Calculus 1: The Complete Guide

• Pre-Calculus materials, including number sets, exponents, proof by induction
• All sorts of functions (polynomial, exponential, trigonometric, hyperbolic)
• Inverse functions, logarithms, complex numbers, Argand diagrams
• Euler’s formula, multiplication of complex numbers, polar form, double-angle formulae, de Moivre’s theorem, roots of unity and complex loci
• Limits, continuous functions, intermediate value theorem
• Sandwich theorem, logarithmic vs polynomial vs exponential limits, differentiation from first principles, product rule and chain rule
• Derivatives of implicit functions, inverse functions, parametric functions, differentiable functions
• Mean value theorem
• Integration, the Riemann integral, fundamental theorems of Calculus
• Indefinite and definite integrals, integration by substitution, integration by parts, recursion relations, partial fractions
• Volumes of revolution, length of a curve, infinite sums, convergence criteria, power series
• Taylor’s theorem, l’Hôpital’s rule

Who this course is for:

• High-school students preparing for Maths-related university degree
• University students
• Parents or tutors who are seeking an easy explanation to Maths to support your children or tutees
• Students who are studying a course that requires some basic calculus knowledge
• People who just miss studying Maths or love Maths
• People who what to get into data science