# Calculus Lectures in Videos

We have a series of free Calculus Video Lessons from UMKC - The University of Missouri-Kansas City. The Topics are: Functions, Limits of a Function, The Derivative of a Function, Some Special Derivatives, The Derivative Applied, The Integral of a Function and The Integral Applied.

We also have a series of free Calculus 2 Video Lessons from UNSW - University of New South Wales, Sydney.

### Unit 0 - Functions: A Review of Precalculus

Beginning
Definition of a Function, Visualizing Functions: Graphs, Domain (& Range) of Functions, Some Exercises
Graphing Technology
Viewing Windows, Zooming In or Out Errors in Resolution
New Functions From Old
Operations on Functions, How Operations Affect Function Graphs, Functions with Symmetric Graphs, Some Exercises
Families of Functions
The Power Function Family y = xp, The Polynomial Function, and Rational Function Families
Trigonometry for Calculus
Right Triangle Trigonometry, Trigonometric Graphs, Handy Trigonometric Identities, Laws of Sine and Cosine, Trigonometric Families
Inverse Functions
A Function Inverse to Another Function When do Inverse Functions (& Their Graphs) Exist? Inverse Trigonometric Functions
Exponential & Logarithmic Functions
The Exponential Function Family, The Logarithmic Function Family, Solving Exponential & Logarithmic Equations

### Unit 1 - Limits of Functions: Approach & Destination

Intuitive Beginning
A New Tool: The "Limit", Some Limit Examples, Two-sided & One-sided Limits, Limits that Fail to Exist: When f(x) grows without bound, Limits at Infinity: When x grows without bound, More Limits that Fail to Exist: Infinity & Infinite Indecision, An Exercise on Limits
The Algebra of Limits as x ->a
Basic Limits, Limits of Sums, Differences, Products, Quotients, & Roots, Limits of Polynomial Functions, Limits of Rational Functions & the Apparent Appearance of 0/0, Limits of Piecewise-Defined Functions: When One-sided Limits Matter!, Some Exercises
The Algebra of Limits as x -> +/- inf : End Behavior
Basic Limits, Limits of Sums, Differences, Products, Quotients, & Roots, Limits of Polynomial Functions: Two End Behaviors, Limits of Rational Functions: Three Types of End Behavior, Limits of Functions with Radicals, Some Exercises, Limits of ln(x), ex, and More
Continuous Functions
Functions Continuous (or not!) at a Single Point x=c, Functions Continuous on an Interval, Properties & Combinations of Continuous Functions, The Intermediate Value Theorem & Approximating Roots: f(x) = 0, Some Exercises
Trigonometric Functions
The 6 Trigonometric Functions: Continuous on Their Domains, When Inverses are Continuous, Finding a Limit by "Squeezing", Sin(x)/x -> 1 as x -> 0, and Other Limit Tales, Some Exercises

### Unit 2 - The Derivative of a Function

Measuring Rates of Change
Slopes of Tangent Lines, One-Dimensional Motion, Average Velocity, Instantaneous Velocity, General Rates of Change, Some Exercises
What is a Derivative?
Definition of the Derived Function: The "Derivative", & Slopes of Tangent Lines, Instantaneous Velocity, Functions Differentiable (or not!) at a Single Point, Functions Differentiable on an Interval, A Function Differentiable at a point is Continuous at that point, Other Derivative Notations
Finding Derivatives I: Basic Rules
The Power Rule, Constant Multiple, Sum, & Difference Rules, Notation for Derivatives of Derivatives, Some Exercises
Finding Derivatives II
The Product Rule, The Quotient Rule, Some Exercises
Finding Derivatives III
The Sine Function, The Other Trigonometric Functions, Some Applications
Finding Derivatives IV
The Chain Rule: Derivatives of Compositions of Functions, Generalized Derivative Formulas, Some Exercises
When Rates of Change are Related
Differentiating Equations to "Relate Rates", A Strategy
An Exercise
More on Derivatives
Local Linear Approximations of Non-Linear Functions, Defining "dx" and "dy" Alone

### Unit 3 - Some Special Derivatives

Implicit Differentiation
Functions Defined Implicitly, Derivatives of Functions Defined Implicitly, The Derivative of Rational Powers of x, Some Exercises
Derivatives Involving Logarithms
Derivatives of Logarithmic Functions, The "Logarithmic Differentiation" Technique, The Derivative of Irrational Powers of x, Some Exercises
Derivatives Involving Inverses
Derivatives of Inverse Functions, Derivatives of Exponential Functions, Derivatives of Inverse Trigonometric Functions, Some Exercises
Finding Limits Using Differentiation
Limits of Quotients that appear to be "Indeterminate": The Rule of L'Hopital, Finding Other "Indeterminate" Limits

### Unit 4 - The Derivative Applied

Analyzing the Graphs of Functions I
Increasing & Decreasing Functions: The 1st Derivative Applied, Functions Concave Up or Concave Down: The 2nd Derivative Applied, When Concavity Changes: Inflection Points, Logistic Growth Curves: A Brief Look
Analyzing the Graphs of Functions II
Local Maximums & Minimums
The 1st Derivative Test for Local Maximums & Minimums, The 2nd Derivative Test for Local Maximums & Minimums, Polynomial Function Graphs
Analyzing the Graphs of Functions III
What to Look For in a Graph, Rational Function Graphs, Functions Whose Graphs have Vertical Tangents or Cusps, Some Exercises
Analyzing the Graphs of Functions IV
Global Maximums & Minimums, Global Extrema on (finite) Closed Intervals, Global Extrema on (finite or infinite) Open Intervals, When a Single Local Extremum must be Global, Some Exercises
Optimization Problems
Applied Maximum & Minimum Problems, Optimization over a (finite) Closed Interval: Maximizing Area or Volume, Minimizing Cost, Optimization over Other Intervals: Minimizing Materials or Distance, An Economics Application: Cost, Revenue, Profit, & Marginal Analysis
Newton's Method for Approximating Roots of Equations
Development of the Method, Strength & Weaknesses of the Method
The Mean Value Theorem for Derivatives
A Special Case of the Mean Value Theorem: Rolle's Theorem, The (Full) Mean Value Theorem for Derivatives, Direct Consequences of This Mean Value Theorem, Some Exercises
One-Dimensional Motion & the Derivative
Rectilinear Motion Revisited, Velocity, Speed, & Acceleration, Analyzing a Position Graph, An Exercise

### Unit 5 - The Integral of a Function

The Indefinite Integral
"Undo-ing" a Derivative: Antiderivative = Indefinite Integral, Finding Antiderivatives, The Graphs of Antiderivatives: Integral Curves & the Slope Field Approximation, The Antiderivative as Solution of a Differential Equation, Some Exercises
Indefinite Integration by Substitution
The Substitution Method of Indefinite Integration: A Major Technique, Straightforward Substitutions , More Interesting Substitutions, Some Exercises
Area Defined as a Limit
The Sigma Shorthand for Sums, Summation Properties & Handy Formulas, Definition of Area "Under a Curve", Net "Area", Approximating Area Numerically, Some Exercises
The Definite Integral
The Definite Integral Defined, The Definite Integral of a Continuous Function = Net "Area" Under a Curve, Finding Definite Integrals, A Note on the Definite Integral of a Discontinuous Function, Some Exercises
The Fundamental Theorem of Calculus
The Fundamental Theorem of Calculus, Part 1, Definite & Indefinite Integrals Related,The Mean Value Theorem for Integrals, The Fundamental Theorem of Calculus, Part 2, Differentiation & Integration are Inverse Processes
One-Dimensional Motion & the Integral
Position, Velocity, Distance, & Displacement, Uniformly Accelerated Motion, The Free Fall Motion Model, An Exercise
Definite Integration by Substitution
Extending the Substitution Method of Integration to Definite Integrals, Some Exercises

### Unit 6 - The Definite Integral Applied

Plane Area
Area Between Two Curves [One Floor, One Ceiling], Area Between Two Curves [One Left, One Right], An Exercise
Volumes I
Volumes by Slicing, Volumes of Solids of Revolution: Disks, Volumes of Solids of Revolution: Washers, Some Exercises
Volumes II
Volumes of Solids of Revolution: Cylindrical Shells, An Exercise
Length of a Plane Curve
Finding Arc Lengths, Finding Arc Lengths of Parametric Curves
Average Value of a Function
Average (Mean) Value of a Continuous Function
Work
Work Done by a Constant Force, Work Done by a Variable Force, Do-It-Yourself Integrals: Pumping Fluids, Work as Change in Kinetic Energy, An Exercise

### Calculus 2

Surfaces and Partial Derivatives
Tangent plane and error estimation
Chain rule for functions of two variables
Integrals of trig functions and reduction formulae
Integration by trig substitution and partial fractions, Integration + Partial Fractions, Integration via rationalizing substitutions and other substitutions
Partial derivatives and integration
Introduction to Separable Differential Equations
Linear and Exact Differential Equations
How to solve 2nd order differential equations?
What is a Taylor polynomial?
Sequences and their limits, Introduction to series + the integral test, Integration and differential equations
Series, comparison + ratio tests
Alternating series and absolute convergence, What is a Taylor series?, What is a Power series?
Arc length + average value of a function
Surface area of revolution of functions, Calculus revision lecture
Hydrostatic Force
More Free Videos on Calculus

Calculus Calculator with step by step solutions
Functions, Operations on Functions,
Polynomial and Rational Functions,
Exponential and Logarithmic Functions,
Sequences and Series,
Evaluating Limits, Derivatives,
Applications of Differentiation,
Integrals, Applications of Integration,
Techniques of Integration,
Parametric Equations and Polar Coordinates

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