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14 units · 34 lessons

Calculus & Analytical Geometry

Calculus & Analytical Geometry from the first idea to exam level: every lesson builds on the one before, with a worked example, a step-through diagram where it helps, a quick check and practice that adapts to what you know. Follows Howard Anton, Calculus, 10th ed..

Calculus & Analytical Geometry at a glance

What does Calculus & Analytical Geometry cover?

Limits & Continuity, Differentiation, Extrema, Two-Variable Extrema, Integration Techniques, Area, Arc Length & Revolution, Sequences & Series, Vectors in Space and Planes & Spheres. It follows Howard Anton, Calculus, 10th ed..

How many lessons does the Calculus & Analytical Geometry course on Studious have?

14 units and 34 lessons, from "What a limit is" to "Equation of a sphere". Each lesson has a worked example, a quick check and practice that adapts to what you know, and many have step-by-step diagrams.

Course outline

  1. Unit 1 · Week 1

    Limits and continuity

    1. What a limit is
    2. Finding limits with algebra
    3. Continuity
  2. Unit 2 · Week 2

    Indeterminate forms and L'Hospital's rule

    1. Indeterminate forms
    2. L'Hospital's rule
  3. Unit 3 · Week 3

    Differentiation

    1. Rules of differentiation
    2. Leibniz's theorem
    3. Rolle's theorem and the Mean Value Theorem
  4. Unit 4 · Week 4

    Extreme values of a function

    1. Critical points and the first derivative test
    2. The second derivative test
    3. Absolute extrema on a closed interval
  5. Unit 5 · Week 5

    Applied maximum and minimum problems

    1. Setting up an optimisation problem
    2. Boxes and fences
  6. Unit 6 · Week 6

    Extreme values of a function of two variables

    1. Partial derivatives
    2. Critical points and the second partials test
    3. Extrema with a constraint: Lagrange multipliers
  7. Unit 7 · Week 7

    Integration by parts and improper integrals

    1. Integration by parts
    2. Improper integrals
  8. Unit 8 · Week 8

    Integration by partial fractions

    1. Partial fractions with linear factors
    2. Repeated and quadratic factors
  9. Unit 9 · Week 9

    Area under and between curves

    1. Area under a curve
    2. Area between two curves
  10. Unit 10 · Week 10

    Arc length, surfaces and volumes of revolution

    1. Arc length of a curve
    2. Volume of a solid of revolution
    3. Surface of revolution
  11. Unit 11 · Week 11

    Sequences and infinite series

    1. Sequences and their limits
    2. Infinite series and convergence tests
  12. Unit 12 · Week 12

    Taylor, Maclaurin and power series

    1. Power series and the radius of convergence
    2. Taylor and Maclaurin series
  13. Unit 13 · Weeks 13–14

    Vectors in space

    1. Direction angles, cosines and ratios
    2. Parametric equations of a line
    3. Differentiating and integrating vector functions
  14. Unit 14 · Week 15

    Planes and spheres

    1. Equation of a plane
    2. Equation of a sphere

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