The ideas behind engineering, data science and economics: functions, limits, derivatives, integrals, matrices and vectors. Kanakku keeps a picture in front of each idea, such as a curve with its tangent or sets drawn as overlapping circles, so the formulas mean something before you start drilling them.
Types of relations, one-one and onto functions, composition and inverses.
A function is one-one if different inputs give different outputs, and onto if every output in the codomain is reached.
Order, multiplication, transpose, determinants and inverses.
A matrix is a grid of numbers. To multiply, go along a row of the first and down a column of the second.
Standard derivatives, the chain and product rules, and continuity.
A function is continuous if its graph has no breaks. To differentiate combinations, use the chain, product and quotient rules.
Increasing and decreasing, maxima and minima, tangents and rates.
Where f′(x) > 0 the function rises; where f′(x) < 0 it falls. Where f′(x) = 0 it may have a maximum or minimum.
Integration as reverse differentiation, and as area under a curve.
Integration reverses differentiation. A definite integral gives the area under a curve between two x-values.
Order and degree, and simple solutions.
A differential equation links a function with its derivatives. Solving it means finding the function.
Magnitude, the dot product and perpendicular vectors.
A vector has size and direction. The dot product measures how much two vectors point the same way; 0 means they are at right angles.
Distance, midpoints and direction ratios in 3D.
3D geometry adds a z-coordinate. The formulas are the same as in 2D, with one more term.
Find the best value of Z at the corners of the feasible region.
In linear programming, the maximum or minimum of Z always happens at a corner point of the feasible region.
Conditional probability, independent events and binomial chances.
Conditional probability P(A|B) is the chance of A when you already know B happened: P(A ∩ B) ÷ P(B).
