 # 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 Some Exercises 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 Some Examples 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 Some Exercises 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 Some Exercises 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 Some Exercises 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 Some Exercises 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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