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INTEGRATION BY PARTS
- Summary • 0 pages • 2024
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THE DOCUMENT COVERS INTEGRATION BY PARTS WITH THE AID OF EXAMPLES
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Chapter 2: Limits and Derivatives
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Concise collection of lecture notes and summaries on the concept(s) of Limits and Derivatives of functions
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Limits, Continuity and Differentiability
- Class notes • 4 pages • 2017
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Concise summary for both beginners and intermediate students, covering: 

Limits - finding the limit of a function by first order principles; finding the limit near a point; and one sided limits; 

Continuity - definition of continuity; evaluating functions for signs of continuity;

Differentiability - determining whether a function is differentiable or not; relationship between differentiability and continuity
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Functions
- Summary • 6 pages • 2017
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Concise introduction to functions: definition of a function; examples of functions; ways of representing functions; sketching graphs of functions graphically; identifying functions using the Vertical Line Test (VLT)
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Derivatives: Key Concepts
- Class notes • 3 pages • 2017
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Discusses important features of the derivative:

Differences between average velocity and instantaneous velocity in terms of derivatives; practical applications of the derivative; class test revision example
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Inequalities
- Class notes • 4 pages • 2017
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Providing worked examples of inequalities; introduction to absolute values; relationship between absolute values and inequalities; sketching inequalities and absolute values (graphical representation)
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Interpretations of the Derivative
- Class notes • 4 pages • 2017
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These lecture notes cover: Revision of first and second derivatives; examples of first and second derivatives; common applications through word problems; graphing of first and second derivatives and how to find one from the other; and linear approximation
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Inverse Functions
- Class notes • 3 pages • 2017
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Introduction to Inverse Functions: Discussion of exponential and logarithmic functions as examples of inverse functions; using Vertical Line Test to check if functions are one-to-one or one-to-many; strategy for finding the inverse function; sketching of inverse functions
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New from Old Functions
- Summary • 3 pages • 2017
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Introducing the concept of shifting functions to produce new functions (new from old); how to shift functions; graphical and algebraic representations; combinations of functions algebraically and graphically; compositions of functions and examples
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Derivative Function
- Class notes • 3 pages • 2017
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Basic introduction to the concept of the Derivative: 

Finding the derivative by first principles/ by the definition; graphing of original function and derivative; how to interpret original function from derivative and vice versa
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