exponential Functions Integrating Hyperbolic Functions
Trigonometric Integrals - Integration of the Powers of Sine, Cosine, Tangent and Secant
Integration using Inverse Trigonometric Functions
Integral Test - To determine whether a series is convergent or divergent
Area under a Curve - Calculate area under a curve and between two curves. Centroids/Center of Mass - Calculate the Centroid of a Region
Volume of Revolution - Cylindrical ShellsVolume of Revolution - Disk/Washers
Work Done using Calculus - Tank ProblemWork Done using Calculus - Cable/Rope Problem, Spring Problem
Laplace Transform - Basic Idea and Properties Laplace Transform - Proof and Tables Laplace Transform
Inverse Laplace Transform I Inverse Laplace Transform II
Solutions to Sample Questions
The following are solutions to sample questions of the CollegeBoard AP/AB and AP/BC Calculus examination
AP / AB Calculus Free Response Question AP / AB Calculus Test - Sample Questions 1 to 8 AP / AB Calculus Test - Sample Questions 9 to 16 AP / AB Calculus Test - Sample Questions 17 to 24 AP / AB Calculus Test - Sample Questions 25 to 28
AP / BC Calculus Test - Sample Questions 1 to 8 AP / BC Calculus Test - Sample Questions 9 to 16
Sequences and Series Videos
Arithmetic Sequences and Series Review Geomertic Sequences and Series Review
Absolute Convergence, Conditional Convergence and Divergence
Alternating Series Binomial Series Geometric Series and the Test for Divergence Integral Test Limit Comparison Test and Direct Comparison Test Partial Sums: Showing a Series Diverges Power Series Ratio Test Taylor and Maclaurin Series More Taylor and Maclaurin Series Telescoping Series
Parametric Curves and Polar Coordinates
Parametric Curves Calculus with Parametric Curves Polar Coordinates Calculus and Area in Polar Coordinates Graphing Polar Curves
Multivariable Calculus Videos
Vectors and the Geometry of Space
Three-Dimensional Coordinate System Vectors - Domains and Limits The Dot Product The Cross Product Vector Equation of a Line Equation of a Plane Intersection of a Line and Plane Cylinders and Quadric Surfaces Cylindrical and Spherical Coordinates
Vector Functions
Vector Functions Derivatives of Vector Functions Arc Length of Vector Functions
Partial Derivatives
Partial Derivatives Implicit Differentiation Tangent Planes and Linear Approximations The Chain Rule Directional Derivatives and the Gradient Vector Maximum and Minimum Values Absolute Maximum/Minimum Values of Multivariable Functions Lagrange Multipliers
Multiple Integrals
Double Integrals Iterated Integrals Double Integrals over General Regions Double Integrals in Polar Coordinates Applications of Double Integrals Triple Integrals Triple Integrals in Spherical Coordinates Change of Variables in Multiple Integrals
Vector Calculus
Vector Fields Line Integrals Applications of Line Integrals The Fundamental Theorem for Line Integrals Green's Theorem Curl of a Vector Field Use of Curl to Show that a Vector Field is Conservative Divergence of a Vector Field Surface Integrals
Differential Equations
Introduction to differential equations Exact Equations Intuition Integrating factors First Order Linear Differential Equations First Order Homogenous Differential Equations 2nd Order Linear Homogeneous Differential Equations Homogeneous Second-Order Differential Equations Non-homogeneous Second-Order Differential Equations Homogeneous Differential Equations -
Change of Variables Complex roots of the characteristic equations Repeated roots of the characteristic equation Undetermined Coefficients Laplace Transform 1 Laplace Transform 2 Laplace Transform to solve an equation Laplace Transform of : L{t} n : L{tn } Laplace Transform of the Unit Step Function Dirac Delta Function Introduction to the Convolution
Videos
Big Picture of Calculus
Big Picture: Derivatives
Big Picture: Integrals
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