College Algebra

General Information

READINGS

Sydsæter, K., & Hammond, P. (2012). Essential Mathematics for Economic Analysis. 4th Edition. Pearson Education.

LEARNING OUTCOMES

Students will be able to classify numbers
Students will be able to evaluate or simplify expressions with integer exponents
Students will be able to add, subtract and multiply polynomials
Students will be able to manipulate and factor polynomials
Students will be able to simplify a rational expression
Students will be able to algebraically solve linear equations and inequalities
Students will be able to solve equations by factoring, completing the square and using the Quadratic Formula
Students will be able to graph an equation by plotting points on a Cartesian Plane and by using the graphing tools on the calculator
Students will be able to use the distance and midpoint formulas
Students will be able to write equations in the point-slope and slope-intercept form
Students will be able to graph higher degree functions and find their roots
Students will be able to manipulate logarithms and find inverse functions
Students will be able to manipulate exponential functions and solve growth problems
Students will be able to solve systems of equations by substitution and or elimination
Students will be able to apply their algebraic skills to various types of word problems.

COURSE POLICIES / ADDITIONAL INFORMATION

Attendance is recorded. Unexcused absence lowers the grade accordingly.
It is the students' responsibility to check Canvas and their Webster email regularly.
For every hour spent in class it is expected of the students to invest 3 hours per week outside of class in homework, reviewing material, assignments, etc.

UNIVERSITY POLICIES

Students are required to inform themselves of WUV academic policies.

A full list of these policies is available on the WUV website: http://webster.ac.at/academic-policies

Materials

Introductory Topics [Slides][Mathematica][RCode][Assignment]

Functions [Slides][RCode]

Differentiation [Slides][RCode]

Integration [Slides][RCode]

Difference Equations [Slides][RCode]

Trigonometry [Slides][RCode][Assignment]

Vector Algebra [Slides][RCode][Assignment]

Matrix Algebra [Slides][RCode][CheatSheet]

Multivariate Optimization [Slides][RCode]

Websites

for Mathematica

Lagrange Multiplier Method

for R

Weekly Schedule

Week 1

Introductory Topics

· Introduction to Mathematica

· Set Theory

· Rules of Algebra

· Inequalities

Introductory Topics

· Solve Simple Equations

· Quadratic Equations

· Linear Equations with Two Unknowns

Week 2

Introductory Topics

· Summation and Product

· Mathematical Proofs

· Introduction to Probability

· Mathematical Induction

Functions

· Domain and Range

· Graphs

· Linear Functions

· Quadratic Functions

Week 3

Functions

· Polynomial Functions

· Power Functions

· Exponential Functions

· Logarithmic Functions

Functions

· New Functions from the Old

· Inverse Functions

· Composite Functions

· Distance in Plane, Circles

Week 4

Differentiation

· Slopes of Curves

· Tangents & Derivations

· Increasing & Decreasing Functions

Differentiation

· A Dash of Limits

· Simple Rules of Differentiation

· Sums, Products & Quotients

Week 5

Differentiation

· Chain Rule

· Higher Order Derivatives

· Exponential & Logarithmic Functions

Differentiation

· Implicit Differentiation

· Differentiating the Inverse

· Polynomial Approximation

Week 6

Differentiation

· Continuity

· Convexity/Concavity

· L’Hôpital’s Rule

Differentiation

· Partial Derivatives

· Higher Order Partial Derivatives

· Surfaces and Distance

Week 7

Integrals

· Indefinite Integrals

· Area and Definite Integrals

Integrals

· Properties of Definite Integral

· Integration by Parts

Week 8

Integrals

· Integration by Substitution

· Infinite Intervals of Integration

Mid-Term Exam

Week 9

Vectors

· Introduction to R

· Inner product

· Outer product

· Cross Product

Vectors

· Length

· Orthogonality

· Cardinality

Week 10

Matrices

· Fundamentals of Matrix Algebra

Matrices

· Matrix Operations

· Gaussian Elimination Method

Week 11

Matrices

· Determinants and Inverse Matrices

· Different Types of Matrices

Matrices

· Eigenvalue Decomposition

· Single Value Decomposition

Week 12

Matrices

· QR Decomposition

· Cholesky Decomposition

Optimization

· Local and Global Extreme Values

· Extreme Value Theorem

Week 13

Optimization

· Envelope Theorem

· Lagrange Multiplier Method

Optimization

· A Graphical Approach

· General LP Problem

Week 14

Optimization

· Duality Theorem

· Complementary Slackness

Difference Equations

· First Order Difference Equation

· Cobweb

Week 15

Difference Equations

· Second Order Difference Equation

· Schur’s Theorem

Final Exam

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