# Calculus and Linear Algebra for Commerce

This course provides applications of mathematics and includes selected topics from consumer math and algebra. Some types included are integers, percent, interest, ratio, and proportion, metrics system, probability, linear equations, and problem solving. This is a terminal course designed for students seeking an AAS Degree or Certificate and is not intended to transfer.

## 00 - Pilot

**Course Number** : CLA-C

**Level**: Intermediate

**Course Features** :

Lecture Notes, Assignment, Assignment: Programming, Exam, Projects, and Examples

**Course Description** :

This course provides applications of mathematics and includes selected topics from consumer math and algebra. Some types included are integers, percent, interest, ratio and proportion, metrics system, probability, linear equations, and problem-solving. this is a terminal course designed for students seeking an AAS degree or Certificate and is not intended to transfer, and does not meet the general core requirements for mathematics.

**Course Meeting Times** :

Twice a week under appointment

**Pre-requisite** :

Intermediate Algebra

**Course Recommended Text** :

*Introductory Mathematical Analysis, 12th Edition*, by Haeussler, Paul, and Wood

**Calculators **:

The only calculators allowed for use during the term tests and final exam are TI-30X, TI-30XIIB, or TI-30XIIS

**Grading Policy** :

There will be two-term tests, held during the regular lecture times. Each term test will be 2 hours.

There will be no make-up tests. The instructor will adjust the marking scheme properly for students who have missed a test because of illness or any other (approved) legitimate reason.

The final exam of the course will take place during the examination period in August, and will be 2 hours long. It will cover all of the material presented in lectures, tutorials, and problem sets.

Learner final grade will be computed in the following way:

20% Problem Sets + 20% 1st Term Test + 20% 2nd Term Test + 40% Final Exam

**Topic** :

Compound interest

Present value

Interest compounded continuously

Annuities

Amortization of Loans

Matrices

Matrix Addition and Scalar Multiplication

Matrix Multiplication

Solving Systems by Reducing Matrices

Inverses

Leontief's Input-Output Analysis

Linear Inequalities in Two Variables

Linear Programming

Multiple Optimum Solutions

Limits

Continuity

The Derivative

Rules of Differentiation

The Derivative as a Rate of Change

Product and Quotient Rule

The Chain Rule and the Power Rule

Derivatives of Logarithmic Functions

Derivatives of Exponential Functions

Elasticity of Demand

Implicit Differentiation

Logarithmic Differentiation

Newton's Method

Higher-Order Derivatives

Relative Extrema

Absolute Extrema on a Closed Interval

Concavity

The 2nd Derivative Test

Asymptotes

Applied Maxima and Minima

The Indefinite Integral

Integration with Initial Condition

More integration formulas

Techniques of Integration

The Definite Integral

The Fundamental Theorem of Integral Calculus

Area

Area between Curves

Consumer's and Producer's Surplus

Integration by Parts

Integration by Partial Fractions

Integration by Tables

Average Value of a Function

Differential Equations

Improper Integrals

Functions of Several Variables

Partial Derivatives

Application of Partial Derivatives

Higher-Order Partial Derivatives

Chain Rule

Max and Min for Functions of Two Variables

Lagrange Multipliers

**Problem Sets** :

There will be Nine Problem sets, due almost every week. Problem sets will be posted on the website at least a week before the due date. You are encouraged to work on questions from the assignment with your fellow students. However, the writing of your assignment must be done without anybody's assistance.

Your Problem set mark will be determined by eliminating the worst problem set (provided that you handed in all of them), and computing the average mark of the remaining problem sets.

**Notes** :

Homework problems and other important material will be posted on the web-course, so you should check it regularly. The learner will also be able to see your marks for the problem sets and the term tests online. Some important information may be sent by email, so you should also check your email regularly.

The learner should become familiar with and are expected to adhere to the Code of Behavior on Academic Matters.