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Mathematics

Calculus

Limits, derivatives and integrals, and how they describe change, motion and area.

  • 10 chapters
  • 30 lessons
  • All free
Start hereAverage Versus Instantaneous ChangeChange Motion and Limits · Learn average rate of change, instantaneous rate.Start lesson

Chapters

1

Change Motion and Limits

Calculus: change motion and limits. Review before publishing.

3 lessons

Flashcards Practice test
  1. 1.1Average Versus Instantaneous ChangeLearn average rate of change, instantaneous rate.
  2. 1.2Limits from Graphs and TablesLearn graphical limit evidence, table evidence and a known rule, limits at holes.
  3. 1.3ContinuityLearn continuity at an input, jump discontinuities.
2

Calculating Limits

Calculus: calculating limits. Review before publishing.

3 lessons

Flashcards Practice test
  1. 2.1Limit LawsLearn limit laws for sums, limit laws for quotients.
  2. 2.2One-Sided LimitsLearn left-hand limits, right-hand limits.
  3. 2.3Infinite Limits and AsymptotesLearn limits at infinity, vertical asymptotes.
3

The Derivative

Calculus: the derivative. Review before publishing.

3 lessons

Flashcards Practice test
  1. 3.1Derivative as a LimitLearn derivative definition, derivative of a linear rule.
  2. 3.2Tangent LinesLearn tangent slope, tangent-line equation.
  3. 3.3Derivative Notation and MeaningLearn derivative units and notation, second derivatives.
4

Differentiation Rules

Calculus: differentiation rules. Review before publishing.

3 lessons

Flashcards Practice test
  1. 4.1Power Product and Quotient RulesLearn power rule, product rule, quotient rule.
  2. 4.2Chain RuleLearn chain rule, multiple layers of composition.
  3. 4.3Derivatives of Exponential and Trigonometric FunctionsLearn exponential derivatives, trigonometric derivatives.
5

Applications of Derivatives

Calculus: applications of derivatives. Review before publishing.

3 lessons

Flashcards Practice test
  1. 5.1MotionLearn position and velocity, velocity and acceleration.
  2. 5.2Related RatesLearn related rates for area, related rates for volume.
  3. 5.3Linear ApproximationLearn linear approximation, differentials.
6

Analyzing Functions

Calculus: analyzing functions. Review before publishing.

3 lessons

Flashcards Practice test
  1. 6.1Increasing and DecreasingLearn derivative signs and monotonicity, negative derivative values.
  2. 6.2ExtremaLearn local and absolute minima, closed-interval extrema.
  3. 6.3Concavity and Curve SketchingLearn second-derivative signs, inflection points.
7

Optimization

Calculus: optimization. Review before publishing.

3 lessons

Flashcards Practice test
  1. 7.1Building a ModelLearn building an optimization model, feasible inputs.
  2. 7.2Finding an OptimumLearn verifying an optimum, interpreting the optimal value.
  3. 7.3Interpreting Constraints and UnitsLearn outlier fences, checking constraints and units.
8

Accumulation and Integrals

Calculus: accumulation and integrals. Review before publishing.

3 lessons

Flashcards Practice test
  1. 8.1Area EstimatesLearn left riemann sums, right riemann sums.
  2. 8.2Definite IntegralsLearn definite integrals, signed area and geometric area.
  3. 8.3The Fundamental Theorem of CalculusLearn evaluating with antiderivatives, derivatives of accumulation.
9

Integration Techniques

Calculus: integration techniques. Review before publishing.

3 lessons

Flashcards Practice test
  1. 9.1AntiderivativesLearn antiderivative power rule, the reciprocal exception.
  2. 9.2SubstitutionLearn substitution with a nonlinear input, substitution with a linear input.
  3. 9.3Initial-Value ProblemsLearn initial conditions, checking a particular solution.
10

Applications of Integration

Calculus: applications of integration. Review before publishing.

3 lessons

Flashcards Practice test
  1. 10.1Area Between CurvesLearn area between curves, area with parallel boundaries.
  2. 10.2VolumeLearn disk volumes, washer volumes.
  3. 10.3Accumulated Change in ContextLearn net change and initial amount, displacement and distance.