Elementary Illustrations of the Differential and Integral Calculus

Chapters

1. Differential and Integral Calculus 5 excerpts, 0 equations, 0 problems
2. On the Ratio or Proportion of Two Magnitudes 8 excerpts, 2 equations, 0 problems
3. On the Ratio of Magnitudes that Vanish Together 10 excerpts, 6 equations, 0 problems
4. On the Ratios of Continuously Increasing or Decreasing Quantities 7 excerpts, 5 equations, 0 problems
5. The Notion of Infinitely Small Quantities 11 excerpts, 2 equations, 0 problems
6. On Functions 8 excerpts, 1 equations, 0 problems
7. Infinite Series 6 excerpts, 4 equations, 0 problems
8. Convergent and Divergent Series 8 excerpts, 3 equations, 0 problems
9. Taylor's Theorem. Derived Functions 9 excerpts, 12 equations, 0 problems
10. Differential Coefficients 4 excerpts, 5 equations, 0 problems
11. The Notation of the Differential Calculus 8 excerpts, 6 equations, 0 problems
12. Algebraical Geometry 5 excerpts, 1 equations, 0 problems
13. On the Connexion of the Signs of Algebraical and the Directions of Geometrical Magnitudes 6 excerpts, 16 equations, 0 problems
14. The Drawing of a Tangent to a Curve 6 excerpts, 10 equations, 0 problems
15. Rational Explanation of the Language of Leibnitz 5 excerpts, 5 equations, 0 problems
16. Orders of Infinity 5 excerpts, 1 equations, 0 problems
17. A Geometrical Illustration: Limit of the Intersections of Two Coinciding Straight Lines 6 excerpts, 17 equations, 0 problems
18. The Same Problem Solved by the Principles of Leibnitz 6 excerpts, 26 equations, 0 problems
19. An Illustration from Dynamics: Velocity, Acceleration, etc 5 excerpts, 1 equations, 0 problems
20. Simple Harmonic Motion 5 excerpts, 9 equations, 0 problems
21. The Method of Fluxions 3 excerpts, 5 equations, 0 problems
22. Accelerated Motion 8 excerpts, 14 equations, 0 problems
23. Limiting Ratios of Magnitudes that Increase Without Limit 7 excerpts, 7 equations, 0 problems
24. Recapitulation of Results Reached in the Theory of Functions 6 excerpts, 2 equations, 0 problems
25. Approximations by the Differential Calculus 6 excerpts, 5 equations, 0 problems
26. Solution of Equations by the Differential Calculus 5 excerpts, 8 equations, 0 problems
27. Partial and Total Differentials 6 excerpts, 11 equations, 0 problems
28. Application of the Theorem for Total Differentials to the Determination of Total Resultant Errors 5 excerpts, 1 equations, 0 problems
29. Rules for Differentiation 5 excerpts, 11 equations, 0 problems
30. Illustration of the Rules for Differentiation 5 excerpts, 4 equations, 0 problems
31. Differential Coefficients of Differential Coefficients 4 excerpts, 1 equations, 0 problems
32. Calculus of Finite Differences. Successive Differentiation 6 excerpts, 6 equations, 0 problems
33. Total and Partial Differential Coefficients. Implicit Differentiation 6 excerpts, 10 equations, 0 problems
34. Applications of the Theorem for Implicit Differentiation 4 excerpts, 13 equations, 0 problems
35. Inverse Functions 7 excerpts, 21 equations, 0 problems
36. Implicit Functions 5 excerpts, 20 equations, 0 problems
37. Fluxions, and the Idea of Time 8 excerpts, 0 equations, 0 problems
38. The Differential Coefficient Considered with Respect to its Magnitude 8 excerpts, 0 equations, 0 problems
39. The Integral Calculus 6 excerpts, 6 equations, 0 problems
40. Connexion of the Integral with the Differential Calculus 6 excerpts, 0 equations, 0 problems
41. Nature of Integration 8 excerpts, 3 equations, 0 problems
42. Determination of Curvilinear Areas. The Parabola 6 excerpts, 0 equations, 0 problems
43. Method of Indivisibles 7 excerpts, 7 equations, 0 problems
44. Concluding Remarks on the Study of the Calculus 5 excerpts, 0 equations, 0 problems

Index of terms 195 terms, by chapter

Related books

The books the concept graph relates to this one, most shared terms first.

• A Course of Pure Mathematics 1921
  83 shared terms

  abscissa, approximation, area, binomial coefficient, cartesian coordinates, chord, circle, common logarithm, constant, convergent series, cosine, curve, dependent, derivative, differential, divergent series, equation, Euler's number, explicit function, exponential function, focus, function, function notation, function of several variables, general power, geometrical progression, graph of a function, higher-order derivative, hypotenuse, implicit function, increment, indeterminate form, infinite sequence, infinity, integral, interval, inverse function, limit, limits of integration, line, logarithm, mathematical notation, order of smallness, ordinate, origin, parabola, parallelogram, partial derivative, perimeter, point, positive direction, power, power series, product, reciprocal, rectangle, right angle, right triangle, root, root of an equation, sine, square root of 2, sum, surface, tangent, tangent function, tends to infinity, variable, differentiation, implicit differentiation, integration, Newton's method, substitution, velocity, binomial theorem, Chain rule, fundamental theorem of calculus, necessary condition for convergence, power rule, product rule, quotient rule, Taylor's theorem, total differential

• Calculus Made Easy 1914
  74 shared terms

  abscissa, approximation, area, calculus, common logarithm, constant, convergent series, cosine, derivative, differential, Euler's number, explicit function, exponent, exponential function, fluxional notation, function, function notation, function of several variables, geometric series, higher-order derivative, implicit function, increment, independent variable, infinitesimal, integral, intersection of two curves, inverse function, limit, limits of integration, line, logarithm, mathematics, natural logarithm, negative number, operation, order of smallness, ordinate, partial derivative, partial differential, power, product, rate of change, ratio, reciprocal, rectangle, relation between variables, root, sine, slope of a curve, sum, tangent, tangent function, total differential, variable, differentiating from first principles, differentiation, integration, neglecting higher-order small quantities, substitution, Gottfried Wilhelm Leibniz, Isaac Newton, acceleration, angle, angular velocity, distance, force, time, velocity, binomial theorem, power rule, product rule, pythagorean theorem, quotient rule, degree of angle

• An Introduction to Mathematics 1911
  68 shared terms

  abscissa, approximation, arc of a circle, arithmetical progression, calculus, cartesian coordinates, circle, constant, continuous quantity, convergent series, cosine, curve, derivative, divergent series, dynamics, equality, equation, exponential function, fluxional notation, focus, function, function notation, geometrical progression, graph of a function, incommensurable magnitudes, infinite sequence, infinitesimal, infinity, integral, interval, limit, line, mathematical notation, mathematics, mechanics, negative number, number, operation, ordinate, origin, parabola, rate of change, ratio, rectangle, relation between variables, root, similarity, sine, slope of a curve, specific gravity, standard of approximation, tangent, variable, vertex of a conic section, transit instrument, Gottfried Wilhelm Leibniz, Isaac Newton, acceleration, angle, angular velocity, circumference, distance, force, length, radius, time, velocity, unit

• Plane Geometry 1899
  39 shared terms

  approximation, arc of a circle, area, chord, circle, commensurable magnitudes, constant, curvilinear figure, diagonal, equality, hypotenuse, incommensurable magnitudes, limit, line, parallelogram, perimeter, perpendicular, point, polygon, proportion, ratio, rectangle, rectilinear figure, regular polygon, right angle, right triangle, similarity, surface, tangent, three-dimensional figure, variable, composition of proportions, angle, circumference, distance, radius, pythagorean theorem, degree of angle, unit

• Mathematical Recreations and Essays 1905
  35 shared terms

  abscissa, approximation, area, arithmetical progression, calculus, circle, diagonal, equation, fluxional notation, geometrical progression, impulse, incommensurable magnitudes, logarithm, mathematical notation, mathematics, mechanics, parabola, regular polygon, similarity, sine, sum, tangent, tangent function, uniform motion, weight, differentiation, Archimedes, Isaac Newton, Leonhard Euler, angle, circumference, density, force, time, velocity

• Elements of Plane Trigonometry 1863
  24 shared terms

  common logarithm, constant, cosine, function, limit, logarithm, negative direction, origin, positive direction, ratio, regular polygon, sine, tangent, tangent function, variable, Archimedes, Isaac Newton, angle, arc of a circle, circumference, distance, radius, degree of angle, minute of arc

• First Course in the Theory of Equations 1922
  23 shared terms

  abscissa, circle, coefficient, curve, degree, derivative, graph of a function, higher-order derivative, infinity, interval, ordinate, origin, root, root of an equation, sign, slope of a curve, tangent, differentiation, Newton's method, Isaac Newton, Leonhard Euler, binomial theorem, Taylor's theorem

• The First Steps in Algebra 1894
  22 shared terms

  algebraic expression, arithmetical progression, arrangement, coefficient, degree, equality, equation, exponent, geometrical progression, negative number, number, power, product, reciprocal, root, sign, variable, solving an equation, substitution, verification, time, unit

• Solid Geometry with Problems and Applications 1919
  19 shared terms

  circle, constant, cosine, function, incommensurable magnitudes, infinite sequence, limit, line, perimeter, perpendicular, point, right triangle, sine, tangent function, three-dimensional figure, variable, angle, circumference, radius

• Spherical Trigonometry, for the Use of Colleges and Schools 1886
  18 shared terms

  approximation, area, chord, circle, cosine, diagonal, hypotenuse, logarithm, perpendicular, polygon, sine, tangent function, neglecting higher-order small quantities, verification, Leonhard Euler, force, radius, degree of angle

• Vector Analysis and Quaternions 1906
  16 shared terms

  area, cartesian coordinates, cosine, exponent, infinitesimal, mathematical notation, polygon, product, reciprocal, sine, sum, angle, force, length, velocity, binomial theorem

• A First Book in Algebra 1895
  15 shared terms

  algebraic expression, arrangement, coefficient, degree, difference, equality, equation, exponent, negative number, power, product, root, solving an equation, substitution, binomial theorem

• Treatise on Thermodynamics 1903
  10 shared terms

  cartesian coordinates, differential, infinitesimal, partial derivative, ratio, singular value, tangent, Leonhard Euler, density, Taylor's theorem

• An Elementary Treatise on Electricity 1888
  2 shared terms

  geometrical progression, force

Errata (0)

None recorded yet.