# Foundational Math for Actuaries – Calculus

MJ the Fellow Actuary

Course Overview

What you’ll learn

• Set Theory.
• Functions and terminology.
• Differentiation.
• Chain Rule, Product Rule & Quotient Rule.
• Stationary Points for univariate and bivariate functions.
• Lagrange Multipliers for Constrained Problems.
• Integration.
• Technique 1: Integration by Inspection.
• Technique 2: Partial Fractions.
• Technique 3: Integration by Substitution.
• Technique 4: Integration by Parts.
• Double Integrals.

Course Content

• Set Theory and Functions – Precalculus –> 2 lectures • 19min.
• Differentiation – Calculus Part 1 –> 7 lectures • 33min.
• Integration – Calculus Part 2 –> 6 lectures • 26min. Requirements

• School Maths.

Course Overview

Before writing the Actuarial Exams, you need to have a solid understanding of Mathematics. In this course we will go through the International Actuarial Association syllabus requirements for Foundational Maths. We will look at Set Theory, Functions, Differentiation and Integration. Once you have completed this course you will be able to attempt the Mathematical Statistics and Financial Mathematics exams of the Actuarial Profession.

Contents

1. Sets and Function
1. Set Theory
2. Functions
2. Differentiation
1. Rules of Differentiation
2. Finding Stationary Points on a curve
3. Chain Rule
4. Product & Quotient Rule
5. Partial Derivatives
6. Finding Stationary Points on a surface
7. Lagrange Multipliers for Optimal Solutions
3. Integration
1. Introduction to the Integral
2. Integration by Inspection
3. Partial Fractions
4. Integration by Substitution
5. Integration by Parts
6. Double Integrals