Differential Calculus

Calculus I is a course on differential Calculus

Differential Calculus is the study of the rates of changes in systems

Prerequisites: Precalculus, Algebra, Geometry

The main book used in colleges today is Stewart Calculus 8th edition and is covered in chapters 2-5

 


[expand title=”2. Limits and Derivatives” rel=”submenu-highlander”]
[expandsub2 title=”2.1-The Tangent and Velocity Problems” rel=”submenu-highlander1″]

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[expandsub2 title=”2.2-The Limit of a Function” rel=”submenu-highlander1″]

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[expandsub4 title=”Basic Description of Limits” rel=”submenu-highlander2″]

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[expandsub4 title=”Finding Limits from a Graph” rel=”submenu-highlander2″]

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[expandsub4 title=”One Sided Limits, Example 1″ rel=”submenu-highlander2″]

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[expandsub4 title=”One Sided Limits, Example 2″ rel=”submenu-highlander2″]

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[expandsub4 title=”One Sided Limits, Example 3″ rel=”submenu-highlander2″]

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[expandsub4 title=”Limits at Infinity – Basic Idea and Shortcuts!” rel=”submenu-highlander2″]

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[expandsub4 title=”Limits at Infinity – Basic Example and Shortcuts” rel=”submenu-highlander2″]

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[expandsub4 title=”Calculating a Limit at Infinity with a Radical” rel=”submenu-highlander2″]

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[expandsub3 title=”Notes”]Good Sht[/expandsub3]
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[expandsub2 title=”2.3-Calculating Limits Using the Limit Laws” rel=”submenu-highlander1″]

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[expandsub4 title=”Limit Laws to Evaluate a Limit , Example 1″ rel=”submenu-highlander2″]

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[expandsub4 title=”Limit Laws to Evaluate a Limit , Example 2″ rel=”submenu-highlander2″]

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[expandsub4 title=”Limit Laws to Evaluate a Limit , Example 3″ rel=”submenu-highlander2″]

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[expandsub3 title=”Notes”]Good Sht[/expandsub3]
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[expandsub2 title=”2.4-The Precise Definition of a Limit” rel=”submenu-highlander1″]

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[expandsub2 title=”2.5-Continuity” rel=”submenu-highlander1″]

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[expandsub4 title=”The Limit Definition of Continuity – Making Sense of the Definition” rel=”submenu-highlander2″]

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[expandsub4 title=”Continuity and Limits Made Easy – Part 1 of 2″ rel=”submenu-highlander2″]

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[expandsub4 title=”Continuity – Part 2 of 2″ rel=”submenu-highlander2″]

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[expandsub3 title=”Notes”]Good Sht[/expandsub3]
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[expandsub2 title=”2.6-Limits at Infinity; Horizontal Asymptotes” rel=”submenu-highlander1″]

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[expandsub3 title=”Notes” ]Good Sht[/expandsub3]
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[expandsub2 title=”2.7-Derivatives and Rates of Change” rel=”submenu-highlander1″]

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[expandsub4 title=”Understanding the Definition of the Derivative” rel=”submenu-highlander2″]

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[expandsub4 title=”Sketching the Derivative of a Function” rel=”submenu-highlander2″]

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[expandsub3 title=”Notes” ]Good Sht[/expandsub3]
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[expandsub2 title=”2.8-The Derivative as a Function” rel=”submenu-highlander1″]

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[expandsub4 title=”Derivative Using the Definition, Example 2″ rel=”submenu-highlander2″]

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[expandsub4 title=”Instantaneous Velocity Using Limit Definition of Derivative” rel=”submenu-highlander2″]

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[expandsub4 title=”Instantaneous Velocity, Definition of Derivative” rel=”submenu-highlander2″]

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[expandsub4 title=”Limit Definition of Derivative, Rational Function Example” rel=”submenu-highlander2″]

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[expandsub4 title=”Derivative Using Definition: Rational Function Example” rel=”submenu-highlander2″]

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[expandsub4 title=”Limit Definition of Derivative, Square Root Example” rel=”submenu-highlander2″]

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[expandsub4 title=”Derivative of Root Function Using Definition of a Derivative” rel=”submenu-highlander2″]

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[expandsub3 title=”Notes” ]Good Sht[/expandsub3]
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[expand title=”3.-Differentiation Rules” rel=”Functions and Models” rel=”submenu-highlander”]

[expandsub2 title=”3.1-Derivatives of Polynomials and Exponential Functions” rel=”submenu-highlander1″]

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[expandsub4 title=”Basic Derivative Rules – The Shortcut Using the Power Rule” rel=”submenu-highlander2″]

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[expandsub4 title=”Power Rule and Derivatives, A Basic Example #1″ rel=”submenu-highlander2″]

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[expandsub4 title=”Power Rule and Derivatives, A Basic Example, #2″ rel=”submenu-highlander2″]

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[expandsub4 title=”Power Rule for Finding Derivatives, Basic Example #3″ rel=”submenu-highlander2″]

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[expandsub4 title=”Basic Derivative Examples” rel=”submenu-highlander2″]

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[expandsub4 title=”More Derivative Examples, #1″ rel=”submenu-highlander2″]

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[expandsub4 title=”More Derivative Examples, #2″ rel=”submenu-highlander2″]

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[expandsub4 title=”More Derivative Examples, #3″ rel=”submenu-highlander2″]

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[expandsub3 title=”Notes”]Good Sht[/expandsub3]
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[expandsub2 title=”3.2-The Product and Quotient Rules” rel=”submenu-highlander1″]

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[expandsub4 title=”Proof of the Product Rule from Calculus” rel=”submenu-highlander2″]

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[expandsub4 title=”Derivatives using the Product Rule” rel=”submenu-highlander2″]

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[expandsub4 title=”The Quotient Rule” rel=”submenu-highlander2″]

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[expandsub4 title=”Derivatives Using the Quotient Rule” rel=”submenu-highlander2″]

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[expandsub3 title=”Notes” ]Good Sht[/expandsub3]
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[expandsub2 title=”3.3-Derivatives of Trigonometric Functions” rel=”submenu-highlander1″]

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[expandsub4 title=”Deriving the Derivative Formulas for Tangent, Cotangent, Secant, Cosecant” rel=”submenu-highlander2″]

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[expandsub4 title=”More Derivatives Involving Trigonometric Functions, Ex 1″ rel=”submenu-highlander2″]

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[expandsub4 title=”More Derivatives Involving Trigonometric Functions, Ex 2″ rel=”submenu-highlander2″]

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[expandsub4 title=”Inverse Trigonometric Functions – Derivatives” rel=”submenu-highlander2″]

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[expandsub4 title=”Derivatives of Inverse Trigonometric Functions – Another Example!” rel=”submenu-highlander2″]

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[expandsub4 title=”Deriving the Derivative of Inverse Tangent or y = arctan (x)” rel=”submenu-highlander2″]

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[expandsub4 title=”Inverse Trigonometric Functions – Derivatives – Example 2″ rel=”submenu-highlander2″]

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[expandsub4 title=”Inverse Trigonometric Functions – Derivatives – Example 3″ rel=”submenu-highlander2″]

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[expandsub3 title=”Notes” ]Good Sht[/expandsub3]
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[expandsub2 title=”3.4-The Chain Rule” rel=”submenu-highlander1″]

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[expandsub4 title=”General Chain Rule , Partial Derivatives – Part 1″ rel=”submenu-highlander2″]

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[expandsub4 title=”General Chain Rule – Part 2″ rel=”submenu-highlander2″]

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[expandsub4 title=”Finding Derivatives using the Chain Rule” rel=”submenu-highlander2″]

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[expandsub4 title=”Basic Chain Rule Problems” rel=”submenu-highlander2″]

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[expandsub4 title=”More Chain Rule Examples #1″ rel=”submenu-highlander2″]

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[expandsub4 title=”More Chain Rule Examples #2″ rel=”submenu-highlander2″]

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[expandsub4 title=”More Chain Rule Examples #3″ rel=”submenu-highlander2″]

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[expandsub4 title=”Using the Chain Rule – Harder Example #1″ rel=”submenu-highlander2″]

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[expandsub4 title=”Using the Chain Rule – Harder Example #2″ rel=”submenu-highlander2″]

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[expandsub4 title=”Using the Chain Rule – Harder Example #3″ rel=”submenu-highlander2″]

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[expandsub3 title=”Notes” ]Good Sht[/expandsub3]
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[expandsub2 title=”3.5-Implicit Differentiation” rel=”submenu-highlander1″]

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[expandsub4 title=”Implicit Differentiation – Basic Idea and Examples” rel=”submenu-highlander2″]

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[expandsub4 title=”Implicit Differentiation – Basic Example 1 / 3″ rel=”submenu-highlander2″]

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[expandsub4 title=”Implicit Differentiation – Basic Example 2 / 3″ rel=”submenu-highlander2″]

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[expandsub4 title=”Implicit Differentiation – Basic Example 3 / 3″ rel=”submenu-highlander2″]

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[expandsub4 title=”Using Implicit Differentiation – Extra Examples” rel=”submenu-highlander2″]

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[expandsub4 title=”Using Implicit Differentiation – Example” rel=”submenu-highlander2″]

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[expandsub4 title=”Using Implicit Differentiation to find a derivative” rel=”submenu-highlander2″]

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[expandsub4 title=”Using Implicit Differentiation to find a Second Derivative” rel=”submenu-highlander2″]

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[expandsub4 title=”Implicit Differentiation – More Examples” rel=”submenu-highlander2″]

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[expandsub4 title=”Implicit Differentiation – More Examples” rel=”submenu-highlander2″]

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[expandsub3 title=”Notes”]Good Sht[/expandsub3]
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[expandsub2 title=”3.6-Derivatives of Logarithmic Functions” rel=”submenu-highlander1″]

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[expandsub4 title=”Derivatives of Logarithmic Functions” rel=”submenu-highlander2″]

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[expandsub4 title=”Derivatives of Logarithm Functions – 1 of 2″ rel=”submenu-highlander2″]

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[expandsub4 title=”Derivatives of Logarithm Functions – 2 of 2″ rel=”submenu-highlander2″]

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[expandsub4 title=”Derivatives of Logarithmic Functions and Examples” rel=”submenu-highlander2″]

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[expandsub4 title=”Derivatives of Logarithmic Functions – More Examples” rel=”submenu-highlander2″]

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[expandsub4 title=”Logarithmic Differentiation” rel=”submenu-highlander2″]

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[expandsub4 title=”Logarithmic Differentiation – Example 2″ rel=”submenu-highlander2″]

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[expandsub4 title=”Logarithmic Differentiation – Example 3″ rel=”submenu-highlander2″]

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[expandsub3 title=”Notes”]Good Sht[/expandsub3]
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[expandsub2 title=”3.8-Exponential Growth and Decay” rel=”submenu-highlander1″]

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[expandsub4 title=”Derivatives of Exponential Functions” rel=”submenu-highlander2″]

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[expandsub4 title=”Derivatives of Exponential Functions and Examples” rel=”submenu-highlander2″]

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[expandsub4 title=”Exponential Functions and Derivatives, More Example #1″ rel=”submenu-highlander2″]

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[expandsub3 title=”Notes” ]Good Sht[/expandsub3]
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[expandsub2 title=”3.9-Related Rates” rel=”submenu-highlander1″]

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[expandsub4 title=”Related Rates #1 Problem Using Implicit Differentiation” rel=”submenu-highlander2″]

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[expandsub4 title=”Related Rates #2 Using Cones” rel=”submenu-highlander2″]

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[expandsub4 title=”Related Rates #3 – A point on a graph” rel=”submenu-highlander2″]

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[expandsub4 title=”Related Rates #4 Involving Trigonometry” rel=”submenu-highlander2″]

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[expandsub4 title=”Related Rates #5 Involving Baseball!” rel=”submenu-highlander2″]

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[expandsub3 title=”Notes” ]Good Sht[/expandsub3]
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[expandsub2 title=”3.10-Linear Approximations and Differentials” rel=”submenu-highlander1″]

[expandsub3 title=”Videos”]vids[/expandsub3]

[expandsub3 title=”Notes” ]Good Sht[/expandsub3]
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[expandsub2 title=”3.11-Hyperbolic Functions” rel=”submenu-highlander1″]

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[expandsub4 title=”Hyperbolic Functions – Derivatives” rel=”submenu-highlander2″]

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[expandsub4 title=”Inverse Hyperbolic Functions – Derivatives” rel=”submenu-highlander2″]

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[expandsub3 title=”Notes” ]Good Sht[/expandsub3]
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[expand title=”4.-Applications of Differentiation” rel=”Functions and Models” rel=”submenu-highlander”]
[expandsub2 title=”4.1-Maximum and Minimum Values” rel=”submenu-highlander1″]

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[expandsub4 title=”Increasing/Decreasing , Local Maximums/Minimums” rel=”submenu-highlander2″]

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[expandsub4 title=”Finding Intervals of Increase/Decrease Local Max/Mins” rel=”submenu-highlander2″]

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[expandsub4 title=”Finding Critical Numbers – Example 1″ rel=”submenu-highlander2″]

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[expandsub4 title=”Finding Critical Numbers – Example 2″ rel=”submenu-highlander2″]

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[expandsub4 title=”Finding Local Maximums/Minimums – Second Derivative Test” rel=”submenu-highlander2″]

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[expandsub3 title=”Notes” ]Good Sht[/expandsub3]
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[expandsub2 title=”4.2-The Mean Value Theorem” rel=”submenu-highlander1″]

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[expandsub4 title=”The Mean Value Theorem” rel=”submenu-highlander2″]

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[expandsub3 title=”Notes” ]Good Sht[/expandsub3]
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[expandsub2 title=”4.3-How Derivatives Affect the Shape of a Graph” rel=”submenu-highlander1″]

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[expandsub4 title=”Concavity, Inflection Points and Second Derivatives” rel=”submenu-highlander2″]

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[expandsub3 title=”Notes” ]Good Sht[/expandsub3]
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[expandsub2 title=”4.4-Indeterminate Forms and l’Hospital’s Rule” rel=”submenu-highlander1″]

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[expandsub4 title=”L’Hospital’s Rule and Indeterminate Quotients” rel=”submenu-highlander2″]

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[expandsub4 title=”L’Hospital’s Rule – Indeterminate Products” rel=”submenu-highlander2″]

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[expandsub4 title=”L’Hospital’s Rule – Indeterminate Differences” rel=”submenu-highlander2″]

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[expandsub4 title=”L’Hospital’s Rule – Indeterminate Powers” rel=”submenu-highlander2″]

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[expandsub3 title=”Notes” ]Good Sht[/expandsub3]
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[expandsub2 title=”4.5-Summary of Curve Sketching” rel=”submenu-highlander1″]

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[expandsub4 title=”Curve Sketching Using Calculus – Part 1 of 2″ rel=”submenu-highlander2″]

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[expandsub4 title=”Curve Sketching Using Calculus – Part 2of 2″ rel=”submenu-highlander2″]

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[expandsub4 title=”Summary of Curve Sketching – Example 2, Part 1 of 4″ rel=”submenu-highlander2″]

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[expandsub4 title=”Summary of Curve Sketching – Example 2 – Part 2 of 4″ rel=”submenu-highlander2″]

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[expandsub4 title=”Summary of Curve Sketching – Example 2 – Part 3 of 4″ rel=”submenu-highlander2″]

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[expandsub4 title=”Summary of Curve Sketching – Example 2 – Part 4 of 4″ rel=”submenu-highlander2″]

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[expandsub3 title=”Notes” ]Good Sht[/expandsub3]
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[expandsub2 title=”4.7-Optimization Problems” rel=”submenu-highlander1″]

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[expandsub4 title=”Optimization Problem #2″ rel=”submenu-highlander2″]

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[expandsub4 title=”Optimization Problem #3 – Making a Rain Gutter” rel=”submenu-highlander2″]

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[expandsub3 title=”Notes” ]Good Sht[/expandsub3]
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[expandsub2 title=”4.8-Newton’s Method” rel=”submenu-highlander1″]

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[expandsub4 title=”Newton’s Method” rel=”submenu-highlander2″]

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[expandsub3 title=”Notes” ]Good Sht[/expandsub3]
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[expandsub2 title=”4.9-Antiderivatives” rel=”submenu-highlander1″]

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[expand title=”5.-Integrals” rel=”Functions and Models” rel=”submenu-highlander”]

[expandsub2 title=”5.1-Areas and Distances” rel=”submenu-highlander1″]

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[expandsub2 title=”5.2-The Definite Integral” rel=”submenu-highlander1″]

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[expandsub4 title=”The Definite Integral – Understanding the Definition” rel=”submenu-highlander2″]

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[expandsub4 title=”Approximating a Definite Integral Using Rectangles” rel=”submenu-highlander2″]

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[expandsub4 title=”Calculating a Definite Integral Using Riemann Sums – Part 1″ rel=”submenu-highlander2″]

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[expandsub4 title=”Calculating a Definite Integral Using Riemann Sums – Part 2″ rel=”submenu-highlander2″]

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[expandsub3 title=”Notes”]Good Shit[/expandsub3]
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[expandsub2 title=”5.3-The Fundamental Theorem of Calculus” rel=”submenu-highlander1″]

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[expandsub4 title=”Fundamental Theorem of Calculus Part 1″ rel=”submenu-highlander2″]

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[expandsub4 title=”The Fundamental Theorem of Calculus. Part 2″ rel=”submenu-highlander2″]

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[expandsub3 title=”Notes”]Good Shit[/expandsub3]
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[expandsub2 title=”5.4-Indefinite Integrals and the Net Change Theorem” rel=”submenu-highlander1″]

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[expandsub2 title=”5.5-The Substitution Rule” rel=”submenu-highlander1″]

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[expandsub4 title=”Integration by U-Substitution, Definite Integral” rel=”submenu-highlander2″]

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[expandsub4 title=”U-substitution – Indefinite Integral, Another 2 examples” rel=”submenu-highlander2″]

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[expandsub4 title=”U-Substitution – More Complicated Examples” rel=”submenu-highlander2″]

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[expandsub3 title=”Notes”]Good Shit[/expandsub3]
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