Limits
Limits on Graphs
Continuity on Graphs
Intro to Limits
One-Sided Limits
Piecewise Functions- Limits and Continuity
Infinite Limits
Limits at Infinity
Trig Limits (sin x)
Squeeze Theorem
Derivatives
Definition of Derivative
Average Rate of Change
Tangent Line
Derivative- Constant Rule
Derivatives- Power Rule
Derivatives with Negative Exponents
Derivatives- Constant Multiple Rule
Derivative- Sum and Difference Rules
Derivatives- sin and cos
Trig Derivatives- tan, cot, csc, and sec
Product Rule
Quotient Rule
The Chain Rule
Derivatives- Exponential Functions
Derivative ln(x)
Inverse Trig Derivatives
Implicit Differentiation
Horizontal Tangent Line
Percentage Rate of Change
Mean Value Theorem
Related Rates
Increasing and Decreasing Intervals
Intervals of Concave Up and Down
Inflection Points Calculus
Graph of f(x), f'(x), f”(x)
Newton’s Method
Derivative of the Inverse Function
Hyperbolic Functions
Integrals
Antiderivatives
Fundamental Theorem of Calculus
Riemann Sums
Trapezoidal Rule
Indefinite Integrals (Power Rule)
Integrals of Absolute Value Functions
Indefinite Integrals (Trig Functions)
Definite Integrals
Integration by Substitution “u substitution”
Integration by Parts
Area of Region Between Two Curves
Arc Length
Average Function Value
Volume by Cross Sections
Disk Method
Ring Method aka Washer Method
Volume by Cylindrical Shells Notes
Newton’s Law of Cooling
L’Hôpital’s Rule
Partial Derivatives
First Order Partial Derivatives
Multiple Integrals
Double Integrals
Differential Equations
Differentiable Equations (Separable)
In Summary
Calculus is a branch of mathematics that deals with the study of change and motion. It is used to model and analyze physical phenomena, such as the motion of objects and the growth of populations. Calculus has two main branches: differential calculus, which deals with rates of change and slopes of curves, and integral calculus, which deals with the accumulation of quantities and the areas under and between curves.
Differential calculus is concerned with the study of rates of change, or derivatives, of functions. It is used to analyze the behavior of a function at a particular point, as well as to find the slope of a curve at a given point. Differential calculus is used to model and analyze physical phenomena, such as the motion of objects, and is a crucial tool in many fields, including physics, engineering, and economics.
Integral calculus, on the other hand, is concerned with the accumulation of quantities, or integrals. It is used to find the area under or between curves, as well as to calculate the volume of solid objects. Integral calculus is used to model and analyze physical phenomena, such as the growth of populations, and has numerous applications in the real world.
Calculus is a fundamental tool in many fields, including physics, engineering, and economics, and has numerous applications in the real world. It is used to model and analyze physical phenomena, such as the motion of objects and the growth of populations, and has allowed for significant advancements in these fields. Calculus is an essential subject for anyone interested in pursuing a career in mathematics or the physical sciences.
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