Need some Calculus help? What is Calculus? Calculus is concerned with change and motion; it deals with the quantities that approach certain values.
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.
The topics covered are: Differential Calculus, Integral Calculus, Sequences and Series, Parametric Curves and Polar Coordinates, Multivariable Calculus, and Differential Equations.
AP Calculus AB 2021 Free Response Solutions
AP Calculus AB 2019 Free Response Solutions
AP Calculus AB 2018 Free Response Solutions
AP Calculus AB 2017 Free Response Solutions
AP Calculus AB 2016 Free Response Solutions
AP Calculus AB 2015 Free Response Solutions
AP Calculus AB 2014 Free Response Solutions
AP Calculus AB 2013 Free Response Solutions
AP Calculus AB 2012 Free Response Solutions
AP Calculus AB 2011 Free Response Solutions
AP Calculus AB 2003 Free Response Solutions
AP Calculus BC 2021 Free Response Solutions
AP Calculus BC 2019 Free Response Solutions
AP Calculus BC 2018 Free Response Solutions
AP Calculus BC 2017 Free Response Solutions
AP Calculus BC 2016 Free Response Solutions
AP Calculus BC 2015 Free Response Solutions
AP Calculus BC 2014 Free Response Solutions
AP Calculus AB 2016 Multiple Choice Solutions
AP Calculus AB 2015 Multiple Choice Solutions
AP Calculus AB 2013 Multiple Choice Solutions Part A
AP Calculus AB 2013 Multiple Choice Solutions Part B
AP Calculus AB 2012 Multiple Choice Solutions Part A
AP Calculus AB 2012 Multiple Choice Solutions Part B
AP Calculus AB 2008 Multiple Choice Solutions Part A
AP Calculus AB 2008 Multiple Choice Solutions Part B
AP Calculus AB 2003 Multiple Choice Solutions
AP Calculus AB 1998 Multiple Choice Solutions Part A
AP Calculus AB 1998 Multiple Choice Solutions Part B
The following are solutions to sample questions of the CollegeBoard AP/AB and AP/BC Calculus examination.
AP Calculus Practice Multiple Choice 2020
AP Calculus AB 2020 Exam Sample Questions
AP Calculus BC Sample Free Response Solutions 2020
AP / AB Calculus Free Response Solutions
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
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.
Highlights of Calculus (Part 1)
Big Picture of Calculus
Big Picture: Derivatives
Max and Min & Second Derivative
The Exponential Function
Big Picture: Integrals
Derivative of sin x & cos x
Product Rule & Quotient Rule
Chains f(g(x)) & the Chain Rule
Highlights of Calculus (Part 2)
Limits & Continuous Functions
Inverse Functions f^{-1} (y) & x = ln y
Derivatives of ln y & sin^{-1} (y)
Growth Rates & Log Graphs
Linear Approximation/Newton’s Method
Power Series/Euler’s Great Formula
Differential Equations of Motion
Differential Equations of Growth
Introduction to Calculus
The Limits of a Function Definition & Techniques to find Limits
Mean Value Theorem What is Mean Value Theorem?
L’Hopitals Rule Indeterminate Quotients, Product, Differences & Power
Newton’s Method Used to approximate a root.
Derivatives Definition & Slope of Tangent
Power Rule Constant Multiple Rule, Sum Rule, Difference Rule
Product Rule Find the derivative of the product of two functions
Quotient 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 & Logarithmic Functions, Trigonometric
Functions, Inverse Trigonometric Functions, Hyperbolic
Functions & Inverse Hyperbolic Functions
Examples using the Derivative Rules
More Examples using the Derivative Rules
Trigonometric 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
Deriving the Derivative Formulas for Tan, Cot, Sec, Cosecant, Arctan
Derivatives of Exponential Functions Derivatives of e ^{x},
a^{x}, 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
Hyperbolic Functions Hyperbolic Identities, Derivatives of Hyperbolic Functions & Derivatives of Inverse Hyperbolic Functions
Second Derivative & Higher Derivatives Find the derivatives of derivatives & their applications
Maxima and Minima Maximum amd Minimum Values, Fermat’s Theorem,
Critical Number, Extreme Value Theorem, Closed Interval Method
Maximum & Minimum
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, & extremum
Concavity Problems II Analyze functions through increasing,
decreasing, concavity, inflection points, critical points, & extremum
Curve Sketching using Calculus
Asymptotes Vertical Asymptote, Horizontal Asymptote, Oblique Asymptote
The Fundamental Theorem of Calculus What is the
Fundamental Theorem of Calculus?
Approximating Integrals using Rectangles, Trapezoid Rule, Simpsons Rule
Calculating a Definite Integral Using Riemann Sums
Definite Integral Area, Riemann Sum, Properties of Definite Integral
Antiderivative Formulas for powers of x, trigonometric functions, exponential functions
Indefinite Integrals Integral Notation, Integral Formulas
Improper Integrals
Integration by Parts Formula & Examples
Integration by Parts Examples
Integration using U-Substitution
Integration using Partial Fractions
Long Partial Fractions Problem Repeated Irreducible Quadratic Factors
Area under a Curve Calculate area under a curve & between two curves.
Centroids/Center of Mass Calculate the Centroid of a Region
Volume of Revolution Cylindrical Shells
Volume of Revolution Disk/Washers
Work Done using Calculus Tank Problem
Work Done using Calculus Cable/Rope Problem, Spring Problem
Integrating Exponential Functions
Integrating Hyperbolic Functions
Trigonometric Integrals Integration of the Powers of Sine, Cosine, Tangent & Secant
Integration using Inverse Trigonometric Functions
Absolute Convergence, Conditional Convergence & Divergence Sequences & Series Convergence & Divergence
Geometric Series & the Test for Divergence
Integral Test To determine whether a series is convergent or divergent
Integral Test
Limit Comparison Test & Direct Comparison Test
Partial Sums: Showing a Series Diverges
Ratio Test Root Test
Telescoping Series & Strategies for Testing Series
Introduction to differential equations; Separable Differential Equations
Exact Equations Intuition; Exact Equations Examples
Integrating factors
First Order Linear Differential Equations
First Order Homogeneous 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 Basic Idea & Properties
Laplace Transform Proof & Tables
Laplace Transform
Laplace Transform 1
Laplace Transform 2
Laplace Transform to solve an equation
More Laplace Transform tools
Using the Laplace Transform
Laplace Transform of L{t}
Laplace Transform of t^{n} L{t^{n}}
Laplace Transform of the Unit Step Function
Inverse Laplace Examples
Laplace/Step Function Differential Equation
Dirac Delta Function
Function
Laplace Transform of the Dirac Delta Function
Introduction to the Convolution & the Laplace Transform Using the Convolution Theorem
Inverse Laplace Transform I
Inverse Laplace Transform II
Big Picture of Calculus
Calculus is about change. One function tells how quickly another function is changing. Professor Strang shows how calculus applies to ordinary life situations, such as: driving a car, climbing a mountain, growing to full adult height.
Big Picture: Derivatives
Calculus finds the relationship between the distance traveled and the speed - easy for constant speed, not so easy for changing speed. Professor Strang is finding the “rate of change” & the “slope of a curve” & the “derivative of a function.”
Big Picture: Integrals
The second half of calculus looks for the distance traveled even when the speed is changing. Finding this “integral” is the opposite of finding the derivative. Professor Strang explains how the integral adds up little pieces to recover the total distance. I know the speed at each moment of my trip, so how far did I go?
Calculus Calculator with step by step solutions
Functions,
Operations on Functions,
Polynomial & Rational Functions,
Exponential & Logarithmic Functions,
Sequences & Series
Evaluating Limits,
Derivatives,
Applications of Differentiation,
Integrals,
Applications of Integration,
Techniques of Integration,
Parametric Equations & Polar Coordinates
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