Outline of IB Maths HL option Calculus

Limits of sums,
products, Continuity and differentiability, Fundamental theorem of calculus, Differential Equations, Slope fields, Rolle’s theorem, Mean value theorem, Taylor series developed from differential equations

Outline of IB Maths HL option Calculus

Postby ib maths » Mon Feb 25, 2013 4:25 pm

Outline of IB Mathematics Higher Level option Calculus

Here you can find a description of the course not so detailed.
You can find the official syllabus of IB maths SL on the following link of IBO
http://www.ibo.org or http://store.ibo.org

Infinite sequences of real numbers and their convergence or divergence.
Convergence of infinite series. Tests for convergence: comparison test, limit comparison test, ratio test, integral test.
Continuity and differentiability of a function at a point. Continuous functions and differentiable functions.
The integral as a limit of a sum; lower and upper Riemann sums. Fundamental theorem of calculus.
Improper integrals, First-order differential equations.Geometric interpretation using slope fields, including identification of isoclines.
Euler’s method, Variables separable, Homogeneous differential equation, integrating factor.
Rolle’s theorem.Mean value theorem.Taylor polynomials; the Lagrange form.
Maclaurin series, Use of substitution, products, integration and differentiation to obtain other series.
Taylor series developed from differential equations.
The evaluation of limits, Using l’Hôpital’s rule or the Taylor series.
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