Calculus 1

Reviews lines, slope, angle of inclination, and the distance formula as preparation for calculus.

Introduces functions, notation, domain, range, inputs, outputs, and graph interpretation.

Reviews trigonometric functions, unit-circle values, and graphing trig behavior.

Covers algebra with functions, including sums, products, quotients, and composition.

Introduces limits as the value a function approaches near a point.

Develops limit laws and algebraic techniques for computing limits.

Explains continuity and how it depends on function value, limit existence, and equality between them.

Connects slope of a curve, average velocity, instantaneous velocity, and rates of change.

Introduces the derivative as a limit that measures instantaneous rate of change and tangent slope.

Develops efficient differentiation rules for common functions.

Explains product and quotient rules for differentiating multiplied and divided functions.

Applies derivatives to tangent lines, rates of change, and other practical interpretations.

Covers derivatives of sine, cosine, tangent, and other trigonometric functions.

Explains the chain rule for differentiating composite functions.

Introduces implicit differentiation when variables are mixed together in an equation.

Uses derivatives to solve related rates problems where multiple quantities change together.

Uses first and second derivatives to analyze increasing, decreasing, and concavity.

Briefly discusses Rolle Theorem and the Mean Value Theorem.

Uses the first derivative test to identify local maxima and minima.

Uses the second derivative test and concavity to classify critical points.

Studies limits as x approaches infinity or negative infinity.

Combines intercepts, asymptotes, derivatives, and concavity to sketch graphs.

Solves optimization problems using derivatives to find maximum or minimum values.

Introduces antiderivatives and indefinite integrals.

Builds area under a curve using limits and Riemann sums.

Evaluates definite integrals and interprets signed area.

Explains the Fundamental Theorem of Calculus linking derivatives and integrals.

Finds area between two curves using definite integrals.

Computes volumes of solids using disk and washer cross-sections.

Computes volumes of solids using cylindrical shells.

Finds arc length of a curve in the plane using an integral formula.