Calculus Website
Precalculus Website

Math for Business and Economics
by Kiryl Tsishchanka


Sections Handouts Supplementary
Key Concepts
Jan 14
Section 2.1 Graphs Short

Coordinate Plane, Graph of Line, Graph of Equation, Intercepts, Applications
Jan 19, 21
Section 2.2 Equations of Lines Short Problems Slope of Line, Point-Slope Equation, Slope-Intercept Equation, General Equation, Vertical and Horizontal Lines, Parallel and Perpendicular Lines, Applications
Section 3.1 Functions
Short Problems Function (Definition, Examples), Values of Functions, Piecewise Functions, Domain (and Range), Applications
Jan 26, 28
Section 3.2 Graphs of Functions
Short Problems Graph of Function (Definition, Examples), Graph of Piecewise Function, Step Function, Vertical Line Test, Graphs of Basic Functions, Applications
Section 3.3 Applications of Linear Functions

Cost (Fixed Costs, Variable Costs), Average Cost, Revenue, Profit, Rates of Change (Rate of Change of Linear FunctionLinear Depreciation, Marginal Cost, Marginal Revenue), Break-Even Analysis, Supply and Demand, Equilibrium Point
Section 3.4 Quadratic Functions and Applications

Problems Quadratic Function (Definition), Standard Form, Vertex, Maximum and Minimum Values, Applications
Feb 2, 4
Section 3.5 Polynomial Functions + EXCEL

Problems Polynomial Function (Definition, Examples), Monomial, Properties of Polynomial Graphs, End Behavior, Graphing Techniques, Shape of Graph Near Zero, Applications (Regression)
Section 3.6 Rational Functions

Problems Rational Function (Definition, Examples), Linear Rational Functions, Vertical and Horizontal Asymptotes, Nonlinear Rational Functions, Applications
Section 4.1 Exponential Functions

Problems Exponential Function (Definition, Examples), Graphs, Basic Properties, Number e, Natural Exponential Function, Applications; Transformations of Functions
Feb 9
Section 4.2 Applications of Exponential Functions

Exponential Growth Function, Other Exponential Models
Section 4.3 Logarithmic Functions
Problems 1
Problems 2
Logarithmic Functions (Definition, Examples), Graphs, Basic Properties, Natural and Common Logarithms, Three Laws of Logarithms, Change of Base Formula, Applications
Feb 11
Sections 2.1, 2.2, 3.1-3.6, 4.1

Feb 16 Section 4.4 Logarithmic and Exponential Equations
Problems 1
Problems 2
Exponential Equations, Logarithmic Equations, Applications
Feb 18 Section 5.1 Simple Interest and Discount

Interest, Simple Interest, Principal, Future Value, Present Value, Discount; Corporate Bonds, Simple Discount Loan
Feb 23, 25
Section 5.2 Compound Interest

Compound Interest, Continuous Compound Interest, Nominal and Effective Rate (APY), Present Value for Compound Interest; Zero-Coupon Bond
Section 5.3 Annuities, Future Value, and Sinking Funds

Annuity: Payment Period, Term of the Annuity, Future Value;
Ordinary Annuity, Future Value of Ordinary Annuity, Sinking Fund, Annuity Due, Future Value of Annuity Due
Section 5.4
Annuities, Present Value, and Amortization

Present Value of Ordinary Annuity, Amortization Payments, Amortization Schedule, Remaining Balance, Present Value of Annuity Due; Coupon Rate
Mar 1, 3 Section 6.1 Systems of Two Linear Equations in Two Variables

Substitution Method, Elimination Method, Graph, Number of Solutions
Section 6.2 Larger Systems of Linear Equations

Substitution Method, Elimination Method, Graph, Number of Solutions; Augmented Matrix, Elementary Row Operations,  Gaussian Elimination, Row-Echelon Form,  Gauss-Jordan Elimination, Reduced Row-Echelon Form
Section 6.3 Applications of Systems of Linear Equations

Mar 8 Section 7.1 Graphing Linear Inequalities in two Variables

Graph of Inequality: Boundary Line, Half-Plane; Graph of System of Inequalities, Feasible Region
Section 7.2 Linear Programming: The Graphical Method

Linear programming: Objective Function, Constraints; Solving Linear Programming Problem Graphically: Bounded and Unbounded Regions, Corner Points, Corner Point Theorem
Section 7.3 Applications of Linear Programming

Mar 10 Sections 4.2-4.4, 5.1-5.4, 6.1-6.3 MIDTERM 2

Mar 22, 24
Section 11.1 Limits

Problems Limit (Definition, Examples), 0/0 Limits, Limit Laws, Calculating Limits: Direct Substitution Property, Factorization, Conjugate Trick; Limits that Do Not Exist
Section 11.2 One-sided Limits and Limits Involving Infinity

Problems One-sided Limits, Limits of Piecewise Functions; Infinite Limits, Vertical Asymptotes,  Limits at Infinity, Horizontal Asymptotes
Section 11.3 Rates of Change

Average Rate of Change, Instantaneous Rate of Change, Marginal Cost, Revenue and Profit
Mar 29, 31
Section 11.4 Tangent Lines and Derivatives + EXCEL
Slope of Tangent Line, Derivative of Function, Existence of Derivative, Price Elasticity of Demand
Section 11.5 Techniques for Finding Derivatives
Basic Differentiation Rules: Derivative of Constant Function, Power Rule, Constant Multiple Rule, Sum/Difference Rule; Marginal Analysis: Marginal Cost, Profit and Revenue, Demand Function
Section 11.6 Derivatives of Products and Quotients
Product Rule, Quotient Rule; Average Cost, Marginal Average Cost
Apr 5, 7
Section 11.7 The Chain Rule
Problems Composition of Functions; Chain Rule, Applications, Marginal-Revenue Product
Section 11.8 Derivatives of Exponential and Logarithmic Functions

Derivatives of Exponential Functions, Derivatives of  Logarithmic Functions, Applications
Section 11.9 Continuity and Differentiability

Continuity at Point,  Continuity from Right/Left,  Continuity on Interval,  Continuity and Differentiability, Applications
Apr 12
Section 12.1 Derivatives and Graphs

Increasing/Decreasing Functions, Critical Number, Increasing/Decreasing Test, Local Maximum/Minimum, Fermat’s Theorem, First Derivative Test, Applications
Apr 14 Section 12.2 The Second Derivative

Higher derivatives, Concave Up/Down Functions, Inflection Point, Concavity Test, Law of Diminishing Returns, Second Derivative Test, Applications
Apr 19
Section 12.3 Optimization Applications

Absolute Maximum/Minimum, Closed Interval Method, Critical-Point Theorem, Optimization Applications
Apr 21 Section 13.1 Antiderivatives
Problems Antiderivative (Definition, Examples), Table of Indefinite Integrals, Applications
Apr 26, 28 Section 13.3 Area and the Definite Integral

Approximate Area of Region by Rectangles, Definite Integral  (Definition, Examples), Net Area, Applications (Total Change)
Section 13.4 The Fundamental Theorem of Calculus

Fundamental Theorem Of Calculus, Properties of Definite Integral, Examples (Definite Integral), Examples (Area), Applications
Section 13.5 Applications of Integrals

Area Between Two Curves and Applications, Consumers’ and Producers’ Surplus, Other Applications
May 4 (Wed), 3:30-6:30pm