Mathematics video tutorials – Niels Bohr Institutet - Københavns Universitet

Niels Bohr Institutet > Uddannelse > Auditoriet > STUDYNOVA > Mathematics video tuto...

The following mathematics videos are appropriate for Danish Gymnasium Matematik A and B, as well as some C. They are also helpful for anyone wanting a review of the key mathematics concepts needed at the university level.

1. Basic numbers, algebra and graphing: order of operations, working with fractions (add, subtract, divide, multiply, common denominator), exponents (including negative and fractional exponents), working with surds (square roots), scientific notation, algebra (rearranging, solving), solving simultaneous linear equations, expanding and factoring, linear graphs, parallel and perpendicular lines, measuring angles, Pythagoras' theorem, sine, cosine and tangent.
2. Sequences and series, exponents, logarithms and binomial expansion: arithmetic and geometric sequences and series, infinite sum, sigma notation, compound interest, exponent laws and equations, logarithms, natural logarithms and e, solving exponential equations, binomial theorem.
3. Functions, transformations, working with and solving quadratics: function notation, domain and range, composite functions, inverse function, graphing by hand and by calculator, features of graphs (zeros, intercepts, asymptotes, vertex), solving by graphing, transformations of functions (stretch, compression, translation, reflection), reciprocal function, solving quadratics (graphing, factoring, completing the square, quadratic equation).
4. Trigonometry: right angle trigonometry (Pythagoras' theorem, sine, cosine, tangent), non-right angle trigonometry (sine rule, cosine rule), arc length and sector area, area of a triangle, unit circle, radians, solving exact values (for sine, cosine, tangent), Pythagorean identity, double angle formulae, solving trig. equations, the mathematics of DJing.
5. Calculus: differentiation definition, product rule, quotient rule, chain rule, equation of a tangent and normal line, second derivative, inflection point, local and global max/min, inflection points, sketching by hand, optimization, antiderivative, definite and indefinite integral, area between two curves, volume of revolution, kinematics with calculus.