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This is the complete lecture note for ECO 207 Mathematics For Economists. You can read it online below, open it in the full viewer, or download the PDF for offline study. It pairs with the course's video lectures, so you can read and watch together.
LA-NET | ONLINE LEARNING VIDEO PLATFORM FOR POST-SECONDARY & HIGHER INSTITUTION STUDENTS
LA-NET | ONLINE LEARNING VIDEO PLATFORM FOR POST-SECONDARY & HIGHER INSTITUTION STUDENTS Course Code: ECN 207 Course Title: Mathematics For Economists Course Units: 2 units Series 1: Calculus Foundations for Economic Analysis Series 2: Sequences, Series, and Taylor Expansions Series 3: Applications of Derivatives in Economics Series 4: Linear and Matrix Algebra in Economic Models Series 5: Optimization, Programming, and Advanced Analytical Tools Proposed Outline: Part 1.1 Fundamentals of Calculus 1.1.1 Definition of calculus and its relevance to economics 1.1.2 Limits and continuity 1.1.3 Differentiation basics Part 1.2 Derivatives of Functions 1.2.1 Rules of differentiation (power, product, quotient, chain) 1.2.2 Derivatives of polynomial functions 1.2.3 Derivatives of trigonometric functions 1.2.4 Higher-order derivatives Part 1.3 Applications of Derivatives in Economics 1.3.1 Marginal analysis (marginal cost, marginal revenue, marginal utility) 1.3.2 Elasticity of demand and supply 1.3.3 Comparative statics using derivatives Part 1.4 Differentials and Integration Basics 1.4.1 Differentials and their economic interpretation 1.4.2 Introduction to integration 1.4.3 Simple applications of integration in economics (consumer surplus, producer surplus)
LA-NET | ONLINE LEARNING VIDEO PLATFORM FOR POST-SECONDARY & HIGHER INSTITUTION STUDENTS Introduction Calculus is one of the most important mathematical tools used in economics. It provides a systematic way of analysing change, growth, and optimisation, which are central to economic reasoning. For example, economists often study how small changes in price affect demand, or how variations in input levels influence production. These questions require the use of derivatives, which measure rates of change, and integrals, which measure accumulation. The aim of this Series is to introduce you to the foundations of calculus and show how they apply to economic analysis. We will begin with the fundamentals of limits and continuity, then move on to differentiation and its rules. Next, we will explore how derivatives are applied in economics, particularly in marginal analysis and elasticity. Finally, we will introduce differentials and the basics of integration, including simple applications such as consumer and producer surplus. By following this sequence, you will gradually build confidence in using calculus as a tool for economic reasoning. Series Learning Outcomes By the end of this Series, you should be able to: define calculus and explain its relevance to economics (SLO 1.1) demonstrate how to evaluate limits and continuity of functions (SLO 1.2) apply rules of differentiation to polynomial and trigonometric functions (SLO 1.3) analyse economic concepts such as marginal cost, marginal revenue, and elasticity using derivatives (SLO 1.4) interpret differentials and perform basic integration in economic contexts (SLO 1.5) 1.1 Fundamentals of Calculus --- 1.1.1 Definition of Calculus and its Relevance to Economics Calculus is a branch of mathematics concerned with studying change and accumulation. It is divided into two main areas: differential calculus, which focuses on rates of change, and integral calculus, which deals with accumulation of quantities. In economics, calculus is used to analyse how small changes in one variable affect another. For example, a firm may want to know how a slight increase in input affects output, or how a small change in price influences demand. These questions require the use of calculus.
LA-NET | ONLINE LEARNING VIDEO PLATFORM FOR POST-SECONDARY & HIGHER INSTITUTION STUDENTS Fill in the blank: Calculus is divided into two main areas, ______ calculus and integral calculus. --- 1.1.2 Limits and Continuity A limit describes the value a function approaches as the input approaches a particular point. Limits are essential for defining derivatives. For example, the derivative of a function is defined as the limit of the average rate of change as the interval becomes very small. Continuity means that a function has no breaks or jumps at a given point. A function is continuous if its limit exists and equals the function’s value at that point.
LA-NET | ONLINE LEARNING VIDEO PLATFORM FOR POST-SECONDARY & HIGHER INSTITUTION STUDENTS Fill in the blank: A function is continuous if its limit exists and equals the ______ at that point. --- 1.1.3 Differentiation Basics Differentiation is the process of finding the derivative of a function. A derivative measures the rate of change of a function with respect to its variable. In economics, derivatives are used to calculate marginal values, such as marginal cost or marginal revenue. For example, if Q = f(L) represents output as a function of labour, then the derivative \frac{dQ}{dL} shows how output changes when labour changes slightly.
LA-NET | ONLINE LEARNING VIDEO PLATFORM FOR POST-SECONDARY & HIGHER INSTITUTION STUDENTS Fill in the blank: The derivative of a function measures the ______ of change of the function with respect to its variable. --- Pilot questions 1.1 Calculus is divided into two main areas, ______ calculus and integral calculus. A function is continuous if its limit exists and equals the ______ at that point. The derivative of a function measures the ______ of change of the function with respect to its variable. Why are limits important in defining derivatives? Give one example of how calculus is applied in economics.
LA-NET | ONLINE LEARNING VIDEO PLATFORM FOR POST-SECONDARY & HIGHER INSTITUTION STUDENTS 1.2 Derivatives of Functions --- 1.2.1 Rules of Differentiation Differentiation is the process of finding the derivative of a function. To make this process easier, mathematicians have established rules that allow us to differentiate functions systematically. The main rules are: Power rule: If f(x) = x^n, then f'(x) = nx^{n-1}. • Product rule: If f(x) = u(x) \cdot v(x), then f'(x) = u'(x)v(x) + u(x)v'(x). • Quotient rule: If f(x) = \frac{u(x)}{v(x)}, then f'(x) = \frac{u'(x)v(x) - u(x)v'(x)}{[v(x)]^2}. • Chain rule: If f(x) = g(h(x)), then f'(x) = g'(h(x)) \cdot h'(x). Fill in the blank: The derivative of x^n using the power rule is ______. ---
LA-NET | ONLINE LEARNING VIDEO PLATFORM FOR POST-SECONDARY & HIGHER INSTITUTION STUDENTS 1.2.2 Derivatives of Polynomial Functions A polynomial function is an expression of the form f(x) = a_nx^n + a_{n-1}x^{n-1} + \dots + a_0. Differentiating polynomials is straightforward using the power rule. Example: If f(x) = 5x^3 + 2x^2 + 7x, then f'(x) = 15x^2 + 4x + 7. Fill in the blank: The derivative of 5x^3 + 2x^2 + 7x is ______. --- 1.2.3 Derivatives of Trigonometric Functions Trigonometric functions are widely used in mathematics and economics, especially in modelling cycles and periodic behaviour. Their derivatives are:
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