Calculus is a branch of mathematics that studies rates of change and areas around curves. From animations to software applications, calculus and its formulas can be found all around us. Differential calculus involves derivatives, which measure a function’s rate of change at a specific point.1 For example, stock analysts can use derivatives to speculate whether a certain stock will rise or fall in a specific time period. By contrast, integral calculus involves the measurement of infinitesimal q...
Review: Precalculus · Limits and Continuity · Differentiation · Derivatives of Transcendental Functions · Limits - Indeterminate Forms
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Set Theory and Relations ; Set Theory and Relations Part - 1 · Preview · 22:44 ; Set Theory and Relations Part - 2 · 18:40
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This calculus 1 derivatives course focuses on differentiating functions. It explains how to find the derivatives of functions that you will typically encounter in your first semester calculus. This course is for university students taking college calculus and high school students who are taking AP Calculus AB. Here is a list of topics: 1. Derivatives of Constants - Examples Include Integers and special constants such as e and pi · 2. The Power Rule and Constant Multiple Rule - Variables Raised...
So you’ve made it through Pre-Calculus and are ready for the good stuff! Calculus is the Mathematics of change and used to model and understand many phenomena in the real world – from science and engineering to finance, economics and medicine – it’s difficult to find a field which doesn’t employ Calculus in some way. Although Calculus 1 is largely focused on differentiation techniques and their applications, it's important to set some foundations first. So, we start by looking at the k...
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Review of Functions, 26:29 ; Compositions of Functions, 12:29 ; Average and Instantaneous Rates of Change, 20:59 ; Limit Investigations, 22:37 ; Algebraic Evaluation of Limits, 28:19 ; Formal Definition of a Limit, 23:39 ; Continuity and the Intermediate Value Theorem, 19:09 ; Limit Definition of the Derivative, 22:52 ; The Power Rule, 26:01 ; The Product Rule, 14:54 ; The Quotient Rule, 19:17 ; Applications of Rates of Change, 17:43 ; Trigonometric Derivatives, 26:58 ; The Chain Rule, 23:47 ; Inverse Trigonometric Functions, 27:05 ; Equation of a Tangent Line, 15:52 ; Implicit Differentiation, 30:05 ; Higher Derivatives, 13:16 ; Logarithmic and Exponential Function Derivatives, 17:42 ; Hyperbolic Trigonometric Function Derivatives, 14:30 ; Related Rates, 29:05 ; Linear Approximation, 23:52 ; Absolute Minima and Maxima, 18:57 ; Mean Value Theorem and Rolle's Theorem, 20:00 ; First Derivative Test, Second Derivative Test, 27:11 ; L'Hopital's Rule, 23:09 ; Curve Sketching, 40:16 ; Applied Optimization, 25:37 ; Newton's Method, 25:13 ; Approximating Areas and Distances, 36:50 ; Riemann Sums, Definite Integrals, Fundamental Theorem of Calculus, 22:02 ; Substitution Method for Integration, 23:19 ; Area Between Curves, 19:59 ; Volume by Method of Disks and Washers, 24:22 ; Volume by Method of Cylindrical Shells, 30:29 ; Average Value of a Function, 16:31 ; Graphs of f, f', f'', 23:58 ; Slope Fields for Differential Equations, 18:32 ; Separable Differential Equations, 17:04