Learn Calculus 101 - The Easy Way

Refresh pre algebra and algebra concepts, focusing on fractions, division by zero, exponents, roots, and logs, then master quadratic solving—factoring, quadratic formula, and completing the square—for calculus readiness.

Explore how to read and graph common functions on the cartesian plane, including linear, quadratic, absolute value, circle, and inverse functions, with axis intercepts and horizontal and vertical transformations.

Review right-triangle trigonometry concepts, including sine, cosine, tangent, and cotangent, using opposite, adjacent, and hypotenuse; explore 45-45-90 and 30-60-90 triangles and introduce identities for calculus readiness.

Explore the concept of limits as the gateway to calculus, covering two-sided and one-sided limits, left/right approaches, and the formal definition for limit existence.

Explore real-life limits with instantaneous speed and motion models. Learn how to distinguish continuous and discontinuous functions using left and right limits and the three conditions for continuity.

Master limit properties and apply rules for constants, sums, and products; recognize left and right limits and examples like cos x minus 1 over x equals zero at zero.

Learn to find limits using tables and graphs, analyzing left- and right-hand approaches and when a function is undefined, with examples like zero over zero and limits existing despite discontinuities.

Test the existence of the limit as x approaches a, and verify it equals f(a). Explore left and right limits with piecewise and rational functions to determine continuity.

Learn to solve limits with algebra by factoring and canceling. Explore examples like (x^2-25)/(x-5) as x approaches 5, giving 10, and a simplification to -1/16 as x approaches 0.

Learn to evaluate limits at infinity by simplifying with division by x or x^2. Discover when the limit is 0, 1, or undefined.

Explore how limits ensure continuity in real life, using a lab temperature problem and a candy pricing model to illustrate left and right limits and solving for K.

Explore the average rate of change, using the slope between two points to express how a property changes over time with the formula (f(x2)-f(x1))/(x2-x1).

Explore the difference quotient as the average rate of change, defined by (f(x+h)−f(x))/h, and its interpretation as the slope between (x, f(x)) and (x+h, f(x+h)).

Learn calculus 101 presents differentiation as the steepness or slope, a measure of the rate of change dy/dx, using rise over run and y equals x plus three.

Explore differentiation through limits of the average quotient to find a tangent line. Define the derivative as the limit of the difference quotient and apply to x squared for 2x.

Master differentiation rules, including the constant rule, constant multiple rule, power rule, and product, quotient, and chain rules. Apply trigonometric, exponential, and logarithmic derivatives for quick problem solving.

Master product rule and chain rule through practical examples, derive derivatives of polynomials, trig functions, and quotients, and apply power and constant rules for efficient calculus.

Apply the power rule to derive polynomials and fractional exponents, such as y = x^-3 and f(x) = x^(4/3). Distribute derivatives across sums and manage constants and coefficients.

Master advanced power rule examples and chain rule techniques by differentiating complex expressions like x^2/√x, converting division to multiplication, and simplifying fractional powers.

Learn to differentiate exponential, logarithmic, and rooted functions using chain rule and e^u and ln rules, with examples like e^{3x^2-5x+5} and ln(2x^2+3x).

Explore higher order derivatives from first to fifth order, learn to derive functions twice or more, and apply notation like f′(x) and f″(x) with clear examples.

See how derivatives explain real life motion, deriving velocity from displacement and linking acceleration to velocity. Apply to balloon and sphere volumes, radius changes, and rate problems in tanks.

Explore integration as the antiderivative, illustrated by slicing a lamp base into cross sections to compute volume, and learn the constant, power, logarithmic, and exponential rules with checks by differentiation.

Master integration properties by learning how constants factor out, how to integrate sums and differences, how to apply the power rule, division rules, and constant of integration in indefinite integrals.

Explore how definite integrals compute the area under a curve between two bounds using limits and F(b) minus F(a), with examples like area and volume.

Explore definite integral properties, including additivity over subintervals, handling piecewise and absolute value functions, and computing area between curves by top minus bottom function.

Explore the basic integration formulas, derivative rules, and properties of integrals with a handy formula sheet and tables to solve problems quickly in exams or open-book or closed-book settings.

Use substitution to solve integrals by selecting a u, applying power, exponential, or natural logarithmic rules, then compute du, integrate, and substitute back for the final result.

Explore integration by parts: choose u and dv, compute v and du, and apply the formula to integrals like x e^x; repeat when necessary or use tables.

Explore advanced integration topics, focusing on double integrals, solving inner and outer integrals, and applying to volumes and shapes with a simple illustrative example.

Embrace calculus as approachable and powerful by applying it to real-life and work challenges, push your brain to its limits, stay creative, and keep learning.